The document presents a machine learning approach for real-time reachability analysis of dynamical systems. The approach uses regression to learn a cost function from simulated data and classify states as reachable or not reachable based on a cost threshold. It was tested on a Dubins car and deep-space spacecraft, showing orders of magnitude faster computation times than traditional methods while maintaining high accuracy.
Marina South, as zoned by Singapore’s Urban Redevelopment Authority (URA), will be the new Central Business District for international business and financial activities.
Marina South, as zoned by Singapore’s Urban Redevelopment Authority (URA), will be the new Central Business District for international business and financial activities.
Международная научно-практическая конференция International Conference on Big Data and its Applications (ICBDA) выросла из мероприятия Big Data Russia и проводится один раз в год, объединяя на одной площадке создателей новых технологий в области больших данных, представителей бизнеса, а также научных сотрудников и молодых ученых. В этом году конференция прошла 16 сентября в коворкинге Deworkracy.
Организаторы ICBDA благодарят Data-Centric Alliance (DCA) за поддержку мероприятия, а также отдельное спасибо Artox Media и NVIDIA.
Are you ready for the 4th industrial revolution?Sylvain Kalache
It's been a year that I left my job at LinkedIn to start my new professional life in the world of education, I wanted to share the biggest thing I learnt during this time.
Our world as we know it is about to drastically change, with the recent huge improvements in the world of deep learning and artificial intellligence, we are about to enter a new world where robot will take over a lot of tasks that were done by humans. What will be the impact? How shall we react? How to train the workforce? Are few questions I answer in this deck.
Linked blog post here: https://www.linkedin.com/pulse/you-ready-4th-industrial-revolution-sylvain-kalache
A time study in numerical methods programmingGlen Alleman
A 1974 graduate school (Physics) paper comparing the performance of numerical methods in FORTRAN and APL for modeling systems of differential equations
A time study in numerical methods programmingGlen Alleman
With the digital computer firmly established as a
research tool used by the scientist and engineer alike, a
careful examination of some of the techniques used to solve
the problems faced by the scientific user is warranted,
This paper describes a test undertaken to determine the
effectiveness of two different programming languages in
providing solutions to numerical analysis problems found
in scientific investigation. Some of the questions asked
were; 1) Can APL compete with a batch processed FORTRAN
job in solving common numerical analysis problems?
2) Is it useful to trade execution speed for code density
or vice-versa? 3) Is APL an easier language, from the
view-point of the novice user, in which to code his problem?
4) Can APL be cost effective in an environment where large
"number-crunching" problems are an everyday event,
A Non Parametric Estimation Based Underwater Target ClassifierCSCJournals
Underwater noise sources constitute a prominent class of input signal in most underwater signal processing systems. The problem of identification of noise sources in the ocean is of great importance because of its numerous practical applications. In this paper, a methodology is presented for the detection and identification of underwater targets and noise sources based on non parametric indicators. The proposed system utilizes Cepstral coefficient analysis and the Kruskal-Wallis H statistic along with other statistical indicators like F-test statistic for the effective detection and classification of noise sources in the ocean. Simulation results for typical underwater noise data and the set of identified underwater targets are also presented in this paper.
Going Smart and Deep on Materials at ALCFIan Foster
As we acquire large quantities of science data from experiment and simulation, it becomes possible to apply machine learning (ML) to those data to build predictive models and to guide future simulations and experiments. Leadership Computing Facilities need to make it easy to assemble such data collections and to develop, deploy, and run associated ML models.
We describe and demonstrate here how we are realizing such capabilities at the Argonne Leadership Computing Facility. In our demonstration, we use large quantities of time-dependent density functional theory (TDDFT) data on proton stopping power in various materials maintained in the Materials Data Facility (MDF) to build machine learning models, ranging from simple linear models to complex artificial neural networks, that are then employed to manage computations, improving their accuracy and reducing their cost. We highlight the use of new services being prototyped at Argonne to organize and assemble large data collections (MDF in this case), associate ML models with data collections, discover available data and models, work with these data and models in an interactive Jupyter environment, and launch new computations on ALCF resources.
