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arXiv · 2301.00923

Exploring Complex Dynamical Systems via Nonconvex Optimization

Hunter Elliott
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Abstract

Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only resort. We present an alternative, optimization-driven approach using tools from machine learning. We apply this approach to a novel, fully-optimizable, reaction-diffusion model which incorporates complex chemical reaction networks (termed "Dense Reaction-Diffusion Network" or "Dense RDN"). This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.

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Hunter Elliott. 2023-01-03. Exploring Complex Dynamical Systems via Nonconvex Optimization. https://arxiv.org/abs/2301.00923

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