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Machine Learning methods and Space Engineering
By Dario Izzo
Mission
Created in 2002 “to monitor, perform and foster research on advanced space
systems, innovative concepts and working methods”
2
too immature for regular
ESA programmes or projects
concepts, techniques &
scientific domains with
no/weak links to space
emerging from cutting-edge
basic scientific research
topics on which ESA is
expected to have a
position
biomimetic approaches to engineering, brain-machine interfaces,
liquid breathing, curiosity cloning, peer-to-peer computing, crowd
sourcing gaming, innovation diffusion and dynamics
mathematical global optimisation techniques, cloud-based
uncertainty modelling, helicon thrusters, pure general
relativistic approach to GNSS constellation design, vibrating
systems in general relativity, metamaterials in the optical
frequency range, distributed/swarm intelligence, laser
filamentation
planetary protection research, space nuclear power sources,
asteroid deflection, liquid ventilation, pulsar navigation,
biomimetic drilling
solar power from space, torpor/hibernation, asteroid deflection,
active removal of space debris, novel working methods,
terraforming, geoengineering
Learning from others…Interdisciplinary
Most game-changing
developments emerge around
the fringes or intersections of
disciplines
Regular renewal of
personnel
Regular in-flow of new
insights keeps team on
the leading edge
Encourage taking risks
Encourage and reward
high risk / high gain
activities
Scientific rigour and
competence
Avoid drifting into the realm of
science fiction
Support from top-management
Activities tend to be ridiculed, admired,
not taken seriously or seen as threat to
core of the establishment.
Close ties with academia
Most relevant ideas/concepts
on a time horizon of 10+ years are
generated within academia and
research centres
ACT Research AreasFundamental Physics
Impact of new ideas in
physics on the space
sector
Biomimetics & Bioengineering
Benefitting from Darwinian
evolution to solve engineering
problems
Mission Analysis
Mathematical
techniques for future
mission analysis
Artificial Intelligence
Engineering of intelligent
computer systems
Advanced Energy Systems
Innovating energy systems
Planetary System Science
Options and opportunities
from complex climate
systems
Computer Science &
Applied Mathematics
Post von neumann
architectures
Advanced Propulsion
Explore and review break-
through propulsion concepts
Computational Management Science
Explore computational aspects of
management
Advanced Materials
Benefitting from the control
at micro/nano scale
We are currently hiring 5 new Research fellows
(post-docs)!
1 - Artificial Intelligence
2 - Computer science
3 - Biomimetics
4 - Fundamental Physics
5 - Mission Analysis
Deadline 6th July!
www.esa.int/act
2040
How intelligent will satellites be?
80486
Before looking 25 ahead, let
us look 25 back at AI and CS
Today19901970
Today19901965
19901970 Today
And what about algorithms?
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN
ImageNet
2006
2012
• 1980-1990: attempts to train DNNs failed
• 2006: first worldwide success stories in 2006
Deep Belief Networks and autoencoders: networks
trained layer by layer
• 2006-2016: great success and explosion of DL, for example:
Convolutional Neural Networks (CNNs): ImageNet success
Long Short-Term Memory (LSTM): huge success in speech
recognition
.
Just A Hype? No, DL is here to stay.
Deep Learning
First DL
success
Genetic Programming
Symbolic regression (SR): Learn the underlying physics from data
Symbolic regression leverages an “evolutionary” approach
to model creation, testing billions of potential models per
second, and converging on the simplest, most accurate ones
that explain your data. S.R. makes no prior assumptions about
the data set, instead fitting models to the data
dynamically.
Schmidt M., Lipson H. (2009)
"Distilling Free-Form Natural Laws from
Experimental Data," Science, Vol. 324,
no. 5923, pp. 81 - 85.
Companies using Nutonian SR tool:
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR
ImageNet
2006
2012
2009Nutonian
First DL
success
Smart “search” (optimization) methods
Evolutionary algorithms: exploiting artificial selection to evolve
increasingly better solutions to design problems
Orders of magnitude better from Genetic Algorithm (80s) to
modern techniques:
Covariant Adaptation Evolutionary Strategy (CMA-ES),
Multi-objective Evolutionary techniques via decomposition
(MOEA/D) and Self-adaptive Differential Evolution (jDE)
Monte Carlo Tree Search: for sequential decision-making problems
One of the most successful techniques in AI for games
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009Nutonian
First DL
success, jDE
2003CMA-ES
2007MOEA/D
Perception, understanding and
communication
Sensors:
Dynamic Vision Sensors (DVS)
Elementary Motion detectors (EMD)
Light Field cameras (LFC)
...
Algorithms:
SIFT - Scale-invariant feature
transform
CNN - Convolutional Networks
Using TTC, OF - Time to contact, optic
flow
LSTM - Long Short Term Memory
Networks
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009Nutonian
A LSTM wins ICDAR
handwriting
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
What did all this progress buy us?
1. Text recognition
2. Colorization of black and white images
3. Adding sounds to silent movies
4. Object classification and detection in
photographs
5. Generate image from caption
6. Handwriting generation
7. Text Generation (scripts, poetry, etc.)
8. Image Caption Generation
9. Music Composition
10. Software continuous integration
11. Manage currencies
12. Drive cars
13. Navigate
14. Chat
15. Generative Design
Some jobs computers can perform (and that
could not 25 years ago)
Application Areas of AI
Self-driving vehicles
Google, Tesla,
Mercedes-Benz, etc.
Autonomous flying (drones)
Amazon Prime Air delivery
Military Drones
Robotics
Factory automation,
Medicine,
Scientific exploration
...
Application Areas of AI
Virtual Assistants
Cortana, Siri, Viv
Language-based services
Machine translation
Document summarization
Emotionally aware interfaces
Affective computing
The next big things in AI/CS (10-20 years ahead)
100,000,000,000
1,000,000,000,000
10,000,000,000,000
2040
100,000,000,000,000
Number of neurons in the human brain (~2025)
GV100 Volta (NVIDIA GPU)
In the same place as where ANNs were in the 90s, these
technologies hold great potential, and may become the
next big things
● Artificial Evolution (Evolutionary Computing)
-> Designing the unexpected
● Genetic Programming
-> Computers programming themselves
● Artificial Life
-> Digital ecologies
tHE nEXT bIG tHINGS are today’s “failures”
The seeds of these innovations are well planted
The 2006 NASA ST5 spacecraft antenna
(found by Genetic Programming)
The ST5 mission successfully launched on March 22, 2006, and so this
evolved antenna represents the world's first artificially-evolved object to
fly in space
The ESA (ACT) VLBI GTOC8 trajectory
In 2011 the Humies Gold Medal Award was awarded to the ACT work on “Search for
a grand tour of the Jupiter Galilean moons” for human-competitive results that
were produced by any form of genetic and evolutionary computation.
Spacecraft CPUs too?
