A Duality Principle for Chaotic Systems: From Data Assimilation to Efficient Control

E. N. Lorenz discovered the highly sensitive nature of a chaotic dynamical system and conveyed it vividly by his famous “butterfly effect”; namely, a flip of a butterfly could cause a storm a few days later somewhere far away. Extreme weather like intense storms tends to be more chaotic and harder to predict, with increasing threat due to climate change. This motivates us to ask if we could possibly modify extreme weather in a favorable manner by taking advantage of its strong chaoticity. Here, the problem is that the causality from a flip of a butterfly to a storm formation is not trivial due to the limited predictability. Due to chaos, a small perturbation grows exponentially and leads to a different future state, but the difference becomes large enough only after the predictable range. This paper addresses this apparent paradox by formalizing the Control Simulation Experiment (CSE) framework, an extension of the data assimilation (DA) paradigm. We propose a duality principle based on chaos synchronization: while DA uses observations to synchronize a model to nature’s trajectory, we argue that control uses interventions to synchronize nature to a chosen target trajectory. The feasibility of this control rests on the key insight that these target trajectories can be selected to have distinct dynamical properties from the original system, reframing the challenge from taming a fully chaotic system to maintaining synchronization with a more manageable path.