Denoising Hamiltonian Network for Physical Reasoning
This work addresses physical reasoning tasks in machine learning, offering a more flexible approach, though it appears incremental as it builds on existing Hamiltonian-based methods.
The paper tackles the limitations of existing machine learning frameworks for physical problems, which often overlook non-local interactions and broader reasoning tasks, by proposing the Denoising Hamiltonian Network (DHN) that generalizes Hamiltonian mechanics operators with a denoising mechanism and global conditioning, demonstrating effectiveness across three diverse physical reasoning tasks.
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.