Data-Efficient Training with Physics-Enhanced Deep Surrogates

Raphaël Pestourie, Youssef Mroueh, Christopher Vincent Rackauckas, Payel Das, Steven Glenn Johnson

Keywords: surrogate model, scientific machine learning, materials optimization, PDEs

TL;DR: We present a new “physics-enhanced deep-surrogate" to PDEs combining a neural network generator with a low-fidelity solver, end-to-end, and show orders of magnitude improvement in data efficiency and evaluation time.

Abstract: We present a “physics-enhanced deep-surrogate” (“PEDS”) approach to fast surrogate models for complex physical systems described by partial differential equations (PDEs) and similar models: we embed a low-fidelity “coarse” solver layer in a neural network that generates “coarsified” inputs, trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. In this way, by incorporating complex physical knowledge in the form of the low-fidelity model, we find that a PEDS surrogate can be trained with at least 10× less data than a “black-box” neural network for the same accuracy. Asymptotically, PEDS appears to learn with a steeper power law than black-box surrogates, and benefits even further in combination with active learning. We demonstrate this using an example problem in electromagnetic scattering that appears in the large-scale optimization of optical metamaterials using scientific computing.