Efficient sampling of unnormalized probability densities such as the Boltzmann distribution of molecular systems is a longstanding challenge. Next to conventional approaches like molecular dynamics or Markov chain Monte Carlo, variational approaches, such as training normalizing flows with the reverse Kullback-Leibler divergence, have been introduced. However, such methods are prone to mode collapse and often do not learn to sample the full configurational space. Here, we present temperature-annealed Boltzmann generators (TA-BG) to address this challenge. First, we demonstrate that training a normalizing flow with the reverse Kullback-Leibler divergence at high temperatures is possible without mode collapse. Furthermore, we introduce a reweighting-based training objective to anneal the distribution to lower target temperatures. We apply this methodology to three molecular systems of increasing complexity and, compared to the baseline, achieve better results in almost all metrics while requiring up to three times fewer target energy evaluations. For the largest system, our approach is the only method that accurately resolves the metastable states of the system.

Interpretable policy learning seeks to estimate intelligible decision policies from observed actions; however, existing models force a tradeoff between accuracy and interpretability, limiting data-driven interpretations of human decision-making processes. Fundamentally, existing approaches are burdened by this tradeoff because they represent the underlying decision process as a universal policy, when in fact human decisions are dynamic and can change drastically under different contexts. Thus, we develop Contextualized Policy Recovery (CPR), which re-frames the problem of modeling complex decision processes as a multi-task learning problem, where each context poses a unique task and complex decision policies can be constructed piece-wise from many simple context-specific policies. CPR models each context-specific policy as a linear map, and generates new policy models on-demand as contexts are updated with new observations. We provide two flavors of the CPR framework: one focusing on exact local interpretability, and one retaining full global interpretability. We assess CPR through studies on simulated and real data, achieving state-of-the-art performance on predicting antibiotic prescription in intensive care units ($+22$% AUROC vs. previous SOTA) and predicting MRI prescription for Alzheimer’s patients ($+7.7$% AUROC vs. previous SOTA). With this improvement, CPR closes the accuracy gap between interpretable and black-box methods, allowing high-resolution exploration and analysis of context-specific decision models.

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been used to learn the Boltzmann distribution directly, without samples. However, this approach is susceptible to mode collapse and thus often does not explore the full configurational space. In this work, we address this challenge by separating the problem into two levels, the fine-grained and coarse-grained degrees of freedom. A normalizing flow conditioned on the coarse-grained space yields a probabilistic connection between the two levels. To explore the configurational space, we employ coarse-grained simulations with active learning which allows us to update the flow and make all-atom potential energy evaluations only when necessary. Using alanine dipeptide as an example, we show that our methods obtain a speedup to molecular dynamics simulations of approximately $15.9$ to $216.2$ compared to the speedup of $4.5$ of the current state-of-the-art machine learning approach.