Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations

2025-06-13

AI Summary

Inverse modeling for stochastic self-organizing systems is severely hindered by highly random macroscopic observations, diverse equivalent pattern classes, and substantial pixel-level variations. Method: We propose a vision-embedding-based invariant representation learning framework that incorporates perceptual invariance into inverse modeling—automatically constructing a low-dimensional, robust parameter embedding space without hand-crafted objective functions. Our approach unifies reaction–diffusion modeling and agent-based social segregation simulation. Contribution/Results: It achieves stable causal parameter inversion on two canonical self-organizing systems and successfully generalizes to real biological pattern analysis. To our knowledge, this is the first end-to-end, data-driven, invariant-representation-guided inverse inference method in this domain, yielding significant improvements in parameter identification accuracy (37% average error reduction) and cross-system generalizability.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Social recommender systems and personalization for the social Web
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Solving inverse problems in stochastic self-organising systems
• Finding unknown causal parameters from macroscopic observations
• Handling stochasticity in observable space with invariant representations

Innovation

• Uses invariant representations for inverse problems
• Leverages visual embeddings for robust pattern matching
• Recovers parameters without handcrafted objective functions