R3000: New Horizons
RAD6000: Spirit-Opportunity, Messenger, Deep Space
1, Dawn
RAD750: Kepler,
Juno, Curiosity
i386: ISS
x86: Falcon 9, Hubble
The Excuses:
Radiation Tolerance
Reliability
Satellite build time
Launch delays
Paperwork
Power Consumption
NGMP (ESA, LEON4)
Scenario #1: the gap is not filled.
in 2040 the intelligence on board spacecraft will
feel as exciting as a videogame from the 90s
Scenario #2: the gap is filled.
in 2040 the intelligence on board spacecraft will
compare to today’s situation as modern VR based
games compare to Pong
ACT and AI research
Explored areas – Neurocontrollers
Evolution in robotic islands: ALife in
the Galapagos
Deep Reinforcement learning for
Spacecraft hovering near unkown
small bodies
Morphological evolution of soft
robots at different gravity levels
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
2009Nutonian
A LSTM wins ICDAR
handwriting
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
Explored areas – Swarm Intelligence
Decentralized Formation Flight with
collision avoidance: Equilibrium Shaping
Autonomous self-assembly of large
space structures
Root Swarm: Sensor webs deployment
ACT MIT SPHERES experiments: first ANN
controlling multiple (homogeneous)
agents in space
Nutonian
A LSTM wins ICDAR
handwriting
Optic flow based lunar landing: from
bees to Apollo
Scent of science: from a female chasing
moth to the chase of methane on Mars
Explored areas – Biomimetic Sensing and
Actuation
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
Explored areas – Vision
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
Nutonian
A LSTM wins ICDAR
handwriting
Astro Drone - gamification for the
acquisition of vision data-sets
Learning “to see” in zero gravity - from
stereo vision to monocular vision (using
the MIT SPHERES platform)
Explored areas – Evolution and smart search
Evolution of Interplanetary Trajectories
Parallel evolution in modern CPU
architectures, the island model, PyGMO
Novel tree search paradigms: Monte Carlo Tree
Search, Ant Colony Optimization, Lazy Race Tree
Search
Humies Gold medal - “for Human-Competitive
Results Produced by Genetic and Evolutionary
Computation”
1st place in the 8th edition of GTOC - “The
America’s cup of rocket science”
Alpha GO 2016
2000
CNN, BP,
LSTM,
RNN, GP,
SR, DE,
MCTS
ImageNet
2006
2012
2009
2003CMA-ES
2007MOEA/D
DVS 2013
EMD,
SIFT
LFC from Stanford 2004
First DL
success, jDE
Nutonian
A LSTM wins ICDAR
handwriting
The scikit-learn of evolutionary algorithms
pip install pagmo
conda config --add channels conda-forge
conda install pagmo
● Provides “free” parallelization via the asynchronous island
model
● mpi, threads, multiprocess, etc.. all encapsulated in the island
● available for osx, linux and windows
● Fully FLOSS philosophy
● Easily extendible with your own algorithms or problems
● Tutorials and doc constantly up to date
● Community support active via a dedicated gitter channel
https://esa.github.io/pagmo2/index.html
pagmo/pygmo 2.x
whats ahead?
Differentiable intelligence
Use of high order derivative information in ML
Background: the algebra of floating points
>>> def my_function(x):
... return cos(x[0])+(x[0]+3*x[1]+x[2])**7
>>> x = [0.1,0.2,0.3]
>>> my_function(x)
1.9896041652780259
Behind this seemingly trivial computation, a number of implicit assumptions we
tend to forget.
Note: we rarely question that the floating
point algebra is “conformal” to the real number
algebra.
Background: the algebra of Truncated Taylor
polynomials
>>> def my_function(x):
... return cos(x[0])+(x[0]+3*x[1]+x[2])**7
>>> x = [gdual(0.1,"x0",5), gdual(0.2,"x1",5), gdual(0.3,"x2", 5)]
>>> my_function(x)
42*dx0*dx2+105*dx0*dx2**2+630*dx0*dx1*dx2+126*dx0*dx1+945*dx0*dx1**2+3
5.0166*dx0**3+6.90017*dx0+20.82*dx2**2+6.946*dx2+125.73*dx1*dx2+314.1*
dx1*dx2**2+105*dx0**2*dx2+34.8*dx2**3+945*dx1**2*dx2+945*dx1**3+20.502
5*dx0**2+189*dx1**2+20.973*dx1+ 1.9896+315*dx0**2*dx1
Substitute the algebra of floating point numbers with
the algebra of Taylor series expansion, trust it to be
conformal to the algebra of continuous functions -> a
differential Algebra [4].
http://darioizzo.github.io/audi/
floats floats
Hi! I am a computer program
Any-order Taylor
expansion of the program
outputs
floats floats
Hi! I am a computer program
Application to Machine learning and Evolutionary Computations
Gradient: widely used
(backprop, SQP, interior
point)
Hessian: less used, often
approximated, anyway
researched
Traditionally the error (or fitness) is conceived as a real number: instead,
consider it as a function (of whatever parameters you choose). Using the new
algebra, represent it, in the computer, as a truncated Taylor polynomial just as
before you were representing it as a floating point.
Application to Machine learning and Evolutionary
Computations
Traditionally the error (or fitness) is conceived as a real number: instead,
consider it as a function (of whatever params you choose). Using the new
algebra, represent it, in the computer, as a truncated Taylor polynomial just as
before you were representing it as a floating point.
Similar complexity as
Hessians and gradients, but
an entirely unresearched
field both in machine
learning and evolutionary
computations.
Deep learning in
deep space
Experiments on landing
Status quo:
Precompute a Reference optimal trajectory
Status quo:
Linearize around it to account for disturbancies
Status quo:
Risk to get unstable behaviour if we go off nominal
Status quo:
Use polynomials and perform regression
Risk to be suboptimal
1. Pre-compute many optimal trajectories
2. Train an artificial neural network to approximate the optimal
behaviour
3. Use the network to drive the spacecraft
Our approach:
Quadrotor
state: [x, vx
, z, zx
, θ]
control:[u1
, u2
]
Spacecraft
state: [m, x, vx
, z, zx
, θ]
control:[u1
, u2
]
state: [m, x, vx
, z, vz
, θ, vθ
]
control: [u1
, u2
, u3
]
Rocket
state: [m, x, vx
, z, vz
, θ, vθ
]
control:[u1
, u2
]
Some landing models:
Goal: Solve the deterministic continuous-time optimal control problem,
that is:
Current methods (direct or indirect) are not suitable for real-time
on-board implementation, an alternative is to correct the deviations from
a precomputed profile or use polynomial fits.
Hamilton-Jacobi-Bellman equation
1 - precompute many optimal solutions:
Direct methods Indirect methods
- Hermite-Simpson transcription and
non-linear programming (NLP)
solver
- Fast and easy implementation
- Chattering effects in the training
data have a huge negative impact on
the results.
- regularization techniques are used to
remove them.
- Suboptimal results
- Solve the Hamilton-Jacobi-
Bellman equations with shooting
methods
- Provides the actual optimal
trajectories
- But… an initial guess is necessary to
solve the problem and it is really
difficult to find them
- More difficult and awkward
implementation
1 - precompute many optimal solutions:
Two methods to generate the data
1 - precompute many optimal solutions:
Optimization for different problems:
Free Landing - Pinpoint Landing, Time optimal - Power optimal - Mass
optimal
Resulting in different control profiles:
1 - precompute many optimal solutions:
- The initial state of each trajectory is randomly selected from a training area
- 150,000 trajectories are generated for each one of the problems
- Computing the trajectory for a specific starting point is difficult, but we speed up the process
of generating random optimal trajectories by:
Random walks Homotopy methods
1 - precompute many optimal solutions:
- The networks are trained on
the state-control action
paris of the trajectories
- Networks with 1 - 5 hidden
layers
- Supervised Learning
- Trained with Stochastic
Gradient Descent (and
momentum)
- Minimize the squared loss
error (C)
2 - Approximate state-action with a DNN
● Deep networks are always better than shallow
networks with the same number of parameters.
