how artificial intelligence is addressing real world physics problems
DESCRIPTION
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. https://bit.ly/3zy4Ee6 For #Enquiry https://www.tutorsindia.com [email protected] (Whatsapp): +91-8754446690 (UK): +44-1143520021TRANSCRIPT
ARTIFICIAL INTELLIGENCE FORSOLVING PHYSICS PROBLEMS
An Academic presentation by Dr. Nancy Agnes, Head, Technical Operations, Tutors India Group www.tutorsindia.comEmail: [email protected]
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
OUTLINE
Today's Discussion
INTRODUCTION
Artificial Intelligence (AI) is beginning to impact science, like physics, by solving someof the most complex, time-consuming, or even impossible problems humans solve.
This post discusses some of the applications of artificial intelligence in physics that havebeen extensively researched.
Physicists are also tasked with deciphering deep learning.
Deep neural networks are being used in a growing number of applications for automatedlearning from data, but core theoretical questions regarding how they function remainunanswered.
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-centuryphysics theory of light and matter.
For example, many experimental effects (such as the photoelectric effect) could not beinterpreted by the current theory because quantum mechanics had not yet beenestablished.
Theoretical physics science, in particular, is heavily reliant on models. Models are ameans of catching the nature of a dilemma while excluding the information that isn’tneeded to clarify experimental findings.
The commonly used Ising model of magnetism is an example: it does not catch somespecifics of the quantum mechanical aspects of magnetic interactions, nor does it includeany details of any particular magnetic substance, but it describes the nature of thetransformation from a ferromagnet to a paramagnet at high temperature More than threedecades ago, physicists, especially those studying statistical dynamics of disorderedsystems, realised the need for machine-learning system modelling.
A dynamical system with several interacting elements (weights of the network) emergingin organised quenched disorder is studied from a physics perspective (given by the dataand the data-dependent network architecture)
A MACHINELEARNINGAPPROACH FORSOLVING THEHEAT TRANSFEREQUATIONBASED ONPHYSICS
In manufacturing and engineering applications whereparts are heated in ovens, a physics-based neuralnetwork is designed to solve conductive heat transferpartial differential equations (PDEs) as boundaryconditions (BCs), as well as convective heat transferPDEs.
New research methods based on trial and error finiteelement (FE) simulations are inefficient sinceconvective coefficients are always uncertain.
The loss function is represented using errors to satisfyPDE, BCs, and the initial state.
Loss words are reduced simultaneously using anintegrated normalising scheme.
Function engineering also employs heat transfer theory. Through comparing 1D and 2Dpredictions to FE outcomes, the predictions for 1D and 2D cases are verified.
Heat transfer outside the training zone can be predicted using engineered elements, asseen.
The trained model enables rapid measurement of various BCs to create feedbackloops, bringing the Industry 4.0 idea of active production management based on sensordata closer to reality.
A first layer for the neural network was created by merging two pre-layers of words, asseen 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 LEARNINGMETHOD FORSOLVING FLUIDFLOW PROBLEMS
The Physical Informed Neural Network (PINN) isused in conjunction with Resnet blocks to solvefluid flow problems based on partial differentialequations (i.e., the Navier- Stokes equation)embedded in the deep neural network's lossfunction.
The initial and boundary parameters are bothconsidered in the loss function.
Burger's equation with a discontinuous solutionand Navier-Stokes (N-S) equation with acontinuous solution was chosen to verify theefficiency of the PINN with Resnet blocks.
The findings show that the PINN with Resnet blocks (Res-PINN) outperformsconventional deep learning approaches in terms of predictive ability.
Furthermore, the Res-PINN can predict the whole velocity and pressure fieldsof spatial-temporal fluid flow, with a mean square error of 10-5.
The streamflow inverse problems are also well-studied. In clean data, theinverse parameters have errors of 0.98 % and 3.1 %, respectively, and in noisydata, they have errors of 0.99 % and 3.1 %.
A schematic diagram of a physics-informed neural network used to solve a fluiddynamics 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?
KOHN-SHAMEQUATIONSASREGULARIZER- A MACHINELEARNEDPHYSICS
Machine learning (ML) techniques have sparked alot of interest to boost DFT approximations.
The implied regularisation provided by solving theKohn-Sham equations with training neural networksfor the exchange-correlation functional improvesgeneralisation.
Two separations are enough to learn the entire one-dimensional H2 dissociation curve, including thehighly correlated field, with chemical precision. Ourmodels also transcend self-interaction error andgeneralise to previously unseen forms of molecules.
The KS-DFT is depicted in Figure 3 as adifferentiable programme
FIG. 3. KS-DFT as a differentiable program
MACHINELEARNINGFORQUANTUMMECHANICS
Quantum information technology and intelligentlearning systems, on the one hand, are bothemerging technologies with the potential to changeour culture in the future.
Quantum knowledge (QI) versus machine learningand artificial intelligence (AI) are two underlyingareas of basic science that both have their own setof questions and challenges.
Using machine learning algorithms, pairF-Net, amodern chemically intuitive method, preciselypredicts the atomic forces in a molecule to quantumchemistry precision.
A residual artificial neural network was developed and trained with features andobjectives focused on pairwise interatomic forces to determine the Cartesian atomicforces suitable for molecular mechanics and dynamics calculations.
The scheme predicts Cartesian forces as a linear combination of a series of forcecomponents on an interatomic basis while maintaining rotational and translationalinvariance implicitly.
The system will estimate the reconstructed Cartesian atomic forces for a set of smallorganic molecules to less than 2 kcal mol-1 Å-1 using reference force values obtainedfrom density functional theory.
The pairF-Net scheme uses a simple and chemically understandable route to haveatomic forces at a quantum mechanical level at a fraction of the cost, paving the wayfor 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].
CONCLUSION
While AI has aided many advances in physics,physics still aids AI methods in various ways.
Quantum machines, for example, are based on thefundamental laws of quantum mechanics.
Many AI approaches have been derived from basicphysics laws.
Both kinds of research complement each other mostsignificantly, benefiting humanity to achieve newerand more comprehensive breakthroughs in Scienceand Technology.
Let us, as physicists, welcome machine learning as a modern method in ourtoolbox, and use it broadly and wisely.
But bear in mind that learning why and how it works necessitates physicsmethodology, so we shouldn't sit back and watch this massive undertakingunfold.
So let us welcome deep neural networks into our field and research them withthe same zeal that fuels our search to comprehend the world around us.
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