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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,…

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…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to 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…

A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of Deep Operator Networks (DeepONets), which is based on…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

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…

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…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

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…

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…

Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$…

In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing. The…

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…

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…