Dr. Nancy Agnes presents the advancements and challenges in computational physics, highlighting the shift from theoretical and experimental methods to sophisticated computational tools that enhance research access. Recent developments include machine learning applications and physics-informed neural networks to tackle complex problems such as simulating incompressible fluid flows. The presentation concludes by emphasizing the need for physicists to adapt to rapid advancements in related fields and integrate modern methods in their research.

1. The Advancement
and Challenges in
Computational
Physics
An Academic presentation by
Dr. Nancy Agnes, Head, Technical Operations, Phdassistance
Group www.phdassistance.com
Email: info@phdassistance.com

2. OUTLINE
Introduction
Recent researches in computational
physics
Computational physics & its challenges
Conclusion

3. INTRODUCTION
For the last five decades, computational physics
has been a valuable scientific instrument in
physics.
In comparison to using only theoretical and
experimental approaches, it has enabled physicists
to understand complex problems better.
Computational physics was mostly a scientific
activity at the time, with relatively few organised
undergraduate study.
Contd...

4. Students were supposed to pick up the requisite computational skills when they
went through with their studies.
This culminated in a small number of highly qualified c omputational physics
graduates.
This pattern has shifted dramatically in recent years, with increasingly sophisticated
commercial applications or freeware computer programmes created by more
specialised groups being used by computational physics research groups.
Contd...

5. The benefit is that a larger number of researchers now have access to more effective
codes that integrate more sophisticated modelling of physical structures of interest.
This post discusses the advancement and challenges in computational physics.

6. RECENT RESEARCHES
IN COMPUTATIONAL
PHYSICS

7. PYTHON FRAMEWORK FOR COMPUTATIONAL
PHYSICS
For rapid prototyping of the latest physics codes, a
newly designed computational system was created.
TurboPy is a lightweight physics simulation
application that is built on the architecture of the
particle-in-cell code turbowave.
Contd...

8. It implements a Simulation class that drives the simulation and maintains coordination
between Physics Module class that handles the specifics of the dynamics of the
different sections of the problem and a few other classes, including a Grid class and a
Diagnostic class to handle various ancillary issues that occur frequently.
Figure 1 depicts one possible implementation of this workflow as turboPy physics units.
The workflow is split into two custom turboPy physics modules in this implementation

9. Figure 1. Custom turboPy physics modules and diagnostics are included in this diagram to show one
alternative implementation of the example workflow. Each box in the flow denotes a PhysicsModule or
Diagnostic subclass that has been written to conduct the action mentioned. [2].

10. MACHINE LEARNING IN COMPUTATIONAL PHYSICS
A new method for sampling training data based on a
Taylor approximation is built to approximate physical
simulation codes in machine learning.
Though not specifically related to Deep Learning, an
approach is used to approximate the solution of a
physical ODE structure using a Deep Neural Network
and improve its precision with the same model
architecture.
Contd...

11. In addition to the reasons stated leads, the concept
of using numerical simulation derivatives to improve
ML model training should be investigated.
Include derivatives as new teaching points to have a
DNN learn these derivatives as an example of
implementation. Figure 2 depicts a Taylor sampling
algorithm
Contd...

12. Figure 2. A Taylor based sampling algorithm

13. FOR THE
PHYSICS-INFORMED NEURAL NETWORKS
INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
To overcome the limitations of simulating incompressible laminar
and turbulent flows, physics-informed neural networks (PINNs)
are used, which encode the governing equations directly into the
deep neural network through automatic differentiation.
The Navier-Stokes flow nets (NSFnets) were created using two
different mathematical formulations of the Navier-Stokes
equations: the velocity-pressure (VP) and the vorticity-velocity
(VV) formulations.
Contd...

14. Even though this is a new methodology, a standard benchmark problem is used to
assess the precision, convergence rate, computational cost, and flexibility of NSFnets;
analytical solutions and direct numerical simulation (DNS) databases provide suitable
initial and boundary conditions for NSFnet simulations.
The ability to use NSFnets for applications other than classical CFD was shown in this
study, such as solving ill-posed (noisy or incomplete boundary conditions) or inverse
problems (unknown fluid properties) that would be impossible or prohibitively costly to
solve using traditional approaches.
Contd...

15. We also use a basic example of transfer learning to demonstrate how we can reduce
NSFnets' comparatively high computational cost.
The velocity-pressure (VP) form and the vorticity-velocity (VV) form of the unsteady
incompressible three-dimensional Navier-Stokes equations, as well as their
corresponding physics-informed neural networks (PINNs), were introduced in this work
(Figure 3)
Contd...

16. Fig. 3. Aschematic of NSFnets

17. COMPUTATIONAL PHYSICS &
ITS CHALLENGES

18. Despite the “early adopters” of computational physics described
above and individuals' desire to transform computer science into
physics analysis, society requires a (new) space to share ideas
and insight.
Any efforts, such as the Program Library of Computer Physics
Communications, have been popular today.
However, such collections must expand in-depth, provide more
groups, and go beyond just storing code libraries.
Contd...

19. Furthermore, the distance between available and validated statistical
methodologies and their application in computational physics inevitably
expands: computer scientists and applied mathematicians have never been
more efficient than they are now.
How will the (computational) physics world as a whole deal with the rapid
development in fields that serve as a methodological foundation? In physics,
the mathematical representation of NP has long been the basic language.
Contd...

20. Computation enables the solution of ever more complicated mathematical
models, reinforcing the mathematical language's strength.
This shows how the synergy effect enhances a specific region. However,
taking advantage of such an advantage poses a significant risk in and of
itself.
The Intergovernmental Panel on Climate Change's (IPCC) global weather
simulations is an example of a move above scientists in either theory or
experiments joined by computation and trying to interact

21. CONCLUSION
The enormous progress made in applied mathematics,
numerics, and computer science is compared with the
progress made in computational physics.
Although physicists are mostly concerned with their
original experiments on physical problems, they cannot
keep up with the latest developments of numerical
analysis on their own.
Contd...

22. Consequently, we see a growing difference between
theoretical findings on the one side and the application and
use of analytical methods focused on those concepts on the
other.
Closing this gap, i.e., introducing modern methods faster
and more consistently and integrating them into successful
computational physics science, seems to be one of the
major challenges.

23. A (computational) physicist's ability to recognise emerging
concepts in applied mathematics, numeric, and c omputer
science and then convert them into research projects is
particularly difficult.
To identify the potential of a new analytical instrument, a
computational physicist will need to be interested in two
different scientific groups, create benchmarks and other
parameters to judge the applicability of a method, and then
apply and test the findings using his or her knowledge in a
subfield of physics.

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