Flow Matching for Geometric Trajectory Simulation

2025-05-24

AI Summary

Existing generative modeling approaches for N-body systems—such as molecular dynamics and pedestrian motion—rely on uninformative noise initialization, hindering incorporation of physical priors and violating permutation symmetry. This work introduces the first geometric trajectory generation framework that integrates flow matching with data-dependent coupling mechanisms, explicitly encoding symmetry constraints and physical priors inherent to N-body systems. Our method employs geometric deep learning to construct a differentiable, scalable architecture that preserves symmetries (e.g., translation, rotation, and permutation invariance) and supports principled injection of domain knowledge. Evaluated across diverse N-body benchmarks, the proposed approach achieves significantly lower trajectory prediction error and improved inference efficiency compared to state-of-the-art baselines. These results empirically validate the effectiveness of physics-informed geometric probabilistic modeling for structured dynamical systems.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Natural Language Processing: Generation
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The simulation of N-body systems is a fundamental problem with applications in a wide range of fields, such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances based on deep generative modeling and geometric deep learning have enabled probabilistic simulation by modeling complex distributions over trajectories while respecting the permutation symmetry that is fundamental to N-body systems. However, to generate realistic trajectories, existing methods must learn complex transformations starting from uninformed noise and do not allow for the exploitation of domain-informed priors. In this work, we propose STFlow to address this limitation. By leveraging flow matching and data-dependent couplings, STFlow facilitates physics-informed simulation of geometric trajectories without sacrificing model expressivity or scalability. Our evaluation on N-body dynamical systems, molecular dynamics, and pedestrian dynamics benchmarks shows that STFlow produces significantly lower prediction errors while enabling more efficient inference, highlighting the benefits of employing physics-informed prior distributions in probabilistic geometric trajectory modeling.

Problem

• Simulating N-body systems with permutation symmetry constraints
• Generating realistic trajectories without uninformed noise reliance
• Incorporating physics-informed priors in probabilistic trajectory modeling

Innovation

• Flow matching for geometric trajectory simulation
• Physics-informed simulation with data-dependent couplings
• Efficient inference with physics-informed prior distributions