Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era

• URL: http://arxiv.org/abs/2505.07222v1
• Date: Mon, 12 May 2025 04:30:42 GMT
• Title: Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era
• Authors: Nima Dehghani,
• Abstract summary: We present a unified framework that locates statistical, algorithmic, and dynamical measures along three axes (regularity, randomness, and complexity)<n>This taxonomy reveals the deep challenges posed by uncomputability and highlights the emergence of modern data-driven methods.<n>We close by outlining implications for physics-informed AI and AI-guided discovery in complex physical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates statistical, algorithmic, and dynamical measures along three axes (regularity, randomness, and complexity) and situates them in a common conceptual space. We map statistical, algorithmic, and dynamical measures into this conceptual space, discussing their computational accessibility and approximability. This taxonomy reveals the deep challenges posed by uncomputability and highlights the emergence of modern data-driven methods (including autoencoders, latent dynamical models, symbolic regression, and physics-informed neural networks) as pragmatic approximations to classical complexity ideals. Latent spaces emerge as operational arenas where regularity extraction, noise management, and structured compression converge, bridging theoretical foundations with practical modeling in high-dimensional systems. We close by outlining implications for physics-informed AI and AI-guided discovery in complex physical systems, arguing that classical questions of complexity remain central to next-generation scientific modeling.

Related papers

• Introduction to Symbolic Regression in the Physical Sciences [0.41998444721319217]
  Symbolic regression has emerged as a powerful method for uncovering interpretable mathematical relationships from data.<n>This article introduces the Special Issue on Symbolic Regression for the Physical Sciences, motivated by the Royal Society discussion meeting held in April 2025.
  arXiv  Detail & Related papers  (2025-12-17T19:32:50Z)
• Hierarchical Physics-Embedded Learning for Spatiotemporal Dynamical Systems [12.832325257647128]
  We propose a hierarchical physics-embedded learning framework that advances both forwardtemporal prediction and inverse discovery of physical laws.<n>Known physical laws are directly embedded into the models computational graph, guaranteeing physical consistency.<n>By building the framework upon adaptive Neural Operators, we can effectively capture the non-local dependencies and high-order operators characteristic of dynamical systems.
  arXiv  Detail & Related papers  (2025-10-29T09:18:41Z)
• World Models Should Prioritize the Unification of Physical and Social Dynamics [57.91940497010114]
  This paper argues that the systematic, bidirectional unification of physical and social predictive capabilities is the next crucial frontier for world model development.<n>We contend that comprehensive world models must holistically integrate objective physical laws with the subjective, evolving, and context-dependent nature of social dynamics.
  arXiv  Detail & Related papers  (2025-10-24T07:42:37Z)
• Simulation-free Structure Learning for Stochastic Dynamics [39.468930729022546]
  We present StructureFlow, a novel and principled simulation-free approach for jointly learning the structure and population dynamics of physical systems.<n>We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics.
  arXiv  Detail & Related papers  (2025-10-18T22:31:39Z)
• Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction [84.26340606752763]
  In this paper, we introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework.<n>The network is designed to conform to the general symmetry conservation law via symmetry where conservative and non-conservative information passes over a multiscale space by a latent temporal marching strategy.<n>Results demonstrate that CiGNN exhibits remarkable baseline accuracy and generalizability, and is readily applicable to learning for prediction of varioustemporal dynamics.
  arXiv  Detail & Related papers  (2024-12-30T13:55:59Z)
• Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics [6.675805308519987]
  We introduce a novel framework for modeling rigid body dynamics and learning collision interactions.<n>We propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model.<n>This work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.
  arXiv  Detail & Related papers  (2024-11-18T11:03:15Z)
• Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings [3.825457221275617]
  We introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering.
  arXiv  Detail & Related papers  (2024-11-01T19:27:47Z)
• Form-Finding and Physical Property Predictions of Tensegrity Structures Using Deep Neural Networks [39.19016806159609]
  We develop a deep neural network (DNN) approach to predict the geometric configurations and physical properties of tensegrity structures. For validation, we analyze three tensegrity structures, including a tensegrity D-bar, prism, and lander.
  arXiv  Detail & Related papers  (2024-06-15T16:39:53Z)
• Learning Discrete Concepts in Latent Hierarchical Models [73.01229236386148]
  Learning concepts from natural high-dimensional data holds potential in building human-aligned and interpretable machine learning models.<n>We formalize concepts as discrete latent causal variables that are related via a hierarchical causal model.<n>We substantiate our theoretical claims with synthetic data experiments.
  arXiv  Detail & Related papers  (2024-06-01T18:01:03Z)
• Next-Generation Simulation Illuminates Scientific Problems of Organised Complexity [14.665628508798319]
  We revisit a classic classification of scientific problems and acknowledge that a series of unresolved problems remain. We focus on next-generation simulation (NGS), which can serve as a platform to integrate methods from different paradigms. We propose a methodology, sophisticated behavioural simulation (SBS), to realise it.
  arXiv  Detail & Related papers  (2024-01-18T10:05:52Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Discrete, compositional, and symbolic representations through attractor dynamics [51.20712945239422]
  We introduce a novel neural systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT) Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuroplausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations
  arXiv  Detail & Related papers  (2023-10-03T05:40:56Z)
• Constructing Custom Thermodynamics Using Deep Learning [10.008895786910195]
  One of the most exciting applications of artificial intelligence (AI) is automated scientific discovery based on previously amassed data. Here we develop a platform based on a generalized Onsager principle to learn macroscopic descriptions of arbitrary dissipative systems. We demonstrate its effectiveness by studying theoretically and experimentally validating the stretching of long polymer chains in an externally applied field.
  arXiv  Detail & Related papers  (2023-08-08T08:19:43Z)
• Quantifying Complexity: An Object-Relations Approach to Complex Systems [0.0]
  This paper develops an object-relations model of complex systems which generalizes to systems of all types. The resulting Complex Information Entropy (CIE) equation is a robust method to quantify complexity across various contexts. Applications are discussed in the fields of engineering design, atomic and molecular physics, chemistry, materials science, psychology, neuroscience, sociology, ecology, economics, and medicine.
  arXiv  Detail & Related papers  (2022-10-22T04:22:21Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)

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.