Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on normalizing flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG) — a novel autoregressive modelling framework — that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132 million parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, E-𝒲₂, on 8-residue systems by over 60%.

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with importance sampling to obtain consistent samples under the target distribution. Current Boltzmann Generators primarily use continuous normalizing flows (CNFs) trained with flow matching for efficient training of powerful models. However, likelihood calculation for these models is extremely costly, requiring thousands of function evaluations per sample, severely limiting their adoption. In this work, we propose Few-step Accurate Likelihoods for Continuous Flows (FALCON), a method which allows for few-step sampling with a likelihood accurate enough for importance sampling applications by introducing a hybrid training objective that encourages invertibility. We show FALCON outperforms state-of-the-art normalizing flow models for molecular Boltzmann sampling and is two orders of magnitude faster than the equivalently performing CNF model.

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from expensive inference, inhibiting their use in numerous scientific applications like Boltzmann Generators (BGs) for molecular conformations that require fast likelihood evaluation. In this paper, we revisit classical normalizing flows in the context of BGs that offer efficient sampling and likelihoods, but whose training via maximum likelihood is often unstable and computationally challenging. We propose Regression Training of Normalizing Flows (RegFlow), a novel and scalable regression-based training objective that bypasses the numerical instability and computational challenge of conventional maximum likelihood training in favour of a simple ℓ₂-regression objective. Specifically, RegFlow maps prior samples under our flow to targets computed using optimal transport couplings or a pre-trained continuous normalizing flow (CNF). To enhance numerical stability, RegFlow employs effective regularization strategies such as a new forward-backward self-consistency loss that enjoys painless implementation. Empirically, we demonstrate that RegFlow unlocks a broader class of architectures that were previously intractable to train for BGs with maximum likelihood. We also show RegFlow exceeds the performance, computational cost, and stability of maximum likelihood training in equilibrium sampling in Cartesian coordinates of alanine dipeptide, tripeptide, and tetrapeptide, showcasing its potential in molecular systems.

The antimicrobial resistance crisis necessitates structurally distinct antibiotics. While deep learning approaches can identify antibacterial compounds from existing libraries, structural novelty remains limited. Here, we developed a generative artificial intelligence framework for designing de novo antibiotics through two approaches: a fragment-based method to comprehensively screen >10⁷ chemical fragments in silico against Neisseria gonorrhoeae or Staphylococcus aureus, subsequently expanding promising fragments, and an unconstrained de novo compound generation, each using genetic algorithms and variational autoencoders. Of 24 synthesized compounds, seven demonstrated selective antibacterial activity. Two lead compounds exhibited bactericidal efficacy against multidrug-resistant isolates with distinct mechanisms of action and reduced bacterial burden in vivo in mouse models of N. gonorrhoeae vaginal infection and methicillin-resistant S. aureus skin infection. We further validated structural analogs for both compound classes as antibacterial. Our approach enables the generative deep-learning-guided design of de novo antibiotics, providing a platform for mapping uncharted regions of chemical space.

Conventional continuum models for ion transport across polyamide membranes require solving partial differential equations (PDEs). These models typically introduce a host of assumptions and simplifications to improve the computational tractability of existing solvers. As a consequence of these constraints, conventional models struggle to generalize predictive performance to new unseen conditions. Deep learning has recently shown promise in alleviating many of these concerns, making it a promising avenue for surrogate models that can replace conventional PDE-based approaches. In this work, we develop a physics-informed deep learning model to predict ion transport across diverse membrane types. The proposed architecture leverages neural differential equations in conjunction with classical closure models as inductive biases directly encoded into the neural framework. The neural methods are pre-trained on simulated data from continuum models and fine-tuned on independent experiments to learn multi-ionic rejection behaviour. We also harness the attention mechanism, commonly observed in language modelling, to learn and infer key paired transport relationships. Gaussian noise augmentations from experimental uncertainty estimates are also introduced into the measured data to improve robustness and generalization. We study the neural framework’s performance relative to conventional PDE-based methods, and also compare the use of hard/soft inductive bias constraints on prediction accuracy. Lastly, we compare our approach to other competitive deep learning architectures and illustrate strong agreement with experimental measurements across all studied datasets.

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs. Code: this https URL.