How Do Adaptive and Nonequilibrium Enhanced-Sampling Methods Work?

Note: This is an early draft page for the executable kUPS MD tutorial series. It is intentionally hidden from site navigation while the simulations, notebooks, figures, and review artifacts mature. This post follows umbrella sampling by asking how adaptive bias and nonequilibrium pulling change the measure being sampled, and what corrections are needed before a free-energy claim is trustworthy. Corrections and replication issues should be tracked in sungsoo-ahn/kups-md-tutorials.

Introduction

Enhanced sampling methods work by changing the probability measure. A metadynamics-style bias discourages revisiting already sampled regions. A steered nonequilibrium protocol drives the system along paths whose work values must be interpreted as a path ensemble, not as equilibrium samples.

For ML researchers working with MLIPs, the important shift is that faster motion across a barrier is not automatically an unbiased result. The bias, history, protocol speed, and path weights are part of the estimator. Jarzynski and Crooks identities give exact nonequilibrium relationships, but their finite-sample reliability still depends on overlap in work space (Jarzynski, 1997; Crooks, 1999; Laio & Parrinello, 2002; Barducci et al., 2008).

This draft demonstrates the executable slice of the eleventh tutorial with a known one-dimensional double-well coordinate. The adaptive-bias diagnostic shows how history-dependent hills fill wells; the nonequilibrium diagnostic uses controlled work ensembles to show mean-work dissipation, Jarzynski estimates, and a Crooks crossing.

• smoke configuration
• full configuration
• enhanced-sampling notebook
• smoke summary
• full summary
• full provenance manifest
• self-review note

What Changes When The Method Is Adaptive?

The full profile deposits 3000 well-tempered Gaussian hills on a double-well coordinate. The resulting diagnostic is intentionally compact:

The adaptive trajectory is not an unbiased trajectory. The bias history is part of the result.

What Changes When The Method Is Nonequilibrium?

The full pulling diagnostic has true free-energy difference effectively zero, but the forward and reverse mean works are positive because the finite-speed protocol dissipates work. Jarzynski and Crooks estimates recover the answer in this controlled case:

Reproduction

The current executable path is:

git clone https://github.com/sungsoo-ahn/kups-md-tutorials
cd kups-md-tutorials
uv sync
uv run kups-tutorial run 11 --profile smoke
uv run kups-tutorial verify 11 --profile smoke
uv run kups-tutorial run 11 --profile full
uv run kups-tutorial verify 11 --profile full
uv run jupyter execute notebooks/post-11-enhanced-sampling.ipynb --inplace

The notebook is deliberately not the implementation source. It imports the configuration loader, enhanced-sampling diagnostics, and figure generator from src/kups_md_tutorials/.

Current Status

This page is not the final article. The implemented pieces are:

• smoke and full controlled enhanced-sampling workflows
• committed compact summaries and diagnostic curves
• executable notebook
• generated SVG/PNG figure and snapshot review
• self-review note covering code, science, notebook, and figure feedback

The missing pieces are:

• final 3,500-10,000-word article prose
• rendered desktop and mobile page snapshots
• production MD context and final uncertainty diagnostics
• final citation pass

The rule for this post is that enhanced sampling is a change of measure. Bias history and path weights are part of the estimator, not implementation details to hide after the trajectory crosses a barrier.

References

• Jarzynski, C. (1997). Nonequilibrium equality for free energy differences. Physical Review Letters, 78, 2690-2693. ↩
• Crooks, G. E. (1999). Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Physical Review E, 60, 2721-2726. ↩
• Laio, A. & Parrinello, M. (2002). Escaping free-energy minima. Proceedings of the National Academy of Sciences, 99, 12562-12566. ↩
• Barducci, A., Bussi, G. & Parrinello, M. (2008). Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Physical Review Letters, 100, 020603. ↩