Challenging landing
example
2 - Approximate state-action with a DNN
DNNs with supervised learning and large datasets successfully approximate the
optimal control
2 - Approximate state-action with a DNN
DNNs with supervised learning and large datasets successfully approximate the
optimal control
2 - Approximate state-action with a DNN
Very accurate results
+
The DNNs can be used as
an on-board reactive
system (32.000x faster
than optimization
methods used to
generate the data)
3 - How good is it?
● Successful landings from states outside of the training initial
conditions
● This suggest that an approximation to the solution of the HJB equations
is learned
Multicopter
(power)
Multicopter
(power)
Spacecraft I
generalization
Training area
generalization
After reaching the target point the spacecraft hovers until it runs of fuel
Is it learning the dynamics of the model?
No training data
below this line
generalization
The system was evaluated with the Parrot Bepop Drone in the TU Delft University
Optimal trajectory and
trajectory followed by the
drone (after some scaling
to adjust them, don’t trust
this image)
Optimal trajectories
generated for the Bepop
drone
4 - thE REAL WORLD
4 - thE REAL WORLD
Adding a cnn for the perception
1 - Train a neural network to guess the state from an on-board camera
2 - Use it together with the previous DNNs to get fully automated
visual landing
CNN for state estimation from camera
A simple setup is used: a 3D model (Blender) of a
rocket landing on a sea platform (Falcon 9 inspired)
CNN for state estimation from camera
CNN for state estimation from camera
CNN for state estimation from camera
CNN for state estimation from camera
Putting everything together
References:
[1] Carlos Sánchez-Sánchez, Dario Izzo and Daniel Hennes. "Optimal
real-time landing using deep networks." Proceedings of the Sixth
International Conference on Astrodynamics Tools and Techniques,
ICATT. Vol. 12. 2016.
[2] Carlos Sánchez-Sánchez, Dario Izzo and Daniel Hennes. "Learning
the optimal state-feedback using deep networks." Computational
Intelligence (SSCI), 2016 IEEE Symposium Series on. IEEE, 2016.
[3] Carlos Sánchez-Sánchez and Dario Izzo. "Real-time optimal
control via Deep Neural Networks: study on landing problems."
arXiv preprint arXiv:1610.08668(2016).
Genetic
programming
Symbolic regression
Encoding a computer program
weighted Cartesian Genetic Program
Miller, Julian F., and Peter Thomson. "Cartesian genetic programming."
European Conference on Genetic Programming. Springer Berlin
Heidelberg, 2000.
weighted dCGP
Case B: all floats except w3,1
and w10,1
-> gduals operating in P3
:
Case A: all floats
The output is a float
The output is a Taylor polynomial in w3,1
and w10,1
truncated at the third
order
Weighted CGP
>>> ks = kernel_set(["sum","diff","mul","div"])()
>>> CGP = expression(1,1,1,10,10,2,ks, seed = 21312312)
>>> print(CGP(["x"]))
[x**2 - x]
>>> print(CGP([0.1]))
[-0.09]
>>> ks = kernel_set(["sum","diff","mul","div"])()
>>> CGPw = expression(1,1,1,10,10,2,ks, seed = 21312312)
>>> print(CGPw(["x"]))
[w1_0*w1_1*w2_0*x**2 - w2_1*x]
Traditional CGP: all floats, no weights
Case A: all floats, weighted expression
Weighted dCGP
Case B: define w1_0, w2_0 and w2_1 as gduals, add also the input
>>> ks = kernel_set(["sum","diff","mul","div"])()
>>> dCGPw = expression(1,1,1,10,10,2,ks, seed = 21312312)
>>> print(dCGPw(["x"]))
[w1_0*w2_0*x**2 - w2_1*x]
>>> ex.set_weight(1, 0, gdual(1., "w1_0", 2))
>>> ex.set_weight(2, 0, gdual(1., "w2_0", 2))
>>> ex.set_weight(2, 1, gdual(1., "w2_1", 2))
>>> print(dCGPw([gdual(0.1)]))
[-0.1*dw2_1+0.01*dw1_0*dw2_0+0.01*dw2_0-0.09+0.01*dw1_0]
>>> print(dCGPw([gdual(0.1, “x”, 2)]))
[0.01*dw1_0*dw2_0+dw1_0*dx0**2+0.2*dw1_0*dw2_0*dx0+0.2*dw1_0*dx0+0.01*d
w1_0+dx0**2-0.1*dw2_1+0.2*dw2_0*dx0+0.01*dw2_0-0.09-0.8*dx0-dw2_1*dx0+d
w2_0*dx0**2]
http://darioizzo.github.io/d-CGP
Example 1: Learning ephemeral constants
Taking the skeleton out of the closet ….
‘‘...the finding of
numerical
constants is a
skeleton in the
GP closet...[and an]
area of research
that requires more
investigation...’’ -
John Koza
1 - The error of a CGP expression is
computed in the new algebra (so it’s a
function, remember….).
2 - We thus get the order n Taylor
expansion of the error: example with
one only constant and order three
3 - We use the differential expression obtained for the error to update
the ephemeral constant values so that the error is minimized
4 - At order 1 and with some type of gradient descent, you may think of
this as a backpropagation to learn ephemeral constant values.
Example 1: Learning ephemeral constants
What order?
Using:
Expressions such as:
Result in the error:
A parabolid! -> A second order Taylor polynomial represents
this error exactly.
The final algorithm
(1-4)-ES evolves the chromosome and thus
the symbolic expression y(x,c). We assign
to each fitness the minimum of the MSE
across all possible values of the
constants:
The solution is approximated by one step
of the Newton method.
Hessian and gradient are extracted from a second order Taylor
approximation
Learning ephemeral constants: results
● Success: MSE < 1e-14 (i.e. we learn the exact value of the
constants)
● We sample ~50 points in a uniform grid within bounds.
● We perform 100 runs.
● We compute the Expected Run Time (ERT): the expected value
of the number of d-CGP expressions that have to be evaluated
before meeting the success criteria set.
● Closest work is Topchy and Punch [1]: not comparable to
these results.
Example 2: Learning constants with weighted dCGP
Destroying the closet
Weight batch learning
(1-4)-ES evolves the chromosome and thus
the symbolic expression y(x,c). We assign
to each fitness the minimum of the MSE
across all possible values of the
weights:
Solution by the Newton method is
now troublesome.
A new learning method: weight
batch learning
We basically perform one Newton step to learn a batch of two weights
at a time. No Lamarckian learning: at each generation weights are
sampled from a normal distribution.
Learning constants with weighted dCGP: results
● Same setup as in the
previous experiments.
● All constants are
learned within the set
precision.
● Generally requires less
generations of the ES
● ERT is higher because of
the Newton iterations.
