MIONet: Learning Multiple-Input Operators via Tensor Product

Jin, Pengzhan; Meng, Shuai; Lu, Lu

doi:10.1137/22m1477751

MIONet: Learning Multiple-Input Operators via Tensor Product

Journal Article · Sun Nov 06 23:00:00 EST 2022 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/22m1477751· OSTI ID:2527397

Jin, Pengzhan ^[1]; Meng, Shuai ^[2]; ^[2]

Peking University, Beijing (China)
University of Pennsylvania, Philadelphia, PA (United States)

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing neural operators are only designed to learn operators defined on a single Banach space; i.e., the input of the operator is a single function. Here, for the first time, we study the operator regression via neural networks for multiple-input operators defined on the product of Banach spaces. We first prove a universal approximation theorem of continuous multiple-input operators. We also provide a detailed theoretical analysis including the approximation error, which provides guidance for the design of the network architecture. Based on our theory and a low-rank approximation, we propose a novel neural operator, MIONet, to learn multiple-input operators. MIONet consists of several branch nets for encoding the input functions and a trunk net for encoding the domain of the output function. Here, we demonstrate that MIONet can learn solution operators involving systems governed by ordinary and partial differential equations. In our computational examples, we also show that we can endow MIONet with prior knowledge of the underlying system, such as linearity and periodicity, to further improve accuracy.

View Accepted Manuscript (DOE)

Research Organization:: University of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0022953

OSTI ID:: 2527397

Alternate ID(s):: OSTI ID: 1980779

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 6 Vol. 44; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
MIONet
multiple-input operators
neural networks
operator regression
scientific machine learning
tensor product
universal approximation theorem

MIONet: Learning Multiple-Input Operators via Tensor Product

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