Research map / Probabilistic and scientific modeling / Dynamical systems
Identifying latent state transitions in non-linear dynamical systems
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Proposes a VAE-based state-space framework that identifies latent states, process noise, and the nonlinear transition function of a latent dynamical system, with identifiability theory under non-stationary or autocorrelated noise.
Problem
Recovering latent states and their nonlinear transition dynamics from high-dimensional sensory observations; prior identifiable dynamics methods only identify latent states with linear or nonparametric transitions and cannot predict complex future behavior.
Approach
Extends nonlinear ICA identifiability to jointly identify latent states, process noise, and the transition function by augmenting the transition with the past state (independent innovation analysis) and encoding process noise from observations, trained with a VAE ELBO using conditional normalizing-flow noise priors conditioned on an auxiliary variable.
Key results
- On the synthetic data, the method reaches latent-state MCC 0.95 versus 0.89 for LEAP-Np and 0.68 for LEAP-Lin.
- Future-prediction MSE at 8 steps is 0.21 for the method versus 0.59 for LEAP-Lin and 1.72 for KalmanVAE.
- On Cartpole, latent MCC is 0.95 versus 0.83 for LEAP-Lin; adapting with 50 target trajectories improves MCC by about 25%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Jointly learn latent states, process noise, and the transition function rather than using LEAP-Np | Synthetic dynamics identification · Synthetic | MCCz: 0.89 -> 0.95 | Helped |
| Jointly learn latent states, process noise, and the transition function rather than using LEAP-Np | Synthetic dynamics identification · Synthetic | MCCs: 0.26 -> 0.66 | Helped |
| Use the proposed joint model instead of LEAP-Lin | Synthetic future prediction · Synthetic, 2-step future | MSE: 0.22 -> 0.06 | Helped |
| Use the proposed joint model instead of LEAP-Lin | Synthetic future prediction · Synthetic, 4-step future | MSE: 0.18 -> 0.09 | Helped |
| Use the proposed joint model instead of LEAP-Lin | Synthetic future prediction · Synthetic, 8-step future | MSE: 0.59 -> 0.21 | Helped |
| Use the proposed model instead of LEAP-Lin | Cartpole dynamics identification · Cartpole | MCCz: 0.83 -> 0.95 | Helped |
| Use the proposed model instead of LEAP-Lin | Cartpole future prediction · Cartpole, 8-step future | MCCz: 0.71 -> 0.93 | Helped |
| Add K independent MLPs for the transition outputs (ablation) | β-VAE ablation model · Synthetic | MCCz | Helped |
| Add a conditional normalizing flow for the nonstationary process-noise prior (ablation) | K-MLP-Dyn ablation model · Synthetic | MCCz | Helped |
| Jointly identify the generative and transition functions instead of fitting a transition offline on LEAP-Np latents | Synthetic future prediction · Synthetic | MSE | Helped |
| Adapt only the dynamics, including the process-noise flow, rather than the entire network | Ours · Cartpole target domain (g=90) | MCC | Helped |
| Adapt the model on 50 target-domain trajectories | Ours · Cartpole target domain (g=90) | MCC: about 25% | Helped |
Surprising findings
- Adapting only the dynamics (including the noise flow) gives better MCC than adapting the entire network.
- LEAP-Lin's MCC does not improve during adaptation regardless of dataset size despite decreasing the loss.
Limitations
- Identifiability relies on strong assumptions (A0-A5) whose violation's effect is not studied.
- Evaluation limited to synthetic data and a physics-simulator cartpole; no real-world datasets.
- Future-prediction performance not tested on downstream tasks such as model-based control.
Experimental setup
Datasets: synthetic multivariate time-series (random MLP generative and transition functions) modified Cartpole video dataset (OpenAI Gym adaptation)
Benchmarks: synthetic multivariate time-series modified Cartpole video
Metrics: MCC MSE
Baselines: beta-VAE PCL TCL iVAE SlowVAE KalmanVAE LEAP-Lin LEAP-Np
Builds on: LEAP TCL iVAE independent innovation analysis beta-VAE
Closest papers by meaning
- End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems (NeurIPS 2026 · similarity 0.90)
- Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning (NeurIPS 2026 · similarity 0.90)
- Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics (NeurIPS 2024 · similarity 0.90)
- eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling (NeurIPS 2024 · similarity 0.89)
- On the Identifiability of Switching Dynamical Systems (ICML 2024 · similarity 0.89)
- Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts (NeurIPS 2026 · similarity 0.89)
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