Transition Path Sampling with Boltzmann Generator-based MCMC Moves

TL;DR

This work tackles sampling the transition path ensemble between two metastable states in a molecular system without resorting to MD-based shooting moves. It introduces a latent-spaceTPS framework that maps path frames into a Boltzmann-generator latent space via $z_i=F^{-1}(x_i)$, applies MCMC moves with a latent-space proposal kernel, and reconstructs proposed paths with $x_i=F( ilde{z}_i)$ to evaluate the path probability $p_{AB}$. Three latent-space proposal strategies are explored—Gaussian noise, GP with the current path as mean, and an adaptive GP trained on historical paths—along with a Langevin-based path probability and Jacobian corrections for MH acceptance. The experiments on alanine dipeptide show that simple Gaussian latent-noise proposals are most effective among the tested kernels, but overall acceptance and diversity remain challenging, indicating a need for better latent-space designs and improved Boltzmann generators. This MD-free, latent-space TPS approach points to a potential route for faster exploration of reaction mechanisms, with code available for replication and further development.

Abstract

Sampling all possible transition paths between two 3D states of a molecular system has various applications ranging from catalyst design to drug discovery. Current approaches to sample transition paths use Markov chain Monte Carlo and rely on time-intensive molecular dynamics simulations to find new paths. Our approach operates in the latent space of a normalizing flow that maps from the molecule's Boltzmann distribution to a Gaussian, where we propose new paths without requiring molecular simulations. Using alanine dipeptide, we explore Metropolis-Hastings acceptance criteria in the latent space for exact sampling and investigate different latent proposal mechanisms.

Figures (13)

• Figure 1: Distribution of alanine dipeptide's 3D configurations visualized via a histogram of its main dihedral angles $\phi, \psi$. Two metastable states are highlighted, between which we aim to sample the ensemble of all possible transition paths.
• Figure 2: MCMC proposals for latent space transition paths. We move a transition path ${\bm{x}}$ into latent space using a Boltzmann generator $F(\cdot)$. With this path ${\bm{z}}$ and our latent space proposal kernel $q_Z(\Tilde{{\bm{z}}}~|~{\bm{z}})$ we propose $\Tilde{{\bm{z}}}$ and bring it back to configuration/atom space to obtain the transition path proposal $\tilde{{\bm{x}}}$. The likelihood of all steps can be computed, and we use them in a Metropolis-Hastings acceptance criterion to sample the transition path ensemble with MCMC.
• Figure 3: Latent Gaussian noise proposal kernel. We apply independent noise $\varepsilon$ to a latent transition path ${\bm{z}}$. This creates a new proposal path $\tilde{{\bm{z}}}$ which will be accepted or rejected.
• Figure 4: Linear (latent space) interpolation.Left: A histogram of the two main dihedral angels $\phi, \psi$ when linearly interpolating the atom coordinates of configurations from the state $C_5$ and $\alpha_R$ in product space. Center: A histogram of the states occurring in the MD simulation and a linear interpolation in latent space (red line) are shown. Right: The resulting density of transition paths when linearly interpolating between those states in latent space.
• Figure 5: Comparison of sampling methods. Each row shows the transitions between two different metastable states. Left: "Ground truth" path ensemble from MD simulation of all paths (sub-left) and the 25% of paths with the highest probability (sub-right). Right: Shooting move MCMC ensemble and the ensembles of our different latent space proposal kernels. Note that it is unclear what a meaningful ground truth ensemble is.