Mori-Zwanzig Formalism for Machine Learning

Using the Mori-Zwanzig formalism to think about what a learned closure model is actually approximating.

The Mori-Zwanzig formalism describes exactly what is lost when you coarse-grain a system — the memory term that a closure model is implicitly trying to represent. Taking that seriously gives a principled way to reason about what machine learning models for coarse-grained fluid dynamics should look like.