# Physics-Informed Spiking Neural Networks via Conservative Flux Quantization

arXiv: https://arxiv.org/abs/2511.21784 · HTML: https://mlsanity.com/paper/2511.21784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 24 of 24)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [BEHAVIOR-1K: A Human-Centered, Embodied AI Benchmark with 1,000 Everyday Activities and Realistic Simulation](https://mlsanity.com/paper/2403.09227/) (2024)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Deep Learning for Event-based Vision: A Comprehensive Survey and Benchmarks](https://mlsanity.com/paper/2302.08890/) (2023)
- [A Review of Differentiable Simulators](https://mlsanity.com/paper/2407.05560/) (2024)
- [InfiniteWorld: A Unified Scalable Simulation Framework for General Visual-Language Robot Interaction](https://mlsanity.com/paper/2412.05789/) (2024)
- [On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it](https://mlsanity.com/paper/2302.07557/) (2023)
- [Neural Brain: A Neuroscience-inspired Framework for Embodied Agents](https://mlsanity.com/paper/2505.07634/) (2025)
- [Neural oscillators for generalization of physics-informed machine learning](https://mlsanity.com/paper/2308.08989/) (2023)
- [Energy Consumption of Neural Networks on NVIDIA Edge Boards: an Empirical Model](https://mlsanity.com/paper/2210.01625/) (2022)
- [Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning](https://mlsanity.com/paper/2308.16372/) (2023)
- [Decoupled Edge Physics algorithms for collaborative XR simulations](https://mlsanity.com/paper/2407.12486/) (2024)

## Abstract (arXiv)

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.