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

• URL: http://arxiv.org/abs/2506.11796v1
• Date: Fri, 13 Jun 2025 14:01:39 GMT
• Title: Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations
• Authors: Elias Najarro, Nicolas Bessone, Sebastian Risi,
• Abstract summary: Self-organising systems demonstrate how simple local rules can generate complex patterns.<n>Many natural systems rely on such dynamics, making self-organisation central to understanding natural complexity.<n>A fundamental challenge in modelling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations.
• Score: 12.394699094197545
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Efficient Deconvolution in Populational Inverse Problems [6.1048542188987085]
  This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations.<n>The potential to solve such distributional inversion problems is driven by increasing availability of data, but a major roadblock is blind deconvolution.<n>We propose a methodology leveraging large data sets of observations, collected from different instantiations of the same physical processes, to simultaneously deconvolve the data corrupting noise distribution.
  arXiv  Detail & Related papers  (2025-05-26T11:25:46Z)
• Identifiable Representation and Model Learning for Latent Dynamic Systems [0.0]
  We study the problem of identifiable representation and model learning for latent dynamic systems.<n>We prove that, for linear and affine nonlinear latent dynamic systems with sparse input matrices, it is possible to identify the latent variables up to scaling.
  arXiv  Detail & Related papers  (2024-10-23T13:55:42Z)
• Neural Persistence Dynamics [8.197801260302642]
  We consider the problem of learning the dynamics in the topology of time-evolving point clouds. Our proposed model - $textitNeural Persistence Dynamics$ - substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.
  arXiv  Detail & Related papers  (2024-05-24T17:20:18Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Learning non-stationary and discontinuous functions using clustering, classification and Gaussian process modelling [0.0]
  We propose a three-stage approach for the approximation of non-smooth functions. The idea is to split the space following the localized behaviors or regimes of the system and build local surrogates. The approach is tested and validated on two analytical functions and a finite element model of a tensile membrane structure.
  arXiv  Detail & Related papers  (2022-11-30T11:11:56Z)
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization [1.2882319878552302]
  This paper develops a new iterative learning algorithm for complex turbulent systems with partial observations. It alternates between identifying model structures, recovering unobserved variables, and estimating parameters. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable parameterizations for many complex nonlinear systems.
  arXiv  Detail & Related papers  (2022-08-19T00:35:03Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective [72.55093886515824]
  We introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables. We devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a causal graph. Experiment results on synthetic and real datasets show that our three proposed components significantly improve the robustness and reusability of the learned motion representations.
  arXiv  Detail & Related papers  (2021-11-29T18:59:09Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• Why Adversarial Interaction Creates Non-Homogeneous Patterns: A Pseudo-Reaction-Diffusion Model for Turing Instability [10.933825676518195]
  We observe Turing-like patterns in a system of neurons with adversarial interaction. We present a pseudo-reaction-diffusion model to explain the mechanism that may underlie these phenomena.
  arXiv  Detail & Related papers  (2020-10-01T16:09:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.