Exploring Complex Dynamical Systems via Nonconvex Optimization

• URL: http://arxiv.org/abs/2301.00923v1
• Date: Tue, 3 Jan 2023 01:35:39 GMT
• Title: Exploring Complex Dynamical Systems via Nonconvex Optimization
• Authors: Hunter Elliott
• Abstract summary: 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. This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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