Learning Stochastic Governing Laws from Noisy Data Using Normalizing Flows
McClure, William Jacob
Applied mathematics
Mathematics
Dynamical systems
Governing laws
Machine learning
Neural networks
Normalizing flows
Stochastic dynamics
With the increasing availability of massive collections of data, researchers in all sciences need tools to synthesize useful and pertinent descriptors of the systems they study. Perhaps the most fundamental knowledge of a dynamical system is its governing laws, which describe its evolution through time and can be lever-aged for a number of analyses about its behavior. We present a novel technique for learning the infinitesimal generator of a Markovian stochastic process from large, noisy datasets generated by a stochastic system. Knowledge of the generator in turn allows us to find the governing laws for the process. This technique relies on normalizing flows, neural networks that estimate probability densities, to learn the density of time-dependent stochastic processes. We establish the efficacy of this technique on multiple systems with Brownian noise, and use our learned governing laws to perform analysis on one system by solving for its mean exit time. Our approach also allows us to learn other dynamical behaviors such as escape probability and most probable pathways in a system. The potential impact of this technique is far-reaching, since most stochastic processes in various fields are assumed to be Markovian, and the only restriction for applying our method is available data from a time near the beginning of an experiment or recording.
Duan, Jinqiao
2021
Thesis
application/pdf
islandora:1011784
http://hdl.handle.net/10560/islandora:1011784
Illinois Institute of Technology
MATH / Applied Mathematics
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In
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