Example 3: Solving differential equations
Cauchy problems, Neumann and Dirichlet problems, TPBV problems
Solving Differential Equations: simple example
with y(0.1)=20.1 and x in [0.1,1]
We assume is represented by our d-CGP expression (1 in 1 out).
We construct a grid of 10 values for x between 0.1 and 1.
Computing x as a gdual with truncation order 1, we get from the
Taylor expansion of the program output.
Following Tsoulos and Lagaris [2], at each generation we use as error the
sum of two terms:
- The violation of the differential equation:
- The violation of the boundary condition:
Solving Differential Equations: results
Problem ERT dCGP ERT Tsoulos
8123 130600
35482 148400
22600 88200
896 38200
24192 40600
327020 797000
Comparison to Tsoulos and Lagaris [2] work possible.
CGP outperforming grammatical evolution in these tasks
d-CGP generalizing Tsoulos and Lagaris [2] method allowing high
order and mixed derivatives
Example 4: Finding prime integrals
From differential equations to the fundamental conservation laws
Finding prime integrals
Prime integrals are typically found by great
mathematicians and their intuition
dynamical system in normal form
a prime integral
Swinging Atwood Machine
Not only energy …
“whatever this is” … is conserved
Found in 1888 as a third example of integrable top
Kovalevskaya Top
Not only angular momentum …
“whatever this is” … is conserved
Finding prime integrals
No need to solve this to create
training data (i.e. no need to observe
the system as in Schmidt and Lipson [3])
We get the derivatives from the
1st order Taylor expansion of
the program output!
Finding prime integrals: results
References:
[1] Topchy, Alexander, and William F. Punch. "Faster genetic programming
based on local gradient search of numeric leaf values." Proceedings
of the 3rd Annual Conference on Genetic and Evolutionary
Computation. Morgan Kaufmann Publishers Inc., 2001.
[2] Tsoulos, Ioannis G., and Isaac E. Lagaris. "Solving differential
equations with genetic programming." Genetic Programming and
Evolvable Machines 7.1 (2006): 33-54.
[3] Schmidt, Michael, and Hod Lipson. "Distilling free-form natural laws
from experimental data." Science 324.5923 (2009): 81-85.
[4] Ritt, Joseph Fels. Differential algebra. Vol. 33. American
Mathematical Soc., 1950.
[5] Izzo, Dario, Francesco Biscani, and Alessio Mereta. "Differentiable
Genetic Programming." European Conference on Genetic
Programming. Springer, Cham, 2017.
The kelvins
platform
Compete to learn and train
Kelvins Portal: compete to excel
• Asking the correct questions is essential to be
successful in science.
• A dedicated competition portal: Kelvins, reach the
absolute zero (error).
• AlgoritHmic and data mining competitions co-exist
• Targeting machine learning, data mining communities
but also space engineers.
• Portal: https://kelvins.esa.int/
• Competitions in the pipeline: Asteroid belt / debris
surrogate models, orbital propagation error
prediction.
Mars Express Power Challenge
• predict the power consumption
of the spacecraft thermal
subsystem.
• Three years of spacecraft
telemetry are released … can
you predict the fourth year?
• The ultimate goal is to
automate operations and
extend satellite life time,
which in turn increases the
scientific return.
Fact sheet
● Downloads: 650
● Number of different countries > 20
● Teams in the final leaderboard: 40
● Registered teams: 133
● Submitted solutions: ~200
Winners
Jozef Stefan Institute, Lujbjana, Slovenia
Codename: MMMe8
Department Of Knowledge Technologies: Prof. Saso Dzeroski
SCORE
(RMSE
lower is
better)
0.07916
Runner-up
Stephanos Stephani
Codename: redrock
github.com/stephanos-stephani/MarsExpressChallenge
SCORE
(RMSE
lower is
better)
0.08030
Final results and public leader-board
Evolution of the scores and events
Competition time
Starter
Kit
RMSE
Score
Fair
Perfect
Outcome
Colors: MEX Model/Measured/Predicted
Colors: MEX Model/Measured/Predicted
Outcome
Colors: MEX Model/Measured/Predicted
Outcome
Colors: MEX Model/Measured/Predicted
Outcome
Colors: MEX Model/Measured/Predicted
Outcome
Colors: MEX Model/Measured/Predicted
Outcome
Star Trackers: First Contact (ongoing)
• A spacecraft is lost in space
and needs to autonomously
determine its attitude based
on the camera image of a star
tracker.
• Given 10 000 images of such a
scenario, participants of the
competition have to identify
stars visible in the images.
• The goal is to improve
state-of-the-art algorithms in
terms of speed, accuracy and
robustness
The Kessler Run: GTOC9
It is the year 2060 and the commercial exploitation
of Low Earth Orbits (LEOs) went well beyond the
trillion of Euros market size. Following the
unprecedented explosion of a Sun-synchronous
satellite, the Kessler effect triggered further
impacts and the Sun-synchronous LEO environment
was severely compromised. Scientists from all
main space agencies and private space companies
isolated a set of 123 orbiting debris pieces that, if
removed, would restore the possibility to operate
in that precious orbital environment and prevent
the Kessler effect to permanently compromise it.
You are thus called to design a series of missions
able to remove all critical debris pieces while
minimizing the overall cumulative cost of such an
endeavour. Each single mission cost (in EUR) will
depend on how early the mission is submitted via
this web-site (regardless of their actual launch
epoch) and on the spacecraft initial mass.
The Kessler Run: GTOC9
● Number of different countries: 19
● Teams in the final leaderboard: 36
● Registered teams: 69
● Registered institutions: 125
● Scientists registered: ~320
● Missions submitted:~1200
● A difficult combinatorial problem with
complex optimization procedures to evaluate
the various heuristics / costs involved in
transfers.
● Some Links to tsp variants or set cover.
● Won by an approach based on genetic
algorithms and ant colony optimization by Jet
propulsion Laboratory.
● Surrogate models suggested and used
successfully.
Interplanetary Trajectory Planning with Monte Carlo Tree Search
Hennes, Daniel, and Dario Izzo. "Interplanetary trajectory planning with Monte Carlo tree search."
Proceedings of the 24th International Conference on Artificial Intelligence,” AAAI Press. 2015.
http://ijcai.org/Proceedings/15/Papers/114.pdf
Optimal real-time landing using deep networks
Sánchez-Sánchez, Carlos, Dario Izzo, and Daniel Hennes. "Optimal Real-Time Landing Using Deep Networks."
http://www.esa.int/gsp/ACT/doc/AI/pub/ACT-RPR-AI-2016-ICATT-optimal_landing_deep_networks.pdf
Evolving solutions to TSP variants for active space debris removal.
Izzo, Dario, et al. "Evolving solutions to TSP variants for active space debris removal." Proceedings of the 2015
Annual Conference on Genetic and Evolutionary Computation. ACM, 2015.
An evolutionary robotics approach for the distributed control of satellite formations
Izzo, Dario, Luís F. Simões, and Guido CHE de Croon. "An evolutionary robotics approach for the distributed
control of satellite formations."Evolutionary Intelligence 7.2 (2014): 107-118.
Search for a grand tour of the jupiter galilean moons
Izzo, Dario, et al. "Search for a grand tour of the jupiter galilean moons." Proceedings of the 15th annual
conference on Genetic and evolutionary computation. ACM, 2013.
