When Is a Trajectory Long Enough to Trust?

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 the initialization, integrator, error, thermostat, and barostat diagnostics by asking when a finite trajectory has enough independent information to support a numerical claim. Corrections and replication issues should be tracked in sungsoo-ahn/kups-md-tutorials.

Introduction

A molecular-dynamics trajectory is long only relative to the question being asked. Ten million correlated frames can still contain little independent information if the observable relaxes slowly. A short set of independent replicas can sometimes say more than a single long trace that has not forgotten its initial condition.

For ML researchers working with MLIPs, this matters because the simulation may look stable while the estimator is still biased or overconfident. The practical question is not how many frames were written. It is whether warmup was removed, whether autocorrelation was measured, whether uncertainty reflects effective sample size, and whether independent replicas agree.

This draft demonstrates the executable slice of the sixth tutorial with a controlled correlated observable. The model has a known equilibrium mean, so it can expose estimator failure modes cleanly before the final argon/kUPS observable diagnostics are added.

• smoke configuration
• full configuration
• trajectory-length notebook
• smoke summary
• full summary
• full provenance manifest
• self-review note

What Does Long Mean?

The current diagnostic compares trajectory-length checkpoints for a correlated observable with a known answer:

The full run keeps the underlying process fixed and changes only how much data is allowed into the estimator. This separates the effect of trajectory length from changes in the model, integrator, or ensemble.

What Should The Diagnostic Show?

The diagnostic reports naive standard error, autocorrelation-aware standard error, block standard error, replica standard error, and a conservative uncertainty used for review. The conservative uncertainty is intentionally not the smallest number available.

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 06 --profile smoke
uv run kups-tutorial verify 06 --profile smoke
uv run kups-tutorial run 06 --profile full
uv run kups-tutorial verify 06 --profile full
uv run jupyter execute notebooks/post-06-trajectory-length.ipynb --inplace

The notebook is deliberately not the implementation source. It imports the configuration loader, uncertainty 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 trajectory-length workflows
• committed compact summaries and downsampled samples
• executable notebook
• generated SVG/PNG figure and snapshot review
• self-review note covering code, science, notebook, and figure feedback

The missing pieces are:

• final article prose
• citations for autocorrelation, effective sample size, blocking analysis, and equilibration diagnostics
• rendered desktop and mobile page snapshots
• argon/kUPS trajectory-length diagnostics for physical observables

The rule for this post is the same as the rest of the series: a trajectory is not trustworthy because it is large. It becomes useful when the estimator, uncertainty, and independent checks support the claim being made.

References

• Frenkel, D. & Smit, B. (2001). Understanding Molecular Simulation: From Algorithms to Applications. Academic Press.
• Tuckerman, M. E. (2010). Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press.
• Flyvbjerg, H. & Petersen, H. G. (1989). Error estimates on averages of correlated data. Journal of Chemical Physics, 91, 461-466.