On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them

• URL: http://arxiv.org/abs/2406.06812v1
• Date: Mon, 10 Jun 2024 21:37:36 GMT
• Title: On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them
• Authors: David W. Sroczynski, Felix Dietrich, Eleni D. Koronaki, Ronen Talmon, Ronald R. Coifman, Erik Bollt, Ioannis G. Kevrekidis,
• Abstract summary: We attempt to learn a function between two (sets of) observables of a physical process. We first decide what the inputs and what the outputs of the desired function are going to be. We construct mappings from a single set of observations of one process to entire level sets of measurements of the process.
• Score: 4.741643704615452
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of initially deciding ``the right quantities'' to relate through such a function, and then proceed to learn it. This is accomplished by processing multiple simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: multiple observation processes of the system. We thus determine (a) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function); and (b) what information is unrelated to these common observables, and therefore particular to each observation process, and not contributing to the desired function. Any data-driven function approximation technique can subsequently be used to learn the input-output relation, from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular ``twists'' of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations of one process to entire level sets of measurements of the process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures ``now'', while the second observation process measures ``in the future'', the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution.

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