Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations
This addresses a fundamental challenge for researchers modelling natural systems with stochastic patterns, offering a tool for theorists and experimentalists, though it appears incremental as it builds on embedding techniques.
The authors tackled the inverse problem of finding unknown causal parameters from macroscopic observations in stochastic self-organising systems, where traditional methods fail due to pixel-wise metrics. They introduced a novel method using visual embeddings to create invariant representations, reliably recovering parameters in canonical models and real biological patterns.
Self-organising systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organisation central to understanding natural complexity. A fundamental challenge in modelling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations. This task becomes particularly difficult when observations have a strong stochastic component, yielding diverse yet equivalent patterns. Traditional inverse methods fail in this setting, as pixel-wise metrics cannot capture feature similarities between variable outcomes. In this work, we introduce a novel inverse modelling method specifically designed to handle stochasticity in the observable space, leveraging the capacity of visual embeddings to produce robust representations that capture perceptual invariances. By mapping the pattern representations onto an invariant embedding space, we can effectively recover unknown causal parameters without the need for handcrafted objective functions or heuristics. We evaluate the method on two canonical models--a reaction-diffusion system and an agent-based model of social segregation--and show that it reliably recovers parameters despite stochasticity in the outcomes. We further apply the method to real biological patterns, highlighting its potential as a tool for both theorists and experimentalists to investigate the dynamics underlying complex stochastic pattern formation.