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Electronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory (DFT),…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

As the key component that facilitates long-haul transmission in optical fiber communications by increasing capacity and reducing costs, accurate characterization and gain settings of erbium-doped fiber amplifiers (EDFAs) are essential for…

The accurate modeling of semiconductor devices plays a critical role in the development of new technology nodes and next-generation devices. Semiconductor device designers largely rely on advanced simulation software to solve the…

Physics-informed neural networks have been widely applied to partial differential equations with great success because the physics-informed loss essentially requires no observations or discretization. However, it is difficult to optimize…

Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information.…

Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be…

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…