Physically Plausible Multi-System Trajectory Generation and Symmetry Discovery

2025/09/26 by Jiayin Liu, Liu, Jiayin, Yulong Yang +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Social Sciences · #Artificial neural network #Configuration space #Data Management and Algorithms #Dynamical systems theory #Genome Rearrangement Algorithms #Geometric mechanics #Hamiltonian mechanics #Interpretability #Leverage (statistics) #Physical system #Software Engineering and Design Patterns #Trajectory

paper · pdf · doi:10.48550/arxiv.2509.23003

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/09/26 · openalex created_date 2025/10/19 · openalex updated_date 2026/08/05

Abstract

From metronomes to celestial bodies, mechanics underpins how the world evolves in time and space. With consideration of this, a number of recent neural network models leverage inductive biases from classical mechanics to encourage model interpretability and ensure forecasted states are physical. However, in general, these models are designed to capture the dynamics of a single system with fixed physical parameters, from state-space measurements of a known configuration space. In this paper we introduce Symplectic Phase Space GAN (SPS-GAN) which can capture the dynamics of multiple systems, and generalize to unseen physical parameters from. Moreover, SPS-GAN does not require prior knowledge of the system configuration space. In fact, SPS-GAN can discover the configuration space structure of the system from arbitrary measurement types (e.g., state-space measurements, video frames). To achieve physically plausible generation, we introduce a novel architecture which embeds a Hamiltonian neural network recurrent module in a conditional GAN backbone. To discover the structure of the configuration space, we optimize the conditional time-series GAN objective with an additional physically motivated term to encourages a sparse representation of the configuration space. We demonstrate the utility of SPS-GAN for trajectory prediction, video generation and symmetry discovery. Our approach captures multiple systems and achieves performance on par with supervised models designed for single systems.

Citations

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Related

• Hamiltonian GAN
• GeoHNNs: Geometric Hamiltonian Neural Networks
• Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks
• Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures
• Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems