Related papers: Neural oscillators for generalization of physics-i…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…

Physics-informed machine learning (PIML) provides a promising solution for building energy modeling and can serve as a virtual environment to enable reinforcement learning (RL) agents to interact and learn. However, challenges remain in…

Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…

Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators…

Neural oscillators, originating from second-order ordinary differential equations (ODEs), have demonstrated strong performance in stably learning causal mappings between long-term sequences or continuous temporal functions, as well as in…

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…