arXiv:2511.21784cs.LG2025-11

将物理守恒定律融入脉冲神经网络,实现低功耗高精度的实时仿真。

Physics-Informed Spiking Neural Networks via Conservative Flux Quantization

  • 设计守恒型脉冲神经元,从结构上保证质量守恒。
  • 提出通量离散化策略,使模型在长期时间尺度上保持稳定精度。
  • 适合需要节能与物理一致性融合的智能系统研发人员。

实时、物理一致的预测对下一代具身人工智能系统至关重要,但仍是重大挑战。物理信息神经网络(PINNs)结合数据驱动学习与物理约束,确保预测符合物理规律,但能耗高且难以严格满足守恒律。脑启发的脉冲神经网络(SNNs)为边缘计算和实时处理提供了前景。然而,直接将PINNs转换为SNN会降低物理保真度并影响长期泛化。本文提出新型物理信息脉冲神经网络(PISNN)框架:设计保守漏电整合-放电(C-LIF)神经元,其动力学结构保证局部质量守恒;引入保守通量量化(CFQ)策略,将神经脉冲重新定义为离散的物理通量包,学习时间不变的物理演化算子,使PISNN成为构造性守恒的通用求解器。大量实验表明,无论是一维热方程还是更复杂的二维拉普拉斯方程,该模型均能准确模拟系统动态,并天然保持质量守恒——这是传统PINNs难以实现的。本工作建立了一个融合科学计算严谨性与类脑工程高效性的稳健框架,为智能系统实现复杂、长期、低功耗的物理预测铺平道路。

原文摘要 · Abstract (English)

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with physics-based constraints to ensure the model's predictions are with underlying physical principles.However, PINNs are energy-intensive and struggle to strictly enforce physical conservation laws. Brain-inspired spiking neural networks (SNNs) have emerged as a promising solution for edge computing and real-time processing. However, naively converting PINNs to SNNs degrades physical fidelity and fails to address long-term generalization issues. To this end, this paper introduce a novel Physics-Informed Spiking Neural Network (PISNN) framework. Importantly, to ensure strict physical conservation, we design the Conservative Leaky Integrate-and-Fire (C-LIF) neuron, whose dynamics structurally guarantee local mass preservation. To achieve robust temporal generalization, we introduce a novel Conservative Flux Quantization (CFQ) strategy, which redefines neural spikes as discrete packets of physical flux. Our CFQ learns a time-invariant physical evolution operator, enabling the PISNN to become a general-purpose solver -- conservative-by-construction. Extensive experiments show that our PISNN excels on diverse benchmarks. For both the canonical 1D heat equation and the more challenging 2D Laplace's Equation, it accurately simulates the system dynamics while maintaining perfect mass conservation by design -- a feat that is challenging for conventional PINNs. This work establishes a robust framework for fusing the rigor of scientific computing with the efficiency of neuromorphic engineering, paving the way for complex, long-term, and energy-efficient physics predictions for intelligent systems.

脉冲神经网络物理信息守恒律边缘计算

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