Related papers: When Network Architecture Meets Physics: Deep Oper…

In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…

Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the…

The Li-ion battery is a complex physicochemical system that generally takes applied current as input and terminal voltage as output. The mappings from current to voltage can be described by several kinds of models, such as accurate but…

Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

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…

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…

This paper designs an Operator Learning framework to approximate the dynamic response of synchronous generators. One can use such a framework to (i) design a neural-based generator model that can interact with a numerical simulator of the…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…

The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of…

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…

We present the data-driven coupled-cluster deep network (DDCCNet), a family of multitask, physics-enhanced deep learning architectures designed to predict coupled-cluster singles and doubles (CCSD) amplitudes and correlation energies from…

While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

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…

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard…

Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-based models can be computationally expensive and may suffer…