Research map / Probabilistic and scientific modeling / Variational and generative sampling
Free energy Estimation on Any State Space
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Generalizes escorted Jarzynski equality and Crooks fluctuation theorem from continuous Langevin transports to arbitrary Markov processes and state spaces, learns forward-backward neural transports (FEAT-style), and reveals a generalized dihedral group structure of infinitesimal reversals and Doob h-transforms.
Problem
Free energy (log normalizing constant) estimation via finite-time nonequilibrium transports suffers high variance; existing learned escort methods are limited to continuous state spaces with SDE transports.
Approach
Derives generalized escorted Jarzynski and Crooks identities for any Markov generator on arbitrary state spaces, with a work functional including an escort term defined via the adjoint generator, and learns forward/backward transports via generator matching or marginal score/concrete score to minimize dissipation; a BAR-style combined estimator is used.
Key results
- CTMC-FEAT on Ising models of size up to 32x32 (1024 spins) gives free energy estimates within roughly 0.1-1 x10^-3 per dimension of reference values across DFM, GM-no mask and GM-w. mask variants.
- AR-FEAT on Ising models at beta=0.2, 0.4, 0.6 matches reference free energies to about 0.01 x10^-3 per dimension for 15x15 to 32x32 lattices.
- Momentum-augmented transport is reported as comparable to standard SDE transport on 40D Gaussian mixtures and slightly more robust to larger noise.
Surprising findings
- Autoregressive transport achieves very strong performance, attributed to the strong learning signal of AR training.
- Masked generator matching is slightly less robust than no-mask choices in discrete settings, and at larger beta gap the discrepancy grows.
Limitations
- Expressiveness limited by network parameterization and may need domain-specific tuning
- Heavy-tailed targets (e.g., Cauchy) pose difficulties for finite-time transport models
Experimental setup
Datasets: Ising model samples Ising fluid 40-dimensional Gaussian mixtures
Benchmarks: Ising models (discrete) Ising fluid (multimodal) 40D Gaussian mixture (momentum transport)
Metrics: free energy difference estimates vs reference forward-backward estimator gap standard deviation across estimator runs
Baselines: DFM FEAT MBAR
Builds on: escorted Jarzynski estimator FEAT generator matching discrete flow matching Bennett acceptance ratio
Closest papers by meaning
- FEAT: Free energy Estimators with Adaptive Transport (NeurIPS 2025 · similarity 0.91)
- Learning Physics Informed Neural ODEs with Partial Measurements (AAAI 2025 · similarity 0.87)
- Energy-guided Entropic Neural Optimal Transport (ICLR 2024 · similarity 0.86)
- Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning (ICLR 2025 · similarity 0.85)
- Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport (NeurIPS 2024 · similarity 0.84)
- Learning the Infinitesimal Generator of Stochastic Diffusion Processes (NeurIPS 2024 · similarity 0.84)
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