Earth system forecasting has traditionally relied on complex physical models that are
computationally expensive and require significant domain expertise. In the past decade, the …

Numerical simulations are computationally demanding in three-dimensional (3D) settings
but they are often required to accurately represent physical phenomena. Neural operators …

Recent years have witnessed the promise of coupling machine learning methods and
physical domain-specific insights for solving scientific problems based on partial differential …

Abstract Solving parametric Partial Differential Equations (PDEs) for a broad range of
parameters is a critical challenge in scientific computing. To this end, neural operators …

We explain how to use diffusion models to learn inverse renormalization group flows of
statistical and quantum field theories. Diffusion models are a class of machine learning …

Neural operators (NOs) have emerged as effective tools for modeling complex physical
systems in scientific machine learning. In NOs, a central characteristic is to learn the …

This survey examines the broad suite of methods and models for combining machine
learning with physics knowledge for prediction and forecast, with a focus on partial …

We introduce a method that combines neural operators, physics-informed machine learning,
and standard numerical methods for solving PDEs. The proposed approach extends each of …

Throughout many fields, practitioners often rely on differential equations to model systems.
Yet, for many applications, the theoretical derivation of such equations and/or the accurate …

Despite their successes, deep learning models struggle with tasks requiring complex
reasoning and function composition. We present a theoretical and empirical investigation …