Related papers: Variationally Mimetic Operator Networks

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

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…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

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…

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…

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 Material Network (DMN) has recently emerged as a data-driven surrogate model for heterogeneous materials. Given a particular microstructural morphology, the effective linear and nonlinear behaviors can be successfully approximated by…

Deep Operator Networks (DeepONets) have become a central tool in data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk design based…

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…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

Multiphysics simulation is critical for system-technology co-optimization (STCO) in chiplet-based design, but repeated finite-element solutions of PDE-governed problems are computationally expensive in parametric design exploration. This…

Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator…

Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…

Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

Deep operator networks (DeepONets) are powerful architectures for fast and accurate emulation of complex dynamics. As their remarkable generalization capabilities are primarily enabled by their projection-based attribute, we investigate…

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…

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…

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large…

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…