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Poster
in
Workshop: World Models: Understanding, Modelling and Scaling

Reconstructing Dynamics from Steady Spatial Patterns with Partial Observations

Xinyue Luo · Xuzhe Qian · Yu Chen · Huaxiong Huang · Jin Cheng

Keywords: [ Learning dynamics ] [ Turing pattern ] [ Inverse problems ]


Abstract:

Self-organized spatial patterns, ubiquitous in biological and chemical systems, are often modeled via reaction-diffusion equations. However, real-world scenarios frequently provide only partial observations—such as a single component’s steady-state snapshot—challenging the discovery of underlying dynamics.In this work, we address the inverse problem of identifying reaction-diffusion systems from partial observations. We establish the theoretical feasibility of identifying reaction terms and their corresponding coefficients, and introduce a constructive two-stage approach that combines hidden component inference with reaction coefficient identification. Numerical experiments validate the approach’s effectiveness. This work provides a novel framework with theoretical guarantees, advancing the study of pattern dynamics with limited data and offering new perspectives for uncovering unknown reaction-diffusion dynamics in real-world scenarios.

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