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 …

We consider solving partial differential equations (PDEs) with Fourier neural operators
(FNOs), which operate in the frequency domain. Since the laws of physics do not depend on …

A large class of inverse problems for PDEs are only well-defined as mappings from
operators to functions. Existing operator learning frameworks map functions to functions and …

A Transformer-based deep direct sampling method is proposed for electrical impedance
tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A …

Abstract Mathematics lies at the heart of engineering science and is very important for
capturing and modeling of diverse processes. These processes may be naturally-occurring …

We propose a novel multi-scale message passing neural network algorithm for learning the
solutions of time-dependent PDEs. Our algorithm possesses both temporal and spatial multi …

We introduce a novel grid-independent model for learning partial differential equations
(PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a …

While complex simulations of physical systems have been widely used in engineering and
scientific computing, lowering their often prohibitive computational requirements has only …

This paper explores the recent advancements in enhancing Computational Fluid Dynamics
(CFD) tasks through Machine Learning (ML) techniques. We begin by introducing …

Transformer models are increasingly used for solving Partial Differential Equations (PDEs).
Several adaptations have been proposed, all of which suffer from the typical problems of …