相关论文: Learning in PINNs: Phase transition, total diffusi…

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing…

Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by…

Training Deep Neural Networks relies on the model converging on a high-dimensional, non-convex loss landscape toward a good minimum. Yet, much of the phenomenology of training remains ill understood. We focus on three seemingly disparate…

Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…

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…

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…

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Physics-Informed machine learning models have recently emerged with some interesting and unique features that can be applied to reservoir engineering. In particular, physics-informed neural networks (PINN) leverage the fact that neural…

Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…

Learning in deep neural networks (DNNs) is implemented through minimizing a highly non-convex loss function, typically by a stochastic gradient descent (SGD) method. This learning process can effectively find good wide minima without being…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Despite tremendous success of deep neural network in machine learning, the underlying reason for its superior learning capability remains unclear. Here, we present a framework based on statistical physics to study dynamics of stochastic…

Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques. Motivated by this, we explore…