deeptime package.MaximumLikelihoodMSM and validation.KoopmanModel and macrostate analysis.In this episode we reuse OpenMM Application Layer scripts to build consistent data:
simulatePdb.py: fast trajectories for Koopman validation.simulateAmber.py: long series for spectrum estimation and CK validation.simulateTinker.py: AMOEBA examples to compare with classical models.These outputs are processed with deeptime to stay consistent with PyEMMA.
The Koopman operator acts on an observable $g(\mathbf{x})$ by propagating it in time
\[(\mathcal{K}_\tau g)(\mathbf{x}) = \mathbb{E}[g(\mathbf{x}_{t+\tau}) | \mathbf{x}_t = \mathbf{x}],\]which in practice is approximated with matrices $K_{ij}$ relating microstates. Diagonalizing $K$ yields eigenvalues $\lambda_k$ and eigenfunctions $\psi_k$, allowing reconstruction of the stationary state
\[\rho(\mathbf{x}) \approx \sum_k \lambda_k \psi_k(\mathbf{x}).\]deeptime complements this view by estimating the transfer matrix and computing spectral projections to distinguish macrostates.
This episode now follows the Deeptime-managed Alanine dipeptide example (Ala2 Example <https://deeptime-ml.github.io/latest/notebooks/examples/ala2-example.html>__). We imported that notebook into the repository (see the iframe below) so you can open it locally in the same environment we use for the course. It fetches the heavy-atom positions and backbone dihedrals from mdshare, runs the same Torch-let Koopman/TICA flow, and highlights how the spectral models compare with PyEMMA’s timelines.
mdshare provides the alanine datasets (alanine-dipeptide-3x250ns-*) used by the official example, so no extra downloads are needed.KoopmanModel/MaximumLikelihoodMSM estimators for the same relaxation timescales you saw in the PyEMMA workflow.Ala2 Example (see the iframe and download link above).