Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment
and accelerate research, hel** 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 …

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

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

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this
date PINNs have not been successful in simulating dynamical systems whose solution …

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 …

One of the most promising applications of machine learning in computational physics is to
accelerate the solution of partial differential equations (PDEs). The key objective of machine …

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

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold
Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs …

The curse-of-dimensionality taxes computational resources heavily with exponentially
increasing computational cost as the dimension increases. This poses great challenges in …