Calculation of solar radiation by using regression methodsmehmet şahin
Abstract. In this study, solar radiation was estimated at 53 location over Turkey with
varying climatic conditions using the Linear, Ridge, Lasso, Smoother, Partial least, KNN
and Gaussian process regression methods. The data of 2002 and 2003 years were used to
obtain regression coefficients of relevant methods. The coefficients were obtained based on
the input parameters. Input parameters were month, altitude, latitude, longitude and landsurface
temperature (LST).The values for LST were obtained from the data of the National
Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer
(NOAA-AVHRR) satellite. Solar radiation was calculated using obtained coefficients in
regression methods for 2004 year. The results were compared statistically. The most
successful method was Gaussian process regression method. The most unsuccessful method
was lasso regression method. While means bias error (MBE) value of Gaussian process
regression method was 0,274 MJ/m2, root mean square error (RMSE) value of method was
calculated as 2,260 MJ/m2. The correlation coefficient of related method was calculated as
0,941. Statistical results are consistent with the literature. Used the Gaussian process
regression method is recommended for other studies.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Международная научно-практическая конференция International Conference on Big Data and its Applications (ICBDA) выросла из мероприятия Big Data Russia и проводится один раз в год, объединяя на одной площадке создателей новых технологий в области больших данных, представителей бизнеса, а также научных сотрудников и молодых ученых. В этом году конференция прошла 16 сентября в коворкинге Deworkracy.
Организаторы ICBDA благодарят Data-Centric Alliance (DCA) за поддержку мероприятия, а также отдельное спасибо Artox Media и NVIDIA.
Are you ready for the 4th industrial revolution?Sylvain Kalache
It's been a year that I left my job at LinkedIn to start my new professional life in the world of education, I wanted to share the biggest thing I learnt during this time.
Our world as we know it is about to drastically change, with the recent huge improvements in the world of deep learning and artificial intellligence, we are about to enter a new world where robot will take over a lot of tasks that were done by humans. What will be the impact? How shall we react? How to train the workforce? Are few questions I answer in this deck.
Linked blog post here: https://www.linkedin.com/pulse/you-ready-4th-industrial-revolution-sylvain-kalache
A time study in numerical methods programmingGlen Alleman
A 1974 graduate school (Physics) paper comparing the performance of numerical methods in FORTRAN and APL for modeling systems of differential equations
A time study in numerical methods programmingGlen Alleman
With the digital computer firmly established as a
research tool used by the scientist and engineer alike, a
careful examination of some of the techniques used to solve
the problems faced by the scientific user is warranted,
This paper describes a test undertaken to determine the
effectiveness of two different programming languages in
providing solutions to numerical analysis problems found
in scientific investigation. Some of the questions asked
were; 1) Can APL compete with a batch processed FORTRAN
job in solving common numerical analysis problems?
2) Is it useful to trade execution speed for code density
or vice-versa? 3) Is APL an easier language, from the
view-point of the novice user, in which to code his problem?
4) Can APL be cost effective in an environment where large
"number-crunching" problems are an everyday event,
A Non Parametric Estimation Based Underwater Target ClassifierCSCJournals
Underwater noise sources constitute a prominent class of input signal in most underwater signal processing systems. The problem of identification of noise sources in the ocean is of great importance because of its numerous practical applications. In this paper, a methodology is presented for the detection and identification of underwater targets and noise sources based on non parametric indicators. The proposed system utilizes Cepstral coefficient analysis and the Kruskal-Wallis H statistic along with other statistical indicators like F-test statistic for the effective detection and classification of noise sources in the ocean. Simulation results for typical underwater noise data and the set of identified underwater targets are also presented in this paper.
Going Smart and Deep on Materials at ALCFIan Foster
As we acquire large quantities of science data from experiment and simulation, it becomes possible to apply machine learning (ML) to those data to build predictive models and to guide future simulations and experiments. Leadership Computing Facilities need to make it easy to assemble such data collections and to develop, deploy, and run associated ML models.
We describe and demonstrate here how we are realizing such capabilities at the Argonne Leadership Computing Facility. In our demonstration, we use large quantities of time-dependent density functional theory (TDDFT) data on proton stopping power in various materials maintained in the Materials Data Facility (MDF) to build machine learning models, ranging from simple linear models to complex artificial neural networks, that are then employed to manage computations, improving their accuracy and reducing their cost. We highlight the use of new services being prototyped at Argonne to organize and assemble large data collections (MDF in this case), associate ML models with data collections, discover available data and models, work with these data and models in an interactive Jupyter environment, and launch new computations on ALCF resources.
