Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment
and accelerate research, helping scientists to generate hypotheses, design experiments …

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 …

Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …

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 …

Diffusion models have found widespread adoption in various areas. However, their
sampling process is slow because it requires hundreds to thousands of network evaluations …

Abstract Fourier Neural Operators (FNOs) have proven to be an efficient and effective
method for resolution-independent operator learning in a broad variety of application areas …

Abstract Machine learning-based modeling of physical systems has experienced increased
interest in recent years. Despite some impressive progress, there is still a lack of …

We propose the geometry-informed neural operator (GINO), a highly efficient approach to
learning the solution operator of large-scale partial differential equations with varying …

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