Machine Learning and Data Assimilation for Blending Incomplete Models and Noisy Data

Author: Levine, Matthew Emanuel

Year: 2023

Degree: Dissertation (Ph.D.)

Advisor: Stuart, Andrew M.

Committee Members: Yue, Yisong; Owhadi, Houman; Bouman, Katherine L.; Stuart, Andrew M.

Option: Computing and Mathematical Sciences

DOI: 10.7907/b82h-ye78

Abstract

The prediction and inference of dynamical systems is of widespread interest across scientific and engineering disciplines. Data assimilation (DA) offers a well-established and successful paradigm for blending such models with noisy observational data. However, traditional DA-based inference often fails when available data are insufficiently informative. Chapter 2 copes with this challenge by introducing constraints into Ensemble Kalman Filtering, which is shown to improve forecasting of glucose dynamics in real patient-level clinical data. Chapter 3 addresses this identifiability challenge by instead developing a simplified, reduced-order stochastic model for glucose dynamics that is more easily identified from patient data. Despite these successes, the forecasting performance of the methods are fundamentally limited by the fidelity of the employed model, which is often not fully understood a priori.

Chapter 4 presents a general picture of how noisy, partially-observed time-series data can be used to learn flexible (e.g., neural network-based) corrections to a pre-specified mechanistic model. In Chapter 5, the proposed methodology is then validated in simulated settings for glucose-insulin models. Chapter 6 provides further perspective on learning flexible model corrections, comparing approaches that use i) gradient-based or gradient-free optimization, ii) temporal or time-averaged data, iii) different model parameterizations, iv) deterministic and stochastic corrections, and v) physical conservation laws to constrain inference.

Chapter 7 studies how these perspectives on machine learning and dynamical systems can help us understand the roles of biochemical networks. In particular, it considers protein dimerization networks from the lens of approximation theory and evaluates how the equilibria of these networks can be fine-tuned to perform a variety of biological computations.

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