ARTIFICIAL INTELLIGENCE FOR
SOLVING PHYSICS PROBLEMS
An Academic presentation by
Dr. Nancy Agnes, Head, Technical Operations, Tutors India
Group www.tutorsindia.com
Email: info@tutorsindia.com
Today's Discussion
OUTLINE
Introduction
A Machine Learning Approach for Solving the Heat Transfer
Equation Based on Physics
Deep Learning Method for Solving Fluid Flow Problems
Kohn-Sham Equations as Regularizer - A Machine Learned Physics
Machine Learning for Quantum Mechanics
Conclusion
INTRODUCTION
Artificial Intelligence (AI) is beginning to impact science, like physics, by solving some
of the most complex, time-consuming, or even impossible problems humans solve.
This post discusses some of the applications of artificial intelligence in physics that have
been extensively researched.
Physicists are also tasked with deciphering deep learning.
Deep neural networks are being used in a growing number of applications for automated
learning from data, but core theoretical questions regarding how they function remain
unanswered.
A physics-based solution may assist in closing the gap.
Here's where physics comes into play: To explain the situation to a scientific audience,
one might equate the present state of deep learning theory to the early twentieth-century
physics theory of light and matter.
For example, many experimental effects (such as the photoelectric effect) could not be
interpreted by the current theory because quantum mechanics had not yet been
established.
Theoretical physics science, in particular, is heavily reliant on models. Models are a
means of catching the nature of a dilemma while excluding the information that isn’t
needed to clarify experimental findings.
The commonly used Ising model of magnetism is an example: it does not catch some
specifics of the quantum mechanical aspects of magnetic interactions, nor does it include
any details of any particular magnetic substance, but it describes the nature of the
transformation from a ferromagnet to a paramagnet at high temperature More than three
decades ago, physicists, especially those studying statistical dynamics of disordered
systems, realised the need for machine-learning system modelling.
A dynamical system with several interacting elements (weights of the network) emerging
in organised quenched disorder is studied from a physics perspective (given by the data
and the data-dependent network architecture)
A MACHINE
LEARNING
APPROACH FOR
SOLVING THE
HEAT TRANSFER
EQUATION
BASED ON
PHYSICS
In manufacturing and engineering applications where
parts are heated in ovens, a physics-based neural
network is designed to solve conductive heat transfer
partial differential equations (PDEs) as boundary
conditions (BCs), as well as convective heat transfer
PDEs.
New research methods based on trial and error finite
element (FE) simulations are inefficient since
convective coefficients are always uncertain.
The loss function is represented using errors to satisfy
PDE, BCs, and the initial state.
Loss words are reduced simultaneously using an
integrated normalising scheme.
Function engineering also employs heat transfer theory. Through comparing 1D and 2D
predictions to FE outcomes, the predictions for 1D and 2D cases are verified.
Heat transfer outside the training zone can be predicted using engineered elements, as
seen.
The trained model enables rapid measurement of various BCs to create feedback
loops, bringing the Industry 4.0 idea of active production management based on sensor
data closer to reality.
A first layer for the neural network was created by merging two pre-layers of words, as
seen in Figure 1, to incorporate function engineering.
Figure 1: A neural network with physics-infirmed engineered features is seen in a schematic to solve the
heat transfer PDE
DEEP LEARNING
METHOD FOR
SOLVING FLUID
FLOW PROBLEMS
The Physical Informed Neural Network (PINN) is
used in conjunction with Resnet blocks to solve
fluid flow problems based on partial differential
equations (i.e., the Navier- Stokes equation)
embedded in the deep neural network's loss
function.
The initial and boundary parameters are both
considered in the loss function.
Burger's equation with a discontinuous solution
and Navier-Stokes (N-S) equation with a
continuous solution was chosen to verify the
efficiency of the PINN with Resnet blocks.
The findings show that the PINN with Resnet blocks (Res-PINN) outperforms
conventional deep learning approaches in terms of predictive ability.
Furthermore, the Res-PINN can predict the whole velocity and pressure fields
of spatial-temporal fluid flow, with a mean square error of 10-5.
The streamflow inverse problems are also well-studied. In clean data, the
inverse parameters have errors of 0.98 % and 3.1 %, respectively, and in noisy
data, they have errors of 0.99 % and 3.1 %.
A schematic diagram of a physics-informed neural network used to solve a fluid
dynamics model is seen in Figure 2
Figure 2. A diagram of the physical informed neural network used to solve the fluid
dynamics model [4].
Interesting blog: Difference Between Artificial Intelligence And Machine
Learning?
Machine learning (ML) techniques have sparked a
lot of interest to boost DFT approximations.
KOHN-SHAM
EQUATIONS
AS
REGULARIZER
- A MACHINE
LEARNED
PHYSICS
The implied regularisation provided by solving the
Kohn-Sham equations with training neural networks
for the exchange-correlation functional improves
generalisation.
Two separations are enough to learn the entire onedimensional H2 dissociation curve, including the
highly correlated field, with chemical precision. Our
models also transcend self-interaction error and
generalise to previously unseen forms of molecules.
The KS-DFT is depicted in Figure 3 as a
differentiable programme
FIG. 3. KS-DFT as a differentiable program
MACHINE
LEARNING
FOR
QUANTUM
M ECHAN ICS
Quantum information technology and intelligent
learning systems, on the one hand, are both
emerging technologies with the potential to change
our culture in the future.
Quantum knowledge (QI) versus machine learning
and artificial intelligence (AI) are two underlying
areas of basic science that both have their own set
of questions and challenges.
Using machine learning algorithms, pairF-Net, a
modern chemically intuitive method, precisely
predicts the atomic forces in a molecule to quantum
chemistry precision.
A residual artificial neural network was developed and trained with features and
objectives focused on pairwise interatomic forces to determine the Cartesian atomic
forces suitable for molecular mechanics and dynamics calculations.
The scheme predicts Cartesian forces as a linear combination of a series of force
components on an interatomic basis while maintaining rotational and translational
invariance implicitly.
The system will estimate the reconstructed Cartesian atomic forces for a set of small
organic molecules to less than 2 kcal mol-1 Å-1 using reference force values obtained
from density functional theory.
The pairF-Net scheme uses a simple and chemically understandable route to have
atomic forces at a quantum mechanical level at a fraction of the cost, paving the way
for effective thermodynamic property calculations.
The artificial neural network architecture is depicted in Figure 4
Figure 4. Artificial neural network architecture: General arrangement of layers, network blocks (NBs), and
connectivity for input block (IB), NBs, and output layer [6].
While AI has aided many advances in physics,
physics still aids AI methods in various ways.
Quantum machines, for example, are based on the
fundamental laws of quantum mechanics.
CONCLUSION
Many AI approaches have been derived from basic
physics laws.
Both kinds of research complement each other most
significantly, benefiting humanity to achieve newer
and more comprehensive breakthroughs in Science
and Technology.
Let us, as physicists, welcome machine learning as a modern method in our
toolbox, and use it broadly and wisely.
But bear in mind that learning why and how it works necessitates physics
methodology, so we shouldn't sit back and watch this massive undertaking
unfold.
So let us welcome deep neural networks into our field and research them with
the same zeal that fuels our search to comprehend the world around us.
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