Evolutionary robotics approach to odor source localization
De Croon, G. C. H. E., et al. "Evolutionary robotics approach to odor source localization." Neurocomputing 121
(2013): 481-497.
Novelty search for soft robotic space exploration
Methenitis, Georgios, et al. "Novelty search for soft robotic space exploration." Proceedings of the 2015
Annual Conference on Genetic and Evolutionary Computation. ACM, 2015.
Lattice formation in space for a swarm of pico satellites
Pinciroli, Carlo, et al. "Lattice formation in space for a swarm of pico satellites." International Conference
on Ant Colony Optimization and Swarm Intelligence. Springer Berlin Heidelberg, 2008.
Selected ACT bibliography (more here)

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Dario izzo - Machine Learning methods and space engineering

  • 1. Machine Learning methods and Space Engineering By Dario Izzo
  • 2. Mission Created in 2002 “to monitor, perform and foster research on advanced space systems, innovative concepts and working methods” 2
  • 3. too immature for regular ESA programmes or projects concepts, techniques & scientific domains with no/weak links to space emerging from cutting-edge basic scientific research topics on which ESA is expected to have a position biomimetic approaches to engineering, brain-machine interfaces, liquid breathing, curiosity cloning, peer-to-peer computing, crowd sourcing gaming, innovation diffusion and dynamics mathematical global optimisation techniques, cloud-based uncertainty modelling, helicon thrusters, pure general relativistic approach to GNSS constellation design, vibrating systems in general relativity, metamaterials in the optical frequency range, distributed/swarm intelligence, laser filamentation planetary protection research, space nuclear power sources, asteroid deflection, liquid ventilation, pulsar navigation, biomimetic drilling solar power from space, torpor/hibernation, asteroid deflection, active removal of space debris, novel working methods, terraforming, geoengineering
  • 4. Learning from others…Interdisciplinary Most game-changing developments emerge around the fringes or intersections of disciplines Regular renewal of personnel Regular in-flow of new insights keeps team on the leading edge Encourage taking risks Encourage and reward high risk / high gain activities Scientific rigour and competence Avoid drifting into the realm of science fiction Support from top-management Activities tend to be ridiculed, admired, not taken seriously or seen as threat to core of the establishment. Close ties with academia Most relevant ideas/concepts on a time horizon of 10+ years are generated within academia and research centres
  • 5. ACT Research AreasFundamental Physics Impact of new ideas in physics on the space sector Biomimetics & Bioengineering Benefitting from Darwinian evolution to solve engineering problems Mission Analysis Mathematical techniques for future mission analysis Artificial Intelligence Engineering of intelligent computer systems Advanced Energy Systems Innovating energy systems Planetary System Science Options and opportunities from complex climate systems Computer Science & Applied Mathematics Post von neumann architectures Advanced Propulsion Explore and review break- through propulsion concepts Computational Management Science Explore computational aspects of management Advanced Materials Benefitting from the control at micro/nano scale
  • 6. We are currently hiring 5 new Research fellows (post-docs)! 1 - Artificial Intelligence 2 - Computer science 3 - Biomimetics 4 - Fundamental Physics 5 - Mission Analysis Deadline 6th July! www.esa.int/act
  • 7. 2040 How intelligent will satellites be?
  • 8. 80486 Before looking 25 ahead, let us look 25 back at AI and CS
  • 12. And what about algorithms?
  • 13. Alpha GO 2016 2000 CNN, BP, LSTM, RNN ImageNet 2006 2012 • 1980-1990: attempts to train DNNs failed • 2006: first worldwide success stories in 2006 Deep Belief Networks and autoencoders: networks trained layer by layer • 2006-2016: great success and explosion of DL, for example: Convolutional Neural Networks (CNNs): ImageNet success Long Short-Term Memory (LSTM): huge success in speech recognition . Just A Hype? No, DL is here to stay. Deep Learning First DL success
  • 14. Genetic Programming Symbolic regression (SR): Learn the underlying physics from data Symbolic regression leverages an “evolutionary” approach to model creation, testing billions of potential models per second, and converging on the simplest, most accurate ones that explain your data. S.R. makes no prior assumptions about the data set, instead fitting models to the data dynamically. Schmidt M., Lipson H. (2009) "Distilling Free-Form Natural Laws from Experimental Data," Science, Vol. 324, no. 5923, pp. 81 - 85. Companies using Nutonian SR tool: Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR ImageNet 2006 2012 2009Nutonian First DL success
  • 15. Smart “search” (optimization) methods Evolutionary algorithms: exploiting artificial selection to evolve increasingly better solutions to design problems Orders of magnitude better from Genetic Algorithm (80s) to modern techniques: Covariant Adaptation Evolutionary Strategy (CMA-ES), Multi-objective Evolutionary techniques via decomposition (MOEA/D) and Self-adaptive Differential Evolution (jDE) Monte Carlo Tree Search: for sequential decision-making problems One of the most successful techniques in AI for games Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009Nutonian First DL success, jDE 2003CMA-ES 2007MOEA/D
  • 16. Perception, understanding and communication Sensors: Dynamic Vision Sensors (DVS) Elementary Motion detectors (EMD) Light Field cameras (LFC) ... Algorithms: SIFT - Scale-invariant feature transform CNN - Convolutional Networks Using TTC, OF - Time to contact, optic flow LSTM - Long Short Term Memory Networks Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009Nutonian A LSTM wins ICDAR handwriting 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE
  • 17. What did all this progress buy us?
  • 18. 1. Text recognition 2. Colorization of black and white images 3. Adding sounds to silent movies 4. Object classification and detection in photographs 5. Generate image from caption 6. Handwriting generation 7. Text Generation (scripts, poetry, etc.) 8. Image Caption Generation 9. Music Composition 10. Software continuous integration 11. Manage currencies 12. Drive cars 13. Navigate 14. Chat 15. Generative Design Some jobs computers can perform (and that could not 25 years ago)
  • 19. Application Areas of AI Self-driving vehicles Google, Tesla, Mercedes-Benz, etc. Autonomous flying (drones) Amazon Prime Air delivery Military Drones Robotics Factory automation, Medicine, Scientific exploration ...
  • 20. Application Areas of AI Virtual Assistants Cortana, Siri, Viv Language-based services Machine translation Document summarization Emotionally aware interfaces Affective computing
  • 21. The next big things in AI/CS (10-20 years ahead)
  • 23. In the same place as where ANNs were in the 90s, these technologies hold great potential, and may become the next big things ● Artificial Evolution (Evolutionary Computing) -> Designing the unexpected ● Genetic Programming -> Computers programming themselves ● Artificial Life -> Digital ecologies tHE nEXT bIG tHINGS are today’s “failures” The seeds of these innovations are well planted
  • 24. The 2006 NASA ST5 spacecraft antenna (found by Genetic Programming) The ST5 mission successfully launched on March 22, 2006, and so this evolved antenna represents the world's first artificially-evolved object to fly in space
  • 25. The ESA (ACT) VLBI GTOC8 trajectory In 2011 the Humies Gold Medal Award was awarded to the ACT work on “Search for a grand tour of the Jupiter Galilean moons” for human-competitive results that were produced by any form of genetic and evolutionary computation.