Calculation of solar radiation by using regression methodsmehmet şahin
Abstract. In this study, solar radiation was estimated at 53 location over Turkey with
varying climatic conditions using the Linear, Ridge, Lasso, Smoother, Partial least, KNN
and Gaussian process regression methods. The data of 2002 and 2003 years were used to
obtain regression coefficients of relevant methods. The coefficients were obtained based on
the input parameters. Input parameters were month, altitude, latitude, longitude and landsurface
temperature (LST).The values for LST were obtained from the data of the National
Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer
(NOAA-AVHRR) satellite. Solar radiation was calculated using obtained coefficients in
regression methods for 2004 year. The results were compared statistically. The most
successful method was Gaussian process regression method. The most unsuccessful method
was lasso regression method. While means bias error (MBE) value of Gaussian process
regression method was 0,274 MJ/m2, root mean square error (RMSE) value of method was
calculated as 2,260 MJ/m2. The correlation coefficient of related method was calculated as
0,941. Statistical results are consistent with the literature. Used the Gaussian process
regression method is recommended for other studies.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Diagnosis of Faulty Elements in Array Antenna using Nature Inspired Cuckoo Se...IJECEIAES
Detection and correction of faulty elements in a linear array have great importance in radar, sonar, mobile communications and satellite. Due to single element failure, the whole radiation pattern damage in terms of side lobes level and nulls. Once we have detect the position of defective element, then correction method is applied to achieve the desired pattern. In this work, we introduce a nature inspired meta-heuristic cuckoo search algorithm to diagnose the position of defective elements in a linear array. The nature inspired cuckoo search algorithm is new to the optimization family and is used first time for fault detection in an array antenna. Cuckoo search algorithm is a global search optimization technique. The cost function is used as a fitness function which defines an error between the degraded far field power pattern and the estimated one. The proposed technique is used effectively for the diagnosis of complete, as well as, for partial faulty elements position. Different simulation results are evaluated for 40 elements Taylor pattern to validate and check the performance of the proposed technique.
The use of sparse representation in direction of arrival (DoA) estimation has been around for a while. This exploits the angular sparsity of the impinging wavefronts and allows us to use much more efficient algorithms that can perform well in very challenging scenarios like coherent sources, low number of snapshots etc. In applications like channel sounding and RADAR, however, it may not be enough to just have the DoA of the signal but the offset from the carrier frequency or the Doppler frequency can be of equal importance as well in these applications.
Investigation of Parameter Behaviors in Stationarity of Autoregressive and Mo...BRNSS Publication Hub
The most important assumption about time series and econometrics data is stationarity. Therefore, this study focuses on behaviors of some parameters in stationarity of autoregressive (AR) and moving average (MA) models. Simulation studies were conducted using R statistical software to investigate the parameter values at different orders (p) of AR and (q) of MA models, and different sample sizes. The stationary status of the p and q are, respectively, determined, parameters such as mean, variance, autocorrelation function (ACF), and partial autocorrelation function (PACF) were determined. The study concluded that the absolute values of ACF and PACF of AR and MA models increase as the parameter values increase but decrease with increase of their orders which as a result, tends to zero at higher lag orders. This is clearly observed in large sample size (n = 300). However, their values decline as sample size increases when compared by orders across the sample sizes. Furthermore, it was observed that the means values of the AR and MA models of first order increased with increased in parameter but decreased when sample sizes were decreased, which tend to zero at large sample sizes, so also the variances
Inter-site autism biomarkers from resting state fMRIGael Varoquaux
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Similar to AllenClarkStarek.eaIROS2014.Presentation (20)
Inter-site autism biomarkers from resting state fMRI
AllenClarkStarek.eaIROS2014.Presentation
1. A Machine Learning Approach for Real-Time
Reachability Analysis
Ross E. Allen, Ashley A. Clark, Joseph A. Starek, and Marco
Pavone
Autonomous Systems Laboratory
Department of Aeronautics & Astronautics
Stanford University
IROS 2014
September 16th, 2014
2. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Problem Description
Figure: Simplified, 2D illustration of a cost-limited
reachable set for an initial state of a dynamical system.
Green endpoints are reachable and red endpoints are
non-reachable for the given threshold Jth.
R(x0, U, Jth) = xf ∈ X | ∃tf and ∃u(τ) ∈ U, τ ∈ [t0, tf ]
s.t. x(t0) = x0, ˙x(τ) = f (x(τ), u(τ)),
1 / 8
3. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Motivation Slide
• Reachability analysis central to motion planning,
collision avoidance, differential games, etc.
• Simple for geometric systems; difficult/costly for
kinodynamic systems
• Analytical results available for few problems;
numerical solutions necessary for most
2 / 8
4. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
3 / 8
5. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Cost Function Regression
4 / 8
6. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Cost Function Regression
4 / 8
7. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Cost Function Regression
4 / 8
8. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Cost Function Regression
4 / 8
9. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Cost Function Regression
4 / 8
10. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Classification into Reachable and Non-Reachable Sets
5 / 8
11. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Classification into Reachable and Non-Reachable Sets
5 / 8
12. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Classification into Reachable and Non-Reachable Sets
5 / 8
13. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Approach
Classification into Reachable and Non-Reachable Sets
5 / 8
14. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Simulations
Dubins Car
Figure: Predicted reachability set plotted with true cost for
the Dubins Car with 3 different cost thresholds (black
lines). Blue circles = SVM predicted reachable, red
diamonds = SVM predicted non-reachable, blue dot =
linear regression predicted reachable, red cross = linear
regression predicted non-reachable.
