MIONet: Learning Multiple-Input Operators via Tensor Product

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