FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions

Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.

Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes

Finite-time driving of stochastic systems generates excess dissipation, causing the evolving probability distribution to lag behind the instantaneous equilibrium, and consequently degrading the convergence of nonequilibrium free energy estimators based on the Jarzynski equality. Escorted free energy simulations address the non-adiabatic lag by engineering control fields $\mathbf{u}$ that eliminate the lag, enforcing the trajectory-wise equality $\mathcal{W}_\mathbf{u} = Δ\mathcal{F}$, and yielding zero-variance estimators. However, constructing the escorting field in closed form remains a challenge, approached variously through flow-field methods, targeted free energy perturbation, or learned diffeomorphisms. In this work, we construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms for perfect escorting based on the exact spectral decomposition of the time-dependent Fokker-Planck generator. The biorthogonal decomposition of the Liouville operator directly yields a counterdiabatic correction whose action on the instantaneous equilibrium distribution exactly cancels the non-adiabatic lag at arbitrary driving speed in formal analogy with shortcuts-to-adiabaticity techniques such as Berry's transitionless driving for quantum systems. Numerical verification for simulations of an overdamped particle in a time-varying double-well potential and harmonic traps confirms that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude in total variation distance and sixteen orders in KL divergence relative to the unescorted dynamics. As a diagnostic, we demonstrate vanishing dissipated work $\mathcal{W}_{\text{diss}}(t) \approx 0$ for the deterministically propagated Fokker-Planck density across all protocol speeds.

AquaGen: Scaling generative models to molecular dynamics precision on thousands of atoms

We present AquaGen, the first all-atom, explicit solvent, periodic-boundary-condition-aware generative model that produces molecular configurations from the Boltzmann distribution at a fraction of the cost of molecular dynamics (MD). This is in contrast with existing generative models that remove degrees of freedom by operating on coarse-grained, vacuum, or implicit solvent systems. Operating at this resolution allows for post-processing through force field energy evaluations and MD simulations, and enables the prediction of relevant properties in a gray-box manner (as ensemble averages of potential energy evaluations over generated samples). We demonstrate the utility of this paradigm on absolute hydration free energy (AHFE), producing estimates 4-10x faster and with comparable accuracy to standard GPU-based MD. By generating uncorrelated samples from alchemical Boltzmann distributions, we create more accurate, interpretable, and refinable ensemble predictions with calibrated uncertainty estimates, unlike regression methods which are entirely black-box predictors. Our approach also yields predictable benefits from increasing train- and test-time compute, realized by scaling model size and generating more samples, respectively. We believe that this approach demonstrates the utility of high-resolution ensemble generation for free energy estimation, with future potential to replace MD in tasks such as the prediction of lipophilicity, membrane permeability, or absolute binding free energy (ABFE) -- whose grounding and interpretability may be critical for the development of new drugs and materials.

CARD: Coarse-to-fine Autoregressive Modeling with Radix-based Decomposition for Transferable Free Energy Estimation

Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical computational approaches remain prohibitively expensive due to their reliance on extensive molecular dynamics simulations, while deep learning-based methods are constrained by either less-expressive generative models or input dimensions tied to a specific system, resulting in negligible generalization. To address these challenges, we propose CARD, a generative framework that employs a novel radix-based decomposition to bijectively convert 3D coordinates into mixed discrete-continuous sequences, enabling coarse-to-fine autoregressive modeling with enhanced expressiveness. Notably, the model corresponds to a distribution with zero free energy, serving as a proposal for absolute free energy computation of arbitrary systems without relying on alchemical pathways. Experiments across diverse tasks demonstrate that CARD matches the accuracy of classical computational methods on unseen systems with diverse topologies, while achieving an approximately 40-fold speedup in inference.