  • 27. R3000: New Horizons RAD6000: Spirit-Opportunity, Messenger, Deep Space 1, Dawn RAD750: Kepler, Juno, Curiosity i386: ISS x86: Falcon 9, Hubble The Excuses: Radiation Tolerance Reliability Satellite build time Launch delays Paperwork Power Consumption NGMP (ESA, LEON4)
  • 28. Scenario #1: the gap is not filled. in 2040 the intelligence on board spacecraft will feel as exciting as a videogame from the 90s
  • 29. Scenario #2: the gap is filled. in 2040 the intelligence on board spacecraft will compare to today’s situation as modern VR based games compare to Pong
  • 30. ACT and AI research
  • 31. Explored areas – Neurocontrollers Evolution in robotic islands: ALife in the Galapagos Deep Reinforcement learning for Spacecraft hovering near unkown small bodies Morphological evolution of soft robots at different gravity levels Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE 2009Nutonian A LSTM wins ICDAR handwriting
  • 32. Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE Explored areas – Swarm Intelligence Decentralized Formation Flight with collision avoidance: Equilibrium Shaping Autonomous self-assembly of large space structures Root Swarm: Sensor webs deployment ACT MIT SPHERES experiments: first ANN controlling multiple (homogeneous) agents in space Nutonian A LSTM wins ICDAR handwriting
  • 33. Optic flow based lunar landing: from bees to Apollo Scent of science: from a female chasing moth to the chase of methane on Mars Explored areas – Biomimetic Sensing and Actuation Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE
  • 34. Explored areas – Vision Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE Nutonian A LSTM wins ICDAR handwriting Astro Drone - gamification for the acquisition of vision data-sets Learning “to see” in zero gravity - from stereo vision to monocular vision (using the MIT SPHERES platform)
  • 35. Explored areas – Evolution and smart search Evolution of Interplanetary Trajectories Parallel evolution in modern CPU architectures, the island model, PyGMO Novel tree search paradigms: Monte Carlo Tree Search, Ant Colony Optimization, Lazy Race Tree Search Humies Gold medal - “for Human-Competitive Results Produced by Genetic and Evolutionary Computation” 1st place in the 8th edition of GTOC - “The America’s cup of rocket science” Alpha GO 2016 2000 CNN, BP, LSTM, RNN, GP, SR, DE, MCTS ImageNet 2006 2012 2009 2003CMA-ES 2007MOEA/D DVS 2013 EMD, SIFT LFC from Stanford 2004 First DL success, jDE Nutonian A LSTM wins ICDAR handwriting
  • 36. The scikit-learn of evolutionary algorithms
  • 37. pip install pagmo conda config --add channels conda-forge conda install pagmo ● Provides “free” parallelization via the asynchronous island model ● mpi, threads, multiprocess, etc.. all encapsulated in the island ● available for osx, linux and windows ● Fully FLOSS philosophy ● Easily extendible with your own algorithms or problems ● Tutorials and doc constantly up to date ● Community support active via a dedicated gitter channel https://esa.github.io/pagmo2/index.html pagmo/pygmo 2.x
  • 38. whats ahead? Differentiable intelligence Use of high order derivative information in ML
  • 39. Background: the algebra of floating points >>> def my_function(x): ... return cos(x[0])+(x[0]+3*x[1]+x[2])**7 >>> x = [0.1,0.2,0.3] >>> my_function(x) 1.9896041652780259 Behind this seemingly trivial computation, a number of implicit assumptions we tend to forget. Note: we rarely question that the floating point algebra is “conformal” to the real number algebra.
  • 40. Background: the algebra of Truncated Taylor polynomials >>> def my_function(x): ... return cos(x[0])+(x[0]+3*x[1]+x[2])**7 >>> x = [gdual(0.1,"x0",5), gdual(0.2,"x1",5), gdual(0.3,"x2", 5)] >>> my_function(x) 42*dx0*dx2+105*dx0*dx2**2+630*dx0*dx1*dx2+126*dx0*dx1+945*dx0*dx1**2+3 5.0166*dx0**3+6.90017*dx0+20.82*dx2**2+6.946*dx2+125.73*dx1*dx2+314.1* dx1*dx2**2+105*dx0**2*dx2+34.8*dx2**3+945*dx1**2*dx2+945*dx1**3+20.502 5*dx0**2+189*dx1**2+20.973*dx1+ 1.9896+315*dx0**2*dx1 Substitute the algebra of floating point numbers with the algebra of Taylor series expansion, trust it to be conformal to the algebra of continuous functions -> a differential Algebra [4].
  • 42.
  • 43. floats floats Hi! I am a computer program
  • 44. Any-order Taylor expansion of the program outputs floats floats Hi! I am a computer program
  • 45. Application to Machine learning and Evolutionary Computations Gradient: widely used (backprop, SQP, interior point) Hessian: less used, often approximated, anyway researched Traditionally the error (or fitness) is conceived as a real number: instead, consider it as a function (of whatever parameters you choose). Using the new algebra, represent it, in the computer, as a truncated Taylor polynomial just as before you were representing it as a floating point.
  • 46. Application to Machine learning and Evolutionary Computations Traditionally the error (or fitness) is conceived as a real number: instead, consider it as a function (of whatever params you choose). Using the new algebra, represent it, in the computer, as a truncated Taylor polynomial just as before you were representing it as a floating point. Similar complexity as Hessians and gradients, but an entirely unresearched field both in machine learning and evolutionary computations.
  • 47. Deep learning in deep space Experiments on landing
  • 48. Status quo: Precompute a Reference optimal trajectory
  • 49. Status quo: Linearize around it to account for disturbancies
  • 50. Status quo: Risk to get unstable behaviour if we go off nominal
  • 51. Status quo: Use polynomials and perform regression Risk to be suboptimal
  • 52. 1. Pre-compute many optimal trajectories 2. Train an artificial neural network to approximate the optimal behaviour 3. Use the network to drive the spacecraft Our approach:
  • 53. Quadrotor state: [x, vx , z, zx , θ] control:[u1 , u2 ] Spacecraft state: [m, x, vx , z, zx , θ] control:[u1 , u2 ] state: [m, x, vx , z, vz , θ, vθ ] control: [u1 , u2 , u3 ] Rocket state: [m, x, vx , z, vz , θ, vθ ] control:[u1 , u2 ] Some landing models:
  • 54. Goal: Solve the deterministic continuous-time optimal control problem, that is: Current methods (direct or indirect) are not suitable for real-time on-board implementation, an alternative is to correct the deviations from a precomputed profile or use polynomial fits. Hamilton-Jacobi-Bellman equation 1 - precompute many optimal solutions:
  • 55. Direct methods Indirect methods - Hermite-Simpson transcription and non-linear programming (NLP) solver - Fast and easy implementation - Chattering effects in the training data have a huge negative impact on the results. - regularization techniques are used to remove them. - Suboptimal results - Solve the Hamilton-Jacobi- Bellman equations with shooting methods - Provides the actual optimal trajectories - But… an initial guess is necessary to solve the problem and it is really difficult to find them - More difficult and awkward implementation 1 - precompute many optimal solutions:
  • 56. Two methods to generate the data 1 - precompute many optimal solutions:
  • 57. Optimization for different problems: Free Landing - Pinpoint Landing, Time optimal - Power optimal - Mass optimal Resulting in different control profiles: 1 - precompute many optimal solutions:
  • 58. - The initial state of each trajectory is randomly selected from a training area - 150,000 trajectories are generated for each one of the problems - Computing the trajectory for a specific starting point is difficult, but we speed up the process of generating random optimal trajectories by: Random walks Homotopy methods 1 - precompute many optimal solutions:
  • 59. - The networks are trained on the state-control action paris of the trajectories - Networks with 1 - 5 hidden layers - Supervised Learning - Trained with Stochastic Gradient Descent (and momentum) - Minimize the squared loss error (C) 2 - Approximate state-action with a DNN
  • 60. ● Deep networks are always better than shallow networks with the same number of parameters. Challenging landing example 2 - Approximate state-action with a DNN
  • 61. DNNs with supervised learning and large datasets successfully approximate the optimal control 2 - Approximate state-action with a DNN
  • 62. DNNs with supervised learning and large datasets successfully approximate the optimal control 2 - Approximate state-action with a DNN
  • 63. Very accurate results + The DNNs can be used as an on-board reactive system (32.000x faster than optimization methods used to generate the data) 3 - How good is it?
