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Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning
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Proposes PESLA, a physics-informed self-supervised method that learns an energy landscape from stochastic system trajectories by combining an adaptive VQ codebook with a graph neural Fokker-Planck equation and a Boltzmann KL regularizer.
Problem
Estimating the energy landscape of stochastic dynamical systems from evolution trajectories alone, without ground-truth energy supervision, and with limited state-space coverage.
Approach
Map observed states to a discrete adaptive codebook (landscape space), attach a learned energy to each codeword, and model probability evolution with a graph neural Fokker-Planck equation; energy is learned via self-supervised prediction error plus a KL term pulling the long-term distribution toward the Boltzmann distribution, avoiding equilibrium-sampling assumptions.
Key results
- Estimated energy correlates above 0.9 with ground truth on the evaluated systems (abstract claim).
- Evolution prediction accuracy exceeds the baseline by an average of 17.65% (abstract claim).
- On BBA protein, PESLA achieves MJS 0.0207 and TJS 0.2468, versus 0.0231 and 0.3637 for the best baseline NeuralMJP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PESLA instead of NeuralMJP | BBA protein evolution prediction · BBA protein, lag 0.7 μs | MJS: 0.0231±0.0048 -> 0.0207±0.0061 | Helped |
| use PESLA instead of NeuralMJP | BBA protein evolution prediction · BBA protein, lag 0.7 μs | TJS: 0.3637±0.0051 -> 0.2468±0.0215 | Helped |
| add the physics regularization loss L_phy (ablation) | PESLA · 2D Prinz Potential | ρ_t: 0.0641±0.0182 -> 0.9290±0.0342 | Helped |
| add the physics regularization loss L_phy (ablation) | PESLA · Ecological Evolution | ρ_t: -0.0271±0.0281 -> -0.9067±0.0100 | Helped |
| add the latent-space prediction loss L_latent (ablation) | PESLA · 2D Prinz Potential | ρ_t: 0.8089±0.0672 -> 0.9290±0.0342 | Helped |
| add the latent-space prediction loss L_latent (ablation) | PESLA · Ecological Evolution | ρ_t: -0.8982±0.0071 -> -0.9067±0.0100 | Helped |
| encode and decode probabilities with Φ and Ψ (ablation) | PESLA graph neural Fokker-Planck equation · 2D Prinz Potential | MJS: 0.1675 ± 0.0089 -> 0.1031±0.0125 | Helped |
| encode and decode probabilities with Φ and Ψ (ablation) | PESLA graph neural Fokker-Planck equation · Ecological Evolution | MJS: 0.3564 ± 0.0236 -> 0.3111±0.0397 | Helped |
Surprising findings
- Removing the physics-informed KL regularizer L_phy collapses energy correlation on the 2D Prinz potential (rho_t drops from 0.929 to 0.064).
- Cross-protein transfer of the encoder and codebook retains over 80% of specific-trained energy correlation performance.
Limitations
- Applies only to conservative (energy-driven) systems; non-conservative forces have no energy landscape.
- Assumes a time-invariant landscape; time-varying landscapes are not handled.
- Performance depends on the preset codebook size K and drops when energy correlation falls below about 0.5 in the sensitivity study.
Experimental setup
Datasets: 2D Prinz potential (simulated) ecological evolution (simulated) Anton fast-folding protein trajectories (Homeodomain, BBL, BBA, NTL9, A3D)
Benchmarks: 2D Prinz potential ecological evolution simulation Anton protein folding trajectories
Metrics: trajectory energy correlation rho_T full-space energy correlation rho_F marginal JS divergence MJS transition JS divergence TJS
Baselines: Markov state model autoencoder potential energy NeuralMJP T-IB VAMPNets SDE-Net
Builds on: Neural MJP VQ-VAE graph neural diffusion Graph Fokker-Planck equation
Closest papers by meaning
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