用去噪机制增强物理系统建模，支持长程依赖与多系统推理
Denoising Hamiltonian Network for Physical Reasoning
- 将哈密顿力学推广为可学习的神经算子，支持非局部时间关系建模
- 通过去噪机制减少数值积分误差，提升长期动态预测精度
- 支持多系统联合建模，适用于多种物理推理任务
机器学习框架在处理物理问题时需捕捉并强制执行物理约束以保持动力系统的结构。现有方法多通过将物理算子嵌入神经网络来实现，虽具理论保障，但存在两大局限：(i) 主要建模相邻时间步间的局部关系，忽视更长程或更高阶的物理相互作用；(ii) 仅关注前向模拟，忽略更广泛的物理推理任务。本文提出去噪哈密顿网络（DHN），将哈密顿力学算子推广为更灵活的神经算子。DHN通过去噪机制捕捉非局部时间关系，并缓解数值积分误差。同时，借助全局条件机制支持多系统建模。我们在三种不同输入输出的物理推理任务中验证了其有效性和灵活性。
原文摘要 · Abstract (English)
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.
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