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 …

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

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 …

Abstract Machine learning has emerged as a powerful tool in various fields, including
computer vision, natural language processing, and speech recognition. It can unravel …

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural
sciences. Today, AI has started to advance natural sciences by improving, accelerating, and …

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

Neural operators generalize classical neural networks to maps between infinite-dimensional
spaces, eg, function spaces. Prior works on neural operators proposed a series of novel …

Most existing geometry processing algorithms use meshes as the default shape
representation. Manipulating meshes, however, requires one to maintain high quality in the …

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