相关论文: Coupling-Robust Accuracy in Multiphysics Physics I…

This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose…

Accurate methane sorption prediction across heterogeneous coal ranks requires models that combine thermodynamic consistency, efficient knowledge transfer across data-scarce geological systems, and calibrated uncertainty estimates,…

In continuum topology optimization (TO), two essential procedures are involved: structural analysis through the solution of partial differential equations (PDEs) and the subsequent update of design variables. Both procedures can be…

We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…

A physics-constrained deep learning surrogate that predicts the exponential ``avalanche'' growth rate of runaway electrons (REs) for a plasma containing partially ionized impurities is developed. Specifically, a physics-informed neural…

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 numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

We present an application of Physics-Informed Neural Networks (PINNs) to the study of $\mathrm{SU}(N_c)$ lattice gauge theories. Our method enables the learning of eigenfunctions and eigenvalues at arbitrary gauge couplings, smoothly moving…

This paper presents a PINN training framework that employs (1) pre-training steps that accelerates and improve the robustness of the training of physics-informed neural network with auxiliary data stored in point clouds, (2) a net-to-net…

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging. Neural networks have been shown to be a…

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm…

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…

In this work, we introduce the Quantum-Classical Hybrid Physics-Informed Neural Network with Multiplicative and Additive Couplings (QPINN-MAC): a novel hybrid architecture that integrates the framework of Physics-Informed Neural Networks…

Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics…

Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great…

A surrogate model of the runaway electron avalanche growth rate in a magnetic fusion plasma is developed. This is accomplished by employing a physics-informed neural network (PINN) to learn the parametric solution of the adjoint to the…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful mesh-free framework for solving ordinary and partial differential equations by embedding the governing physical laws directly into the loss function. However, their…