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.

本文解决了传统物理问题机器学习方法在建模时对长程物理交互和更广泛推理任务的忽视。提出的去噪哈密顿网络（DHN）通过灵活的神经算子捕捉非局部的时间关系，并通过去噪机制减小数值积分误差。研究表明，DHN在多系统建模和三种不同物理推理任务中展示了其有效性和灵活性。

去噪哈密顿网络用于物理推理