AI for Complexity: Machine Learning Assists Complex System Studies

Complex systems and complexity appear in many domains of study, including life, pattern formation, and intelligence. However, traditional study methods are limited when it comes to complex systems due to their scale and interconnected behavior, especially their decentralized structure, making it hard to find general, simple, interpretable theories. With the development of AI, particularly generative models and large language models (LLMs), we see the potential to use AI to understand complex systems. AI models, themselves complex systems, have shown great capability to capture complex dynamics, including image and text generation. In our study, we show that diffusion models, as generative models, have a fundamental relationship to evolutionary processes—the foundation of much complexity in the real world. There are inherent connections between diffusion and evolution, including selection, mutation, and even reproductive isolation. This connection establishes not only a new algorithm for evolutionary computing but also offers a fresh perspective on understanding evolution and pattern formation through the lens of evolution itself. We also explore the power of LLMs to understand complex dynamical systems, including gene regulatory networks (GRNs). We demonstrate that with the help of LLM AIs, we can unbox GRNs and compare them to fundamentally different systems. This opens a door to general theories of complexity.