  • 64. ● Successful landings from states outside of the training initial conditions ● This suggest that an approximation to the solution of the HJB equations is learned Multicopter (power) Multicopter (power) Spacecraft I generalization
  • 66. After reaching the target point the spacecraft hovers until it runs of fuel Is it learning the dynamics of the model? No training data below this line generalization
  • 67. The system was evaluated with the Parrot Bepop Drone in the TU Delft University Optimal trajectory and trajectory followed by the drone (after some scaling to adjust them, don’t trust this image) Optimal trajectories generated for the Bepop drone 4 - thE REAL WORLD
  • 68. 4 - thE REAL WORLD
  • 69. Adding a cnn for the perception
  • 70. 1 - Train a neural network to guess the state from an on-board camera 2 - Use it together with the previous DNNs to get fully automated visual landing CNN for state estimation from camera
  • 71. A simple setup is used: a 3D model (Blender) of a rocket landing on a sea platform (Falcon 9 inspired) CNN for state estimation from camera
  • 72. CNN for state estimation from camera
  • 73. CNN for state estimation from camera
  • 74. CNN for state estimation from camera
  • 76. References: [1] Carlos Sánchez-Sánchez, Dario Izzo and Daniel Hennes. "Optimal real-time landing using deep networks." Proceedings of the Sixth International Conference on Astrodynamics Tools and Techniques, ICATT. Vol. 12. 2016. [2] Carlos Sánchez-Sánchez, Dario Izzo and Daniel Hennes. "Learning the optimal state-feedback using deep networks." Computational Intelligence (SSCI), 2016 IEEE Symposium Series on. IEEE, 2016. [3] Carlos Sánchez-Sánchez and Dario Izzo. "Real-time optimal control via Deep Neural Networks: study on landing problems." arXiv preprint arXiv:1610.08668(2016).
  • 78. Encoding a computer program weighted Cartesian Genetic Program Miller, Julian F., and Peter Thomson. "Cartesian genetic programming." European Conference on Genetic Programming. Springer Berlin Heidelberg, 2000.
  • 79. weighted dCGP Case B: all floats except w3,1 and w10,1 -> gduals operating in P3 : Case A: all floats The output is a float The output is a Taylor polynomial in w3,1 and w10,1 truncated at the third order
  • 80. Weighted CGP >>> ks = kernel_set(["sum","diff","mul","div"])() >>> CGP = expression(1,1,1,10,10,2,ks, seed = 21312312) >>> print(CGP(["x"])) [x**2 - x] >>> print(CGP([0.1])) [-0.09] >>> ks = kernel_set(["sum","diff","mul","div"])() >>> CGPw = expression(1,1,1,10,10,2,ks, seed = 21312312) >>> print(CGPw(["x"])) [w1_0*w1_1*w2_0*x**2 - w2_1*x] Traditional CGP: all floats, no weights Case A: all floats, weighted expression
  • 81. Weighted dCGP Case B: define w1_0, w2_0 and w2_1 as gduals, add also the input >>> ks = kernel_set(["sum","diff","mul","div"])() >>> dCGPw = expression(1,1,1,10,10,2,ks, seed = 21312312) >>> print(dCGPw(["x"])) [w1_0*w2_0*x**2 - w2_1*x] >>> ex.set_weight(1, 0, gdual(1., "w1_0", 2)) >>> ex.set_weight(2, 0, gdual(1., "w2_0", 2)) >>> ex.set_weight(2, 1, gdual(1., "w2_1", 2)) >>> print(dCGPw([gdual(0.1)])) [-0.1*dw2_1+0.01*dw1_0*dw2_0+0.01*dw2_0-0.09+0.01*dw1_0] >>> print(dCGPw([gdual(0.1, “x”, 2)])) [0.01*dw1_0*dw2_0+dw1_0*dx0**2+0.2*dw1_0*dw2_0*dx0+0.2*dw1_0*dx0+0.01*d w1_0+dx0**2-0.1*dw2_1+0.2*dw2_0*dx0+0.01*dw2_0-0.09-0.8*dx0-dw2_1*dx0+d w2_0*dx0**2]
  • 83.
  • 84. Example 1: Learning ephemeral constants Taking the skeleton out of the closet …. ‘‘...the finding of numerical constants is a skeleton in the GP closet...[and an] area of research that requires more investigation...’’ - John Koza
  • 85. 1 - The error of a CGP expression is computed in the new algebra (so it’s a function, remember….). 2 - We thus get the order n Taylor expansion of the error: example with one only constant and order three 3 - We use the differential expression obtained for the error to update the ephemeral constant values so that the error is minimized 4 - At order 1 and with some type of gradient descent, you may think of this as a backpropagation to learn ephemeral constant values. Example 1: Learning ephemeral constants
  • 86. What order? Using: Expressions such as: Result in the error: A parabolid! -> A second order Taylor polynomial represents this error exactly.
  • 87. The final algorithm (1-4)-ES evolves the chromosome and thus the symbolic expression y(x,c). We assign to each fitness the minimum of the MSE across all possible values of the constants: The solution is approximated by one step of the Newton method. Hessian and gradient are extracted from a second order Taylor approximation
  • 88. Learning ephemeral constants: results ● Success: MSE < 1e-14 (i.e. we learn the exact value of the constants) ● We sample ~50 points in a uniform grid within bounds. ● We perform 100 runs. ● We compute the Expected Run Time (ERT): the expected value of the number of d-CGP expressions that have to be evaluated before meeting the success criteria set. ● Closest work is Topchy and Punch [1]: not comparable to these results.
  • 89. Example 2: Learning constants with weighted dCGP Destroying the closet
  • 90. Weight batch learning (1-4)-ES evolves the chromosome and thus the symbolic expression y(x,c). We assign to each fitness the minimum of the MSE across all possible values of the weights: Solution by the Newton method is now troublesome. A new learning method: weight batch learning We basically perform one Newton step to learn a batch of two weights at a time. No Lamarckian learning: at each generation weights are sampled from a normal distribution.
  • 91. Learning constants with weighted dCGP: results ● Same setup as in the previous experiments. ● All constants are learned within the set precision. ● Generally requires less generations of the ES ● ERT is higher because of the Newton iterations.
