25 research outputs found
Group Equivariant Fourier Neural Operators for Partial Differential Equations
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 the coordinate system used to describe them, it is
desirable to encode such symmetries in the neural operator architecture for
better performance and easier learning. While encoding symmetries in the
physical domain using group theory has been studied extensively, how to capture
symmetries in the frequency domain is under-explored. In this work, we extend
group convolutions to the frequency domain and design Fourier layers that are
equivariant to rotations, translations, and reflections by leveraging the
equivariance property of the Fourier transform. The resulting -FNO
architecture generalizes well across input resolutions and performs well in
settings with varying levels of symmetry. Our code is publicly available as
part of the AIRS library (https://github.com/divelab/AIRS).Comment: Proceedings of the 40th International Conference on Machine Learning
https://icml.cc/virtual/2023/poster/2387
Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
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 enabling our understanding of natural
phenomena at a wide range of spatial and temporal scales, giving rise to a new
area of research known as AI for science (AI4Science). Being an emerging
research paradigm, AI4Science is unique in that it is an enormous and highly
interdisciplinary area. Thus, a unified and technical treatment of this field
is needed yet challenging. This work aims to provide a technically thorough
account of a subarea of AI4Science; namely, AI for quantum, atomistic, and
continuum systems. These areas aim at understanding the physical world from the
subatomic (wavefunctions and electron density), atomic (molecules, proteins,
materials, and interactions), to macro (fluids, climate, and subsurface) scales
and form an important subarea of AI4Science. A unique advantage of focusing on
these areas is that they largely share a common set of challenges, thereby
allowing a unified and foundational treatment. A key common challenge is how to
capture physics first principles, especially symmetries, in natural systems by
deep learning methods. We provide an in-depth yet intuitive account of
techniques to achieve equivariance to symmetry transformations. We also discuss
other common technical challenges, including explainability,
out-of-distribution generalization, knowledge transfer with foundation and
large language models, and uncertainty quantification. To facilitate learning
and education, we provide categorized lists of resources that we found to be
useful. We strive to be thorough and unified and hope this initial effort may
trigger more community interests and efforts to further advance AI4Science