Related papers: An Advanced Physics-Informed Neural Operator for C…

Deep operator networks (DeepONets) are trained to predict the linear amplification of instability waves in high-speed boundary layers and to perform data assimilation. In contrast to traditional networks that approximate functions,…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

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…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

This paper develops a Deep Graph Operator Network (DeepGraphONet) framework that learns to approximate the dynamics of a complex system (e.g. the power grid or traffic) with an underlying sub-graph structure. We build our DeepGraphONet by…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization and real-time control. Conventional deep learning surrogates often struggle with complex,…

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical…