Physics-informed neural networks for PDE-constrained optimization and control

A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers from several deficiencies that can hinder their performance. Using a meta-learning approach, we reformulate the autoencoder problem as a bi-level optimization procedure that explicitly solves the dimensionality reduction task. We prove that the new formulation corrects the identified deficiencies with canonical autoencoders, provide a practical way to solve it, and showcase the strength of this formulation with a simple numerical illustration.

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