Related papers: Operator approximation of the wave equation based …

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…

Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assumption limits applicability to problems with variable sensor…

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin (DG) method with neural networks to solve parametric partial…

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…

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…

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes especially relevant in real-world scenarios where…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…

In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography (EIT), where the goal is to recover the conductivity in a medium from boundary current-to-voltage measurements, i.e., the…

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…

We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a single-hidden layer neural network with randomized…

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…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…