Artificial intelligence for solving physics
problems
Dr. Nancy Agnes, Head, Technical Operations, Tutorsindia info@ tutorsindia.com
Keywords: Artificial Intelligence, Artificial
Intelligence thesis Topics ideas, quantum
mechanics, physics, Machine Learning, neural
networks, research, Theoretical physics, Machine
learning project writing Help for students
I. 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
network) emerging in organised quenched disorder
is studied from a physics perspective (given by the
data and the data-dependent network architecture)
I. 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 [3], to
incorporate function engineering.
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
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Figure 1: A neural network with physicsinfirmed engineered features is seen in a
schematic to solve the heat transfer PDE
Figure 2. A diagram of the physical informed
neural network used to solve the fluid dynamics
model
Interesting blog: Difference Between Artificial
Intelligence And Machine Learning?
III. KOHN-SHAM EQUATIONS AS
REGULARIZER - A MACHINE LEARNED
PHYSICS
II. 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 NavierStokes (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
Machine learning (ML) techniques have sparked a
lot of interest to boost DFT approximations. 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 one-dimensional 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 KSDFT is depicted in Figure 3 as a differentiable
programme
FIG. 3. KS-DFT as a differentiable program
IV. MACHINE LEARNING FOR QUANTUM
MECHANICS
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)
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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 Å1
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
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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REFERENCE:
[1] Zdeborová, L. Understanding deep learning is
also a job for physicists. Nat. Phys. 16, 602–604
(2020). https://doi.org/10.1038/s41567-020-0929-2
Muhammad Aurangzeb Ahmad and Şener
Özönder. 2020. Physics Inspired Models in
Artificial Intelligence. In Proceedings of the 26th
ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining (KDD '20).
Association for Computing Machinery, New York,
NY, USA, 3535–3536.
DOI:https://doi.org/10.1145/3394486.3406464
1. Navid Zobeiry, Keith D. Humfeld, A physicsinformed machine learning approach for solving
heat transfer equation in advanced manufacturing
and engineering applications, Engineering
Applications of Artificial Intelligence, Volume
101, 2021, 104232,
https://doi.org/10.1016/j.engappai.2021.104232.
Figure 4. Artificial neural network
architecture: General arrangement of layers,
network blocks (NBs), and connectivity for
input block (IB), NBs, and output layer [6].
V. CONCLUSION
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. Many AI
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2. Cheng, C.; Zhang, G.-T. Deep Learning Method
Based on Physics Informed Neural Network with
Resnet Block for Solving Fluid Flow
Problems. Water 2021, 13, 423.
https://doi.org/10.3390/w13040423.
3. Li, Li and Hoyer, Stephan and Pederson, Ryan
and Sun, Ruoxi and Cubuk, Ekin D. and Riley,
Patrick and Burke, Kieron, Kohn-Sham Equations
as Regularizer: Building Prior Knowledge into
Machine-Learned Physics, Phys. Rev. Lett., 126,
2021, 036401. 10.1103/PhysRevLett.126.036401.
6. Ramzan, Ismaeel; Kong, Linghan; Bryce,
Richard; Burton, Neil (2021): Machine Learning of
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Atomic Forces from Quantum Mechanics: a Model
Based on Pairwise Interatomic Forces. ChemRxiv.
Preprint.
https://doi.org/10.26434/chemrxiv.14449875.v1.
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