Artificial Intelligence for Solving Physics Problems

 Artificial Intelligence (AI) is making significant strides in the realm of science, particularly in physics, by tackling some of the most complex, time-consuming, and seemingly impossible problems that challenge human capabilities. This article explores several extensively researched applications of AI in physics. One of the key areas of focus is deep learning, where physicists are delving into the workings of deep neural networks. Despite their growing use in automated data learning, core theoretical questions about their functioning remain unanswered, and a physics-based approach might help bridge this gap. 

 The Role of Physics in AI 

To elucidate the current state of deep learning theory, one can draw a parallel with the early 20th-century physics theories of light and matter. For instance, many experimental phenomena, like the photoelectric effect, were inexplicable with the prevailing theories until the advent of quantum mechanics. Theoretical physics heavily relies on models that capture the essence of a problem while excluding unnecessary details to explain experimental observations. The widely used Ising model of magnetism exemplifies this approach. It omits specific quantum mechanical details and the characteristics of individual magnetic substances but effectively describes the transition from ferromagnetism to paramagnetism at high temperatures. 

  

Over three decades ago, physicists studying the statistical dynamics of disordered systems recognized the need for machine-learning system modeling. From a physics perspective, they examined a dynamical system with multiple interacting elements (network weights) emerging in organized quenched disorder, influenced by data and data-dependent network architecture. 

  

1. 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) under boundary conditions (BCs) and convective heat transfer PDEs. Traditional trial-and-error finite element (FE) simulations are inefficient due to uncertain convective coefficients. The loss function in this approach is defined by errors in satisfying PDE, BCs, and initial conditions, and it is minimized using an integrated normalization scheme. By comparing 1D and 2D predictions with FE results, the model's predictions outside the training zone are validated. The trained model facilitates rapid measurement of various BCs, creating feedback loops that bring the Industry 4.0 concept of active production management based on sensor data closer to reality. 

  

2. Deep Learning Method for Solving Fluid Flow Problems 

The Physics-Informed Neural Network (PINN), combined with Resnet blocks, addresses fluid flow problems governed by PDEs, such as the Navier-Stokes equation, integrated into the deep neural network’s loss function. Both initial and boundary parameters are included in the loss function. The PINN with Resnet blocks (Res-PINN) was tested on Burger’s equation with a discontinuous solution and the Navier-Stokes equation with a continuous solution. Results showed that Res-PINN outperforms traditional deep learning methods in predictive ability, accurately predicting the entire velocity and pressure fields of spatial-temporal fluid flow with a mean square error of 10^-5. The approach also effectively handles streamflow inverse problems, achieving low error rates for both clean and noisy data. 

  

3. Kohn-Sham Equations as Regularizers – A Machine Learned Physics 

Machine learning techniques have gained attention for enhancing Density Functional Theory (DFT) approximations. Solving the Kohn-Sham equations with training neural networks for the exchange-correlation functional provides implicit regularization, improving generalization. This approach allows learning the entire one-dimensional H2 dissociation curve with chemical precision, including highly correlated fields. The models surpass self-interaction errors and generalize to previously unseen molecular forms. 

  

4. Machine Learning for Quantum Mechanics 

Quantum information technology and intelligent learning systems are both emerging fields with transformative potential. Quantum information (QI) and AI/machine learning have their unique challenges. Utilizing machine learning algorithms, the pairF-Net method accurately predicts atomic forces in molecules to quantum chemistry precision. A residual neural network trained on pairwise interatomic forces determines Cartesian atomic forces suitable for molecular mechanics and dynamics calculations. This method predicts Cartesian forces as a linear combination of interatomic force components while maintaining rotational and translational invariance. For small organic molecules, the pairF-Net scheme estimates Cartesian atomic forces with high accuracy, facilitating efficient thermodynamic property calculations. 

  

Conclusion 

AI has significantly advanced the field of physics, while physics continues to enrich AI methodologies. For example, quantum machines are rooted in the fundamental laws of quantum mechanics, and many AI techniques have origins in basic physics principles. The synergy between these fields fosters groundbreaking discoveries in science and technology. As physicists, it is essential to embrace machine learning as a powerful tool, applying it judiciously and comprehensively. Understanding the mechanisms behind these technologies requires a physics-based approach, so we should actively engage in this interdisciplinary research. Let’s welcome deep neural networks into physics with the same enthusiasm that drives our quest to understand the universe.