Denoising Hamiltonian Network for Physical Reasoning

2025-03-10

AI Summary

Existing physics-informed machine learning methods are largely confined to local time-step modeling and forward simulation, limiting their ability to capture long-range physical interactions and support diverse inference tasks. To address this, we propose a structure-preserving nonlocal neural operator framework. Our approach generalizes the Hamiltonian mechanics operator into a learnable neural operator, introduces a temporal denoising mechanism to suppress numerical integration errors, and incorporates a global conditional embedding for joint modeling of multiple physical systems. The framework unifies three heterogeneous physics inference tasks—differing in input/output modalities—under a single architecture. Experiments demonstrate substantial improvements in long-horizon prediction accuracy and cross-system generalization over state-of-the-art methods. To our knowledge, this is the first work to achieve an organic integration of Hamiltonian structure preservation with flexible multi-task physical reasoning.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Captures non-local temporal relationships in dynamical systems
• Mitigates numerical integration errors using denoising mechanism
• Supports multi-system modeling with global conditioning mechanism

Innovation

• Generalizes Hamiltonian mechanics into neural operators
• Captures non-local temporal relationships effectively
• Supports multi-system modeling globally