Physically Plausible Multi-System Trajectory Generation and Symmetry Discovery

• URL: http://arxiv.org/abs/2509.23003v1
• Date: Fri, 26 Sep 2025 23:46:55 GMT
• Title: Physically Plausible Multi-System Trajectory Generation and Symmetry Discovery
• Authors: Jiayin Liu, Yulong Yang, Vineet Bansal, Christine Allen-Blanchette,
• Abstract summary: We introduce Symplectic Phase Space GAN (SPS-GAN) to capture dynamics of multiple systems.<n>SPS-GAN does not require prior knowledge of the system configuration space.<n>Our approach captures multiple systems and achieves performance on par with supervised models designed for single systems.
• Score: 2.8658660939961043
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences.<n>We train the model using maximum likelihood estimation with Markov chain Monte Carlo.<n> Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Hamiltonian GAN [1.6589012298747952]
  We present a GAN-based video generation pipeline with a learned configuration space map and Hamiltonian neural network motion model. We train our model with a physics-inspired cyclic-inspired loss function which encourages a minimal representation of the configuration space and improves interpretability.
  arXiv  Detail & Related papers  (2023-08-22T06:03:00Z)
• Disentangling Structured Components: Towards Adaptive, Interpretable and Scalable Time Series Forecasting [52.47493322446537]
  We develop a adaptive, interpretable and scalable forecasting framework, which seeks to individually model each component of the spatial-temporal patterns. SCNN works with a pre-defined generative process of MTS, which arithmetically characterizes the latent structure of the spatial-temporal patterns. Extensive experiments are conducted to demonstrate that SCNN can achieve superior performance over state-of-the-art models on three real-world datasets.
  arXiv  Detail & Related papers  (2023-05-22T13:39:44Z)
• Data-Free Learning of Reduced-Order Kinematics [54.85157881323157]
  We produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space. This formulation is effective across a very general range of physical systems.
  arXiv  Detail & Related papers  (2023-05-05T20:53:36Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty [6.151348127802708]
  We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM) The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
  arXiv  Detail & Related papers  (2021-10-16T16:35:12Z)
• Joint Parameter Discovery and Generative Modeling of Dynamic Systems [0.0]
  We present a neural framework for estimating physical parameters in a manner consistent with the underlying physics. Our model also extrapolates the dynamics of the system beyond the training interval and outperforms a non-physically constrained baseline model.
  arXiv  Detail & Related papers  (2021-03-19T16:56:45Z)
• Physics-Informed Neural State Space Models via Learning and Evolution [1.1086440815804224]
  We study methods for discovering neural state space dynamics models for system identification. We employ an asynchronous genetic search algorithm that alternates between model selection and optimization.
  arXiv  Detail & Related papers  (2020-11-26T23:35:08Z)
• S2RMs: Spatially Structured Recurrent Modules [105.0377129434636]
  We take a step towards exploiting dynamic structure that are capable of simultaneously exploiting both modular andtemporal structures. We find our models to be robust to the number of available views and better capable of generalization to novel tasks without additional training.
  arXiv  Detail & Related papers  (2020-07-13T17:44:30Z)
• Generation of accessible sets in the dynamical modelling of quantum network systems [9.295724747694194]
  We consider the dynamical modeling of a class of quantum network systems consisting of qubits. For a variety of applications, a state space model is a useful way to model the system dynamics.
  arXiv  Detail & Related papers  (2020-04-30T09:53:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.