Related papers: Reduced-Basis Deep Operator Learning for Parametri…

Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…

We introduce BumpNet, a sparse multilayer perceptron (MLP) framework for PDE numerical solution and operator learning. BumpNet is based on basis function expansion, which makes them superficially similar to radial-basis function (RBF)…

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…

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…

Particle-in-Cell (PIC) simulations are widely used for modeling plasma kinetics by tracking discrete particle dynamics. However, their computational cost remains prohibitively high, due to the need to simulate large numbers of particles to…

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions…

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By incorporating…

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…

Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power…

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…

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

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…

Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed…

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…

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…