Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

This review article highlights state-of-the-art data-driven techniques to discover, encode,
surrogate, or emulate constitutive laws that describe the path-independent and path …

In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …

Partial differential equations (PDEs) are central to describing complex physical system
simulations. Their expensive solution techniques have led to an increased interest in deep …

Existing neural operator architectures face challenges when solving multiphysics problems
with coupled partial differential equations (PDEs) due to complex geometries, interactions …

Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …

Stress analysis is an important step in the design of material systems, and finite element
methods (FEM) are a standard approach of performing computational analysis of stresses in …

Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …

We propose a hybrid neural network (NN) and PDE approach for learning generalizable
PDE dynamics from motion observations. Many NN approaches learn an end-to-end model …