The ISOKANN (Invariant Subspaces of Koopman Operators Learned by Artificial Neural Networks) framework provides a data-driven route to extract collective variables (CVs) and effective dynamics from complex molecular systems. In this work, we integrate the theoretical foundation of Koopman operators with Krylov-like subspace algorithms, and reduced dynamical modeling to build a coherent picture of how to describe metastable transitions in high-dimensional systems based on CVs. Starting from the identification of CVs based on dominant invariant subspaces, we derive the corresponding effective dynamics on the latent space and connect these to transition rates and times, committor functions, and transition pathways. The combination of Koopman-based learning and reduced-dimensional effective dynamics yields a principled framework for computing transition rates and pathways from simulation data. Numerical experiments on one-, two-, and three-dimensional benchmark potentials illustrate the ability of ISOKANN to reconstruct the coarse-grained kinetics and reproduce transition times across enthalpic and entropic barriers.

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

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but their practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack the reweighting process required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a principled framework that unifies scalable reduced-order modeling with the exactness of importance sampling. CG-BGs act in a coarse-grained coordinate space, using a learned potential of mean force (PMF) to reweight samples generated by a flow-based model. Crucially, we show that this PMF can be efficiently learned from rapidly converged data via force matching. Our results demonstrate that CG-BGs faithfully capture complex interactions mediated by explicit solvent within highly reduced representations, establishing a scalable pathway for the unbiased sampling of larger molecular systems.

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.

Computing properties of molecular systems rely on estimating expectations of the (unnormalized) Boltzmann distribution. Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities. However, stable simulations rely on very small integration time-steps ($10^{-15}\,\mathrm{s}$), whereas convergence of some moments, e.g.

We introduce JAX MD, a software package for performing differentiable physics simulations with a focus on molecular dynamics. JAX MD includes a number of statistical physics simulation environments as well as interaction potentials and neural networks that can be integrated into these environments without writing any additional code. Since the simulations themselves are differentiable functions, entire trajectories can be differentiated to perform meta-optimization. These features are built on primitive operations, such as spatial partitioning, that allow simulations to scale to hundreds-of-thousands of particles on a single GPU. These primitives are flexible enough that they can be used to scale up workloads outside of molecular dynamics.

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 broadly adopted technique to approximate such quantities.

Molecular Dynamics (MD) simulations are essential for understanding the atomic-level behavior of molecular systems, giving insights into their transitions and interactions. However, classical MD techniques are limited by the trade-off between accuracy and efficiency, while recent deep learning-based improvements have mostly focused on single-domain molecules, lacking transferability to unfamiliar molecular systems. Therefore, we propose \textbf{Uni}fied \textbf{Sim}ulator (UniSim), which leverages cross-domain knowledge to enhance the understanding of atomic interactions. First, we employ a multi-head pretraining approach to learn a unified atomic representation model from a large and diverse set of molecular data. Then, based on the stochastic interpolant framework, we learn the state transition patterns over long timesteps from MD trajectories, and introduce a force guidance module for rapidly adapting to different chemical environments. Our experiments demonstrate that UniSim achieves highly competitive performance across small molecules, peptides, and proteins.

Efficient molecular dynamics (MD) simulation is vital for understanding atomic-scale processes in materials science and biophysics. Traditional density functional theory (DFT) methods are computationally expensive, which limits the feasibility of long-term simulations. We propose a novel approach that formulates MD simulation as a time-series forecasting problem, enabling advanced forecasting models to predict atomic trajectories via displacements rather than absolute positions. We incorporate a physics-informed loss and inference mechanism based on DFT-parametrised pair-wise Morse potential functions that penalize unphysical atomic proximity to enforce physical plausibility. Our method consistently surpasses standard baselines in simulation accuracy across diverse materials. The results highlight the importance of incorporating physics knowledge to enhance the reliability and precision of atomic trajectory forecasting. Remarkably, it enables stable modeling of thousands of MD steps in minutes, offering a scalable alternative to costly DFT simulations.