Michael Plainer

Rare event sampling in dynamical systems is a fundamental problem arising in the natural sciences, which poses significant computational challenges due to an exponentially large space of trajectories. For settings where the dynamical system of interest follows a Brownian motion with known drift, the question of conditioning the process to reach a given endpoint or desired rare event is definitively answered by Doob’s h-transform. However, the naive estimation of this transform is infeasible, as it requires simulating sufficiently many forward trajectories to estimate rare event probabilities. In this work, we propose a variational formulation of Doob’s h-transform as an optimization problem over trajectories between a given initial point and the desired ending point. To solve this optimization, we propose a simulation-free training objective with a model parameterization that imposes the desired boundary conditions by design. Our approach significantly reduces the search space over trajectories and avoids expensive trajectory simulation and inefficient importance sampling estimators which are required in existing methods. We demonstrate the ability of our method to find feasible transition paths on real-world molecular simulation and protein folding tasks.

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.

When a small molecule binds to a protein, the 3D structure and function of the protein can significantly change. Understanding this process, called molecular docking, is crucial in areas such as drug design. Recent learning-based attempts have shown promising results at this task, yet lack the necessary features that traditional approaches support. In this work, we close this gap by proposing DiffDock-Pocket: a diffusion-based all-atom docking algorithm conditioned on a binding target. Our model supports receptor flexibility by extending the generative diffusion process to the manifold describing the main degrees of freedom of the protein’s side chains. Empirically, we improve the state-of-the-art in site-specific-docking on the PDBBind benchmark. In particular, in the realistic scenario that no bound protein structure is available, we double the accuracy of current methods while being 20 times faster than other flexible approaches.

Even the best scientific equipment can only partially observe reality. Recorded data is often lower-dimensional, e.g., two-dimensional pictures of the three-dimensional world. Combining data from multiple experiments then results in a marginal density. This work shows how to transport such lower-dimensional marginal densities into a more informative, higher-dimensional joint space by leveraging time-delayed measurements from an observation process. This can augment the information from scientific equipment to construct a more coherent view. Classical transportation algorithms can be used when the source and target dimensions match. Our approach allows the transport of samples between spaces of different dimensions by exploiting information from the sample collection process. We reconstruct the surface of an implant from partial recordings of bacteria moving on it and construct a joint space for satellites orbiting the Earth by combining one-dimensional, time-delayed altitude measurements.