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FEAT: Free energy Estimators with Adaptive Transport
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Proposes FEAT, which learns a bidirectional non-equilibrium transport between two equilibrium distributions via stochastic interpolants and estimates free energy differences with escorted Jarzynski/controlled Crooks estimators, including a minimum-variance BAR-style estimator.
Problem
Estimating free energy differences between two states with high variance or poor overlap, where existing equilibrium estimators (FEP, BAR, MBAR, targeted FEP, TI) struggle in high dimensions.
Approach
Learn a stochastic-interpolant transport (velocity field plus score network) between samples from both endpoints, then use the escorted Jarzynski equality and controlled Crooks theorem with a forward-backward Radon-Nikodym estimator, which stays asymptotically unbiased under time discretization and imperfect boundary conditions, and combine both directions with a BAR-style minimum-variance estimat
Key results
- On GMM-100 FEAT gives -5.34 ± 1.52 vs targeted FEP (FM) -17.96 ± 1.49 against a reference of 0.
- On LJ-55x3 FEAT gives 232.47 ± 0.15 vs reference 234.77 and targeted FEP 232.06 ± 0.03; targeted FEP fails (divergence cost) on LJ-79x3 and LJ-128x3 while FEAT gives 356.74 and 595.04.
- One-sided FEAT on ALA-4 gives 109.91 ± 2.55 vs reference 107.5 and on Chignolin 320.02 ± 0.70 vs reference 320.19.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FEAT instead of TargetFEP (FM) | free energy estimation · GMM 16 modes to 40 modes, d=40 | ΔF estimate: 0.09 { $\pm 0.26$} -> 0.04 { $\pm 0.04$} | Helped |
| use FEAT instead of TargetFEP (FM) | free energy estimation · GMM 16 modes to 40 modes, d=100 | ΔF estimate: -17.96 { $\pm 1.49$} -> -5.34 { $\pm 1.52$} | Helped |
| use FEAT instead of TargetFEP (FM) | free energy estimation · LJ without to with LJ interaction, d=55×3 | ΔF estimate: 232.06 { $\pm 0.03$} -> 232.47 { $\pm 0.15$} | Hurt |
| use FEAT instead of TargetFEP (FM) | free energy estimation · LJ without to with LJ interaction, d=79×3 | ΔF estimate | Helped |
| use FEAT instead of TargetFEP (FM) | free energy estimation · LJ without to with LJ interaction, d=128×3 | ΔF estimate | Helped |
| use FEAT instead of TargetFEP (FM) | free energy estimation · ALDP-S, d=22×3 | ΔF estimate: 29.47 { $\pm 0.22$} -> 29.38 { $\pm 0.04$} | Helped |
| use FEAT instead of TargetFEP (FM) | free energy estimation · ALDP-T, d=22×3 | ΔF estimate: -4.78 { $\pm0.32$} -> -4.56 { $\pm 0.08$} | Helped |
| remove preconditioning from Neural TI (ablation) | Neural TI · GMM-40 | ΔF estimate: $0.1 \pm 0.2$ -> $-181.6 \pm 6.7$ | Hurt |
| remove preconditioning from Neural TI (ablation) | Neural TI · LJ-79 | ΔF estimate: $356.9 \pm 1.8$ -> $468.8 \pm 391.2$ | Hurt |
| use the minimum-variance estimator instead of forward-only or backward-only estimation | FEAT · LJ-128 and ALDP | free energy estimation accuracy | Helped |
| use one-sided FEAT for absolute free energies and subtract them, rather than directly bridging two states with FEAT | free energy estimation on larger systems · large molecular systems | free energy estimation performance | Helped |
Surprising findings
- Neural TI without problem-specific preconditioning fails badly (GMM-40 -181.6 ± 6.7), showing reliance on preconditioning.
- Using one-sided FEAT with DeepBAR outperformed direct two-state FEAT on large systems.
Limitations
- Estimator variance can be large for larger-scale systems because it is importance sampling over path space.
- Requires samples from both end states, unlike methods that need only one endpoint.
- Demonstrated on molecular systems mainly with small or moderate sizes; larger-scale validation is limited.
Experimental setup
Datasets: Gaussian mixture models Lennard-Jones potentials alanine dipeptide (ALDP) samples alanine tetrapeptide (ALA-4) Chignolin phi^4 lattice field theory
Benchmarks: GMM LJ ALDP-S ALDP-T ALA-4 CHIG phi^4 umbrella sampling
Metrics: free energy difference estimate standard deviation across three seeds
Baselines: targeted FEP (flow matching) neural thermodynamic integration MBAR DeepBAR
Builds on: targeted FEP escorted Jarzynski equality stochastic interpolants bennett acceptance ratio neural thermodynamic integration
Closest papers by meaning
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