6 / 8
15. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Simulations
Deep-Space Spacecraft
Figure: Predicted reachability set plotted with true cost for
the deep-space spacecraft with 3 different cost thresholds
(black lines). Blue circles = SVM predicted reachable, red
diamonds = SVM predicted non-reachable, blue dot =
linear regression predicted reachable, red cross = linear
regression predicted non-reachable
6 / 8
16. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Simulations
Execution Time vs. Accuracy
Table: Average computation time and percent of
misclassification for the two-point boundary value problem
solver, the linear regression cost estimation (best fit model
using all features), and SVM classification (average over all
3 cost thresholds).
System 2PBVP Solve Lin. Reg. SVM
Time % Err Time % Err Time % Err
Dubins 1.23 s 0.0 9.4 ms 3.8 0.44 ms 4.9
Spacecraft 10.3 s 0.0 9.0 ms 5.8 0.40 ms 8.8
• Orders of magnitude decrease in computation time
if you are willing to accept some level of error
• Linear Regression slower than SVM but provides
more information, i.e. approximate cost of query
6 / 8
17. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Thank you!
Ross E. Allen, Ashley A. Clark, Joseph A.
Starek, and Marco Pavone
Stanford University
Aeronautics & Astronautics
6 / 8
18. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
Literature Review
A direct approach requires the numerical solution to a
2PBVP. An alternative, indirect method relies on the
numerical computation of the zero-level set of the
viscosity solution of the Hamilton-Jacobi-Bellman
equations, though with exponential time complexity
[1]. Modern research on reachability analysis has
therefore focused on producing efficient over- or
under-approximations of reachable sets for various
systems:
• discrete linear case [2]
• continuous-time linear case [3]
• general nonlinear dynamics [4, 5]
• nonlinear differential-algebraic dynamics [6]
• hybrid systems [7]
Drawbacks of traditional techniques:
• Computationally intensive
• Do not appear amenable to real-time implementation for
all but the simplest cases.
7 / 8
19. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
References I
Duˇsan M. Stipanovi´c, Inseok Hwang, and Claire J. Tomlin.
Computation of an Over-Approximation of the Backward Reachable Set using
Subsystem Level Set Functions.
In Dyn. of Cont., Discrete and Impulsive Systems, volume 11 of A: Mathematical
Analysis, pages 397–411. Watam Press, 2004.
Francesco Borrelli, A. Bemporad, and M. Morari.
Predictive Control, 2014.
In Preparation.
Antoine Girard and Colas Le Guernic.
Efficient Reachability Analysis for Linear Systems Using Support Functions.
In Myung Jin Chung and Pradeep Misra, editors, IFAC World Congress, volume 17,
pages 8966–8971, Gangnam-gu Seoul, South Korea, July 2008. Int. Fed. of Automatic
Control, IFAC PapersOnLine.
Eugene Asarin, Thao Dang, and Antoine Girard.
Reachability Analysis of Nonlinear Systems Using Conservative Approximation.
In Oded Maler and Amir Pnueli, editors, Hybrid Systems: Comp. and Control, volume
2623 of Lecture Notes in Comp. Science, pages 20–35. Springer, Prague, Czech
Republic, April 2003.
Romain Testylier and Thao Dang.
NLTOOLBOX: A Library for Reachability Computation of Nonlinear Dynamical
Systems.
In Dang Van Hung and Mizuhito Ogawa, editors, Autom. Tech. for Verif. and Analysis,
volume 8172 of Lecture Notes in Comp. Science, pages 469–473. Springer, Hanoi,
Vietnam, Oct 2013.
7 / 8
20. IROS 2014
R. Allen, A. Clark,
J. Starek, M.
Pavone
Introduction
Motivation
Approach
Results
Literature
References II
Matthias Althoff and Bruce H. Krogh.
Reachability Analysis of Nonlinear Differential-Algebraic Systems.
IEEE Trans. on Automatic Control, 59(2):371–383, Feb 2014.
Herv´e Gu´eguen, Marie-Anne Lefebvre, Janan Zaytoon, and Othman Nasri.
Safety Verification and Reachability Analysis for Hybrid Systems.
Annual Reviews in Control, 33(1):25–36, April 2009.
8 / 8