Flow Matching for Geometric Trajectory Simulation
This work addresses the limitation of existing methods that cannot exploit domain-informed priors for probabilistic simulation in fields such as biochemistry and pedestrian dynamics, offering an incremental improvement.
The authors tackled the problem of generating realistic trajectories in N-body systems by proposing STFlow, which uses flow matching and data-dependent couplings to incorporate physics-informed priors, resulting in significantly lower prediction errors and more efficient inference on benchmarks like molecular dynamics and pedestrian dynamics.
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.