Upscaling and automation : symbolic computational methods for multiscale model discovery
- Despite current modeling capabilities and the availability of computational power, complex multi-physical, multiscale systems continue to challenge our physical intuitions due to their elusive behaviors. While high-fidelity simulations have paved the way for understanding these systems, the associated computational costs prohibit such tools from being used to inform experimental investigations in a timely manner and facilitate swift technological advancements. As a result, multiscale models have been increasingly relied upon for efficiently predicting large-scale, or average, multi-physical behaviors of complex systems, and how they are affected by intricate fine-scale variations. Such models can be systematically generated through rigorous upscaling techniques, which provide a priori estimates of modeling error and conditions under which models are valid (i.e., applicability conditions). However, the derivations required in upscaling techniques are time-consuming, prone to analytical error, and become quickly intractable for complex, multi-physical systems. In this dissertation, we advance the paradigm of multiscale modeling beyond these human-centered limitations by developing a symbolic computational framework for automating and accelerating upscaled model development via homogenization theory. By automating the required analytical derivations, we democratize the utilization of upscaling techniques in practical applications and enable model development in a feasible amount of time (i.e., seconds) with no requirements in analytical tractability, nor specialized expertise in mathematical model formulation from users. We demonstrate our software prototype, Symbolica, in both canonical and complex systems by developing models for a variety of advection-diffusion-reaction systems and Li-ion battery modules undergoing thermal runaway. Novel model development strategies are formulated, encoded in Symbolica, and used to discover nontrivial modeling scenarios and multiscale models with 1.) emergent terms, 2.) nonlinear effective parameters, 3.) macroscopic advection that is independent of pore-scale advection, and 4.) effective parameters that couple geometric and physical effects. Ultimately, our work demonstrates how Symbolica can be used to reduce the level of effort in rigorous multiscale modeling and model implementation for real-world applications.
|Type of resource
|electronic resource; remote; computer; online resource
|1 online resource.
|Pietrzyk, Kyle Mitchell
|Degree committee member
|Degree committee member
|Stanford Doerr School of Sustainability
|Stanford University, Department of Energy Resources Engineering
|Statement of responsibility
|Submitted to the Department of Energy Resources Engineering.
|Thesis Ph.D. Stanford University 2023.
- © 2023 by Kyle Mitchell Pietrzyk
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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