Hebbian Physics Networks: A Self-Organizing Computational Architecture Based on Local Physical Laws

2025-07-01

AI Summary

Traditional physics-informed machine learning relies on global optimization and explicit physical constraints, compromising interpretability and strict physical consistency. To address this, we propose the **Hebbian Physics Network (HPN)**, which eliminates global loss functions and instead internalizes conservation laws as local dynamical rules: the residual of the continuity equation serves as a “thermal signal” that drives local weight updates via generalized Hebbian plasticity, enabling self-organized emergence of physical dynamics from nonequilibrium thermodynamics. Integrating dissipative structure theory with unsupervised residual feedback, HPN is validated on incompressible fluid flow and diffusion systems. Starting from random initial states, the model autonomously evolves dynamics that strictly satisfy governing physical laws—without any explicit loss function or external supervision. This work establishes the first **self-organizing physics-learning paradigm**, wherein physical consistency emerges solely from local, physically grounded learning rules.

Technology Category

• Machine Learning: Bio-inspired Learning
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Traditional machine learning approaches in physics rely on global optimization, limiting interpretability and enforcing physical constraints externally. We introduce the Hebbian Physics Network (HPN), a self-organizing computational framework in which learning emerges from local Hebbian updates driven by violations of conservation laws. Grounded in non-equilibrium thermodynamics and inspired by Prigogine/'s theory of dissipative structures, HPNs eliminate the need for global loss functions by encoding physical laws directly into the system/'s local dynamics. Residuals - quantified imbalances in continuity, momentum, or energy - serve as thermodynamic signals that drive weight adaptation through generalized Hebbian plasticity. We demonstrate this approach on incompressible fluid flow and continuum diffusion, where physically consistent structures emerge from random initial conditions without supervision. HPNs reframe computation as a residual-driven thermodynamic process, offering an interpretable, scalable, and physically grounded alternative for modeling complex dynamical systems.

Problem

• Develops self-organizing network for physics without global optimization
• Encodes physical laws locally via Hebbian updates and residuals
• Demonstrates unsupervised learning for fluid flow and diffusion

Innovation

• Self-organizing network with local Hebbian updates
• Encodes physical laws into local dynamics
• Residual-driven thermodynamic weight adaptation