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 …

For many decades, experimental solid mechanics has played a crucial role in characterizing
and understanding the mechanical properties of natural and novel artificial materials …

Deep learning surrogate models have shown promise in solving partial differential
equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy …

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 …

The classical development of neural networks has primarily focused on learning mappings
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Time-dependent partial differential equations (PDEs) are ubiquitous in science and
engineering. Recently, mostly due to the high computational cost of traditional solution …

Failure trajectories, probable failure zones, and damage indices are some of the key
quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that …

Standard neural networks can approximate general nonlinear operators, represented either
explicitly by a combination of mathematical operators, eg in an advection–diffusion reaction …

Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …

Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …