Thoughts on normalizing flows versus physics-inspired neural networks (PINNs) for approximate dynamical system inference


Tags: Bayesian statistics machine learning math

With both normalizing flows and physics-inspired neural networks (PINNs) finally making their way from machine learning and physics literature to be applied in biogeochemical model inference problems, I found myself recently thinking about the similarities in both approaches. I have arrived at the notions below, with the general sentiment that normalizing flows can almost be thought of as belonging to a more specific, less flexible subset of PINNs, except for a key difference in optimization objectives. (As I will touch on later, flows do not involve dynamical system derivative residuals in loss calculations.) Please reach out to me and correct me if you feel that I have erred in understanding.



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