Exploring Complex Dynamical Systems via Nonconvex Optimization
This work addresses the problem of analyzing complex dynamical systems for researchers in fields like physics or chemistry, offering an alternative to brute force simulation, but it appears incremental as it builds on existing optimization and machine learning methods.
The paper tackles the challenge of cataloging complex behaviors in dynamical systems by introducing an optimization-driven approach using machine learning tools, applied to a novel Dense Reaction-Diffusion Network model, resulting in the identification of new states such as pattern formation and replication-like structures.
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.