  • 92. Example 3: Solving differential equations Cauchy problems, Neumann and Dirichlet problems, TPBV problems
  • 93. Solving Differential Equations: simple example with y(0.1)=20.1 and x in [0.1,1] We assume is represented by our d-CGP expression (1 in 1 out). We construct a grid of 10 values for x between 0.1 and 1. Computing x as a gdual with truncation order 1, we get from the Taylor expansion of the program output. Following Tsoulos and Lagaris [2], at each generation we use as error the sum of two terms: - The violation of the differential equation: - The violation of the boundary condition:
  • 94. Solving Differential Equations: results Problem ERT dCGP ERT Tsoulos 8123 130600 35482 148400 22600 88200 896 38200 24192 40600 327020 797000 Comparison to Tsoulos and Lagaris [2] work possible. CGP outperforming grammatical evolution in these tasks d-CGP generalizing Tsoulos and Lagaris [2] method allowing high order and mixed derivatives
  • 95. Example 4: Finding prime integrals From differential equations to the fundamental conservation laws
  • 96. Finding prime integrals Prime integrals are typically found by great mathematicians and their intuition dynamical system in normal form a prime integral
  • 97. Swinging Atwood Machine Not only energy … “whatever this is” … is conserved
  • 98. Found in 1888 as a third example of integrable top Kovalevskaya Top Not only angular momentum … “whatever this is” … is conserved
  • 99. Finding prime integrals No need to solve this to create training data (i.e. no need to observe the system as in Schmidt and Lipson [3]) We get the derivatives from the 1st order Taylor expansion of the program output!
  • 101. References: [1] Topchy, Alexander, and William F. Punch. "Faster genetic programming based on local gradient search of numeric leaf values." Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation. Morgan Kaufmann Publishers Inc., 2001. [2] Tsoulos, Ioannis G., and Isaac E. Lagaris. "Solving differential equations with genetic programming." Genetic Programming and Evolvable Machines 7.1 (2006): 33-54. [3] Schmidt, Michael, and Hod Lipson. "Distilling free-form natural laws from experimental data." Science 324.5923 (2009): 81-85. [4] Ritt, Joseph Fels. Differential algebra. Vol. 33. American Mathematical Soc., 1950. [5] Izzo, Dario, Francesco Biscani, and Alessio Mereta. "Differentiable Genetic Programming." European Conference on Genetic Programming. Springer, Cham, 2017.
  • 103. Kelvins Portal: compete to excel • Asking the correct questions is essential to be successful in science. • A dedicated competition portal: Kelvins, reach the absolute zero (error). • AlgoritHmic and data mining competitions co-exist • Targeting machine learning, data mining communities but also space engineers. • Portal: https://kelvins.esa.int/ • Competitions in the pipeline: Asteroid belt / debris surrogate models, orbital propagation error prediction.
  • 104. Mars Express Power Challenge • predict the power consumption of the spacecraft thermal subsystem. • Three years of spacecraft telemetry are released … can you predict the fourth year? • The ultimate goal is to automate operations and extend satellite life time, which in turn increases the scientific return.
  • 105. Fact sheet ● Downloads: 650 ● Number of different countries > 20 ● Teams in the final leaderboard: 40 ● Registered teams: 133 ● Submitted solutions: ~200
  • 106. Winners Jozef Stefan Institute, Lujbjana, Slovenia Codename: MMMe8 Department Of Knowledge Technologies: Prof. Saso Dzeroski SCORE (RMSE lower is better) 0.07916
  • 108. Final results and public leader-board
  • 109. Evolution of the scores and events Competition time Starter Kit RMSE Score Fair Perfect
  • 116. Star Trackers: First Contact (ongoing) • A spacecraft is lost in space and needs to autonomously determine its attitude based on the camera image of a star tracker. • Given 10 000 images of such a scenario, participants of the competition have to identify stars visible in the images. • The goal is to improve state-of-the-art algorithms in terms of speed, accuracy and robustness
  • 117. The Kessler Run: GTOC9 It is the year 2060 and the commercial exploitation of Low Earth Orbits (LEOs) went well beyond the trillion of Euros market size. Following the unprecedented explosion of a Sun-synchronous satellite, the Kessler effect triggered further impacts and the Sun-synchronous LEO environment was severely compromised. Scientists from all main space agencies and private space companies isolated a set of 123 orbiting debris pieces that, if removed, would restore the possibility to operate in that precious orbital environment and prevent the Kessler effect to permanently compromise it. You are thus called to design a series of missions able to remove all critical debris pieces while minimizing the overall cumulative cost of such an endeavour. Each single mission cost (in EUR) will depend on how early the mission is submitted via this web-site (regardless of their actual launch epoch) and on the spacecraft initial mass.
  • 118. The Kessler Run: GTOC9 ● Number of different countries: 19 ● Teams in the final leaderboard: 36 ● Registered teams: 69 ● Registered institutions: 125 ● Scientists registered: ~320 ● Missions submitted:~1200 ● A difficult combinatorial problem with complex optimization procedures to evaluate the various heuristics / costs involved in transfers. ● Some Links to tsp variants or set cover. ● Won by an approach based on genetic algorithms and ant colony optimization by Jet propulsion Laboratory. ● Surrogate models suggested and used successfully.
  • 119. Interplanetary Trajectory Planning with Monte Carlo Tree Search Hennes, Daniel, and Dario Izzo. "Interplanetary trajectory planning with Monte Carlo tree search." Proceedings of the 24th International Conference on Artificial Intelligence,” AAAI Press. 2015. http://ijcai.org/Proceedings/15/Papers/114.pdf Optimal real-time landing using deep networks Sánchez-Sánchez, Carlos, Dario Izzo, and Daniel Hennes. "Optimal Real-Time Landing Using Deep Networks." http://www.esa.int/gsp/ACT/doc/AI/pub/ACT-RPR-AI-2016-ICATT-optimal_landing_deep_networks.pdf Evolving solutions to TSP variants for active space debris removal. Izzo, Dario, et al. "Evolving solutions to TSP variants for active space debris removal." Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation. ACM, 2015. An evolutionary robotics approach for the distributed control of satellite formations Izzo, Dario, Luís F. Simões, and Guido CHE de Croon. "An evolutionary robotics approach for the distributed control of satellite formations."Evolutionary Intelligence 7.2 (2014): 107-118. Search for a grand tour of the jupiter galilean moons Izzo, Dario, et al. "Search for a grand tour of the jupiter galilean moons." Proceedings of the 15th annual conference on Genetic and evolutionary computation. ACM, 2013. Evolutionary robotics approach to odor source localization De Croon, G. C. H. E., et al. "Evolutionary robotics approach to odor source localization." Neurocomputing 121 (2013): 481-497. Novelty search for soft robotic space exploration Methenitis, Georgios, et al. "Novelty search for soft robotic space exploration." Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation. ACM, 2015. Lattice formation in space for a swarm of pico satellites Pinciroli, Carlo, et al. "Lattice formation in space for a swarm of pico satellites." International Conference on Ant Colony Optimization and Swarm Intelligence. Springer Berlin Heidelberg, 2008. Selected ACT bibliography (more here)