相关论文: Separable Operator Networks

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

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…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior…

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…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks,…

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…

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…