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

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.