去噪哈密顿网络物理推理

[TheMatrix]

谁有空看一下。咋回事？

https://zhuanlan.zhihu.com/p/29702451504

https://arxiv.org/pdf/2503.07596

https://arxiv.org/html/2503.07596

Abstract

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.

Physical learning, Physical reasoning, Hamiltonian Neural Network, Masked modeling, Denoising