标题： 赫布物理网络：一种基于局部物理定律的自组织计算架构 显示英文标题

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

摘要： 传统物理中的机器学习方法依赖于全局优化，这限制了可解释性并需要外部强制物理约束。 我们引入了赫布物理网络（HPN），这是一种自组织计算框架，其中学习通过由守恒定律违反驱动的局部赫布更新产生。 基于非平衡热力学并受到普里戈金耗散结构理论的启发， HPN 通过将物理定律直接编码到系统局部动力学中，消除了对全局损失函数的需求。 残差——连续性、动量或能量中的量化不平衡——作为热力学信号，通过广义赫布可塑性驱动权重适应。 我们在不可压缩流体流动和连续扩散上展示了这种方法，其中物理一致结构从随机初始条件中无监督地出现。 HPN 将计算重新构想为一种由残差驱动的热力学过程，为建模复杂动力系统提供了一种可解释、可扩展且物理基础的替代方案。 显示英文摘要

摘要： 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.