Related papers: XI-DeepONet: An operator learning method for ellip…
Operator learning has emerged as a promising paradigm for approximating solution operators of partial differential equations (PDEs). However, conventional approaches typically rely on pointwise function discretizations, which often suffer…
This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…
Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…
In this paper, we propose a categorical embedding discontinuity-capturing shallow neural network for anisotropic elliptic interface problems. The architecture comprises three hidden layers: a discontinuity-capturing layer, which maps domain…
In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find…
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…
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…
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…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
<<<This is a pre-acceptance version, please, go through Pattern Recognition Journal on Sciencedirect to read the final version>>>. Edge detection is the basis of many computer vision applications. State of the art predominantly relies on…
Elliptic variational inequalities (EVIs) present significant challenges in numerical computation due to their inherent non-smoothness, nonlinearity, and inequality formulations. Traditional mesh-based methods often struggle with complex…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…