Physics-Inspired All-Pair Interaction Learning for 3D Dynamics Modeling

2025-10-05

AI Summary

This paper addresses the challenge of modeling unobserved implicit interactions in multi-body systems. We propose PAINET—the first 3D dynamics model integrating physics-inspired attention with SE(3)-equivariance. Our method derives an attention mechanism from energy-functional trajectory minimization, ensuring physical consistency while explicitly capturing all-pairwise implicit particle interactions. Additionally, we design an equivariant parallel decoder that preserves SE(3) geometric symmetries and enables efficient inference. Evaluated on three real-world benchmarks—human motion capture, molecular dynamics, and protein simulation—PAINET reduces 3D trajectory prediction error by 4.7%–41.5% over state-of-the-art methods, with computational overhead comparable to mainstream approaches. The model consistently achieves superior performance across all benchmarks, establishing new state-of-the-art results.

Technology Category

• Computer Vision: 3D Computer Vision
• Reasoning under Uncertainty: Relational Probabilistic Models
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant neural architecture for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory.

Problem

• Modeling 3D dynamics in multi-body systems
• Capturing unobserved interactions in physical behaviors
• Learning all-pair interactions with SE(3)-equivariant architecture

Innovation

• SE(3)-equivariant architecture for all-pair interactions
• Physics-inspired attention from energy minimization trajectory
• Parallel decoder maintaining equivariance for efficient inference