Deep Operator Networks for Reduced-Order Modeling
Emily Williams, Massachusetts Institute of Technology
Many multiscale systems representing complex physical phenomena contain too many degrees of freedom to simulate accurately given limited computational resources. Reduced-order modeling techniques reduce the prohibitively large system to a computationally feasible size without sacrificing essential dynamical features.
The Mori-Zwanzig (MZ) formalism is an exact formalism for the reduction of the dynamics of a full system to the dynamics of a reduced set of variables. MZ-based model reduction which involves coarsening a representation using standard basis functions, e.g. Fourier functions, is well developed.
In this work, we employ machine-learning extracted basis functions from deep operator networks which are custom-made for the particular system, with the goal of reduced-order modeling with spectral methods.