Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD.Furthermore, new MD simulations need to be performed for each molecular system studied.We present *Timewarp*, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of $10^{5} - 10^{6} \textrm{fs}$.Crucially, Timewarp is *transferable* between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD.Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a normalizing flow from a simple prior distribution to the target Boltzmann distribution of interest. Recently, flow matching has been employed to train Boltzmann Generators for small molecular systems in Cartesian coordinates. We extend this work and propose a first framework for Boltzmann Generators that are transferable across chemical space, such that they predict zero-shot Boltzmann distributions for test molecules without being retraining for these systems. These transferable Boltzmann Generators allow approximate sampling from the target distribution of unseen systems, as well as efficient reweighting to the target Boltzmann distribution. The transferability of the proposed framework is evaluated on dipeptides, where we show that it generalizes efficiently to unseen systems.Furthermore, we demonstrate that our proposed architecture enhances the efficiency of Boltzmann Generators trained on single molecular systems.

The application of machine learning methods in quantum chemistry has enabled the study of numerous chemical phenomena, which are computationally intractable with traditional ab-initio methods. However, some quantum mechanical properties of molecules and materials depend on non-local electronic effects, which are often neglected due to the difficulty of modeling them efficiently. This work proposes a modified attention mechanism adapted to the underlying physics, which allows to recover the relevant non-local effects. Namely, we introduce spherical harmonic coordinates (SPHCs) to reflect higher-order geometric information for each atom in a molecule, enabling a non-local formulation of attention in the SPHC space. Our proposed model So3krates - a self-attention based message passing neural network - uncouples geometric information from atomic features, making them independently amenable to attention mechanisms. Thereby we construct spherical filters, which extend the concept of continuous filters in Euclidean space to SPHC space and serve as foundation for a spherical self-attention mechanism. We show that in contrast to other published methods, So3krates is able to describe non-local quantum mechanical effects over arbitrary length scales. Further, we find evidence that the inclusion of higher-order geometric correlations increases data efficiency and improves generalization. So3krates matches or exceeds state-of-the-art performance on popular benchmarks, notably, requiring a significantly lower number of parameters (0.25 - 0.4x) while at the same time giving a substantial speedup (6 - 14x for training and 2 - 11x for inference) compared to other models.

Coarse-graining (CG) enables molecular dynamics (MD) simulations of larger systems and longer timescales that are otherwise infeasible with atomistic models. Machine learning potentials (MLPs), with their capacity to capture many-body interactions, can provide accurate approximations of the potential of mean force (PMF) in CG models. Current CG MLPs are typically trained in a bottom-up manner via force matching, which in practice relies on configurations sampled from the unbiased equilibrium Boltzmann distribution to ensure thermodynamic consistency. This convention poses two key limitations: first, sufficiently long atomistic trajectories are needed to reach convergence; and second, even once equilibrated, transition regions remain poorly sampled. To address these issues, we employ enhanced sampling to bias along CG degrees of freedom for data generation, and then recompute the forces with respect to the unbiased potential. This strategy simultaneously shortens the simulation time required to produce equilibrated data and enriches sampling in transition regions, while preserving the correct PMF. We demonstrate its effectiveness on the Müller-Brown potential and capped alanine, achieving notable improvements. Our findings support the use of enhanced sampling for force matching as a promising direction to improve the accuracy and reliability of CG MLPs.

Molecular dynamics (MD) is a powerful tool for exploring the behavior of atomistic systems, but its reliance on sequential numerical integration limits simulation efficiency. We present a novel neural network architecture, MDtrajNet, and a pre-trained foundational model, MDtrajNet-1, that directly generates MD trajectories across chemical space, bypassing force calculations and integration. This approach accelerates simulations by up to two orders of magnitude compared to traditional MD, even those enhanced by machine-learning interatomic potentials. MDtrajNet combines equivariant neural networks with a transformer-based architecture to achieve strong accuracy and transferability in predicting long-time trajectories. Remarkably, the errors of the trajectories generated by MDtrajNet-1 for various known and unseen molecular systems are close to those of the conventional ab initio MD. The architecture's flexible design supports diverse application scenarios, including different statistical ensembles, boundary conditions, and interaction types. By overcoming the intrinsic speed barrier of conventional MD, MDtrajNet opens new frontiers in efficient and scalable atomistic simulations.

Efficient sampling from high-dimensional and multimodal unnormalized probability distributions is a central challenge in many areas of science and machine learning. We focus on Boltzmann generators (BGs) that aim to sample the Boltzmann distribution of physical systems, such as molecules, at a given temperature. Classical variational approaches that minimize the reverse Kullback-Leibler divergence are prone to mode collapse, while annealing-based methods, commonly using geometric schedules, can suffer from mass teleportation and rely heavily on schedule tuning. We introduce Constrained Mass Transport (CMT), a variational framework that generates intermediate distributions under constraints on both the KL divergence and the entropy decay between successive steps. These constraints enhance distributional overlap, mitigate mass teleportation, and counteract premature convergence. Across standard BG benchmarks and the here introduced ELIL tetrapeptide, the largest system studied to date without access to samples from molecular dynamics, CMT consistently surpasses state-of-the-art variational methods, achieving more than 2.5x higher effective sample size while avoiding mode collapse.

Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

These authors contributed equally to this work. Order was determined by rolling a dice.