# Exploring Complex Dynamical Systems via Nonconvex Optimization

arXiv: https://arxiv.org/abs/2301.00923 · HTML: https://mlsanity.com/paper/2301.00923/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 60 references that are in the map.
- First posted on arXiv 3 Jan 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Deep learning algorithm for data-driven simulation of noisy dynamical system](https://mlsanity.com/paper/1802.08323/) (2018)
- [Texture Generation with Neural Cellular Automata](https://mlsanity.com/paper/2105.07299/) (2021)
- [Differentiable Programming of Reaction-Diffusion Patterns](https://mlsanity.com/paper/2107.06862/) (2021)

## Abstract (arXiv)

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.