New method improves learning smooth dynamics from position and velocity data
Learning smooth dynamics via Kinematic Interpolants
Machine Learning
Summary
Many different rules can explain how things move when we only look at their positions at certain times. The authors found a better way to use information about both positions and speeds to learn the underlying rules of movement. Their approach, called Kinematic Interpolants, works well for complex systems like cells, fluids, or birds moving together, and it learns faster than other methods.
What this means in practice
- •For biotechnology engineers: Model cell behavior from experimental position and velocity data to improve analysis of biological processes.
- •For aerospace simulation teams: Enhance fluid flow models by accurately reconstructing vortex dynamics using position and velocity measurements.
Authors
Yiheng, Jiang, Youssef Marzouk, Avishek Joey Bose, Aram-Alexandre Pooladian
Abstract
Inferring dynamics from real-world experimental data is inherently ambiguous, as many plausible dynamical systems can explain the same positional observations at measurement times. For higher fidelity modeling of applications ranging from single-cell RNA to vortex dynamics and even flocking of birds, scientific observables increasingly also include velocity estimates that serve to resolve this issue. However, incorporating this rich information in a scalable manner, free of simulation or unnecessary approximations, has remained a difficult challenge. In this paper, we introduce Kinematic Interpolants (KI), a novel framework that extends the seminal methodology of stochastic interpolants to infer nonlinear dynamics across multiple snapshots in phase space, i.e., observables with position and velocity measurements. Empirically, we demonstrate that across several scientific datasets, KI achieves superior reconstruction of the underlying dynamics compared to existing baselines while requiring only a fraction of the training time.