Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics (2510.07589v1)

Abstract: Understanding molecular structure, dynamics, and reactivity requires bridging processes that occur across widely separated time scales. Conventional molecular dynamics simulations provide atomistic resolution, but their femtosecond time steps limit access to the slow conformational changes and relaxation processes that govern chemical function. Here, we introduce a deep generative modeling framework that accelerates sampling of molecular dynamics by four orders of magnitude while retaining physical realism. Applied to small organic molecules and peptides, the approach enables quantitative characterization of equilibrium ensembles and dynamical relaxation processes that were previously only accessible by costly brute-force simulation. Importantly, the method generalizes across chemical composition and system size, extrapolating to peptides larger than those used for training, and captures chemically meaningful transitions on extended time scales. By expanding the accessible range of molecular motions without sacrificing atomistic detail, this approach opens new opportunities for probing conformational landscapes, thermodynamics, and kinetics in systems central to chemistry and biophysics.

• The paper introduces TITO, a deep generative model that learns time-integrated transition probabilities to accelerate molecular dynamics simulations.
• It utilizes SE(3)-equivariant neural ODEs to replicate Boltzmann statistics and accurately capture both fast and slow dynamical processes.
• TITO generalizes to larger systems and uncovers rare metastable states while offering orders-of-magnitude computational speedup.

Transferable Generative Models for Multi-Timescale Molecular Dynamics: The TITO Framework

Introduction

The paper introduces Transferable Implicit Transfer Operators (TITO), a deep generative modeling framework designed to bridge the gap between femtosecond-resolved molecular dynamics (MD) and the nanosecond-to-millisecond timescales relevant for chemical and biological processes. TITO directly learns the time-integrated transition probability distributions of molecular systems, enabling the generation of physically realistic molecular trajectories at arbitrarily large lag times. This approach circumvents the computational bottleneck of explicit time integration at femtosecond resolution, offering orders-of-magnitude acceleration while maintaining atomistic detail and transferability across chemical composition and system size.

Figure 1: TITO: A multi–time-scale surrogate model for molecular dynamics, generating ensembles for diverse molecules at arbitrary lag times from a single initial condition.

Methodology

Implicit Transfer Operator Learning

TITO models the transition density $p(\mathbf{x}_{t+\Delta t}|\mathbf{x}_t)$ for arbitrary lag times $\Delta t$ using a continuous normalizing flow (CNF) parameterized by a neural ODE. The velocity field $\mathbf{v}_\theta$ is trained via equivariant flow matching, ensuring the learned dynamics respect molecular symmetries (rotational, permutational). Training data consists of MD trajectories for small molecules and peptides, sampled at femtosecond resolution, from which TITO learns to generate transitions at much larger lag times.

The model architecture extends SE(3)-equivariant graph neural networks with edge features encoding bond types and interaction strengths. The base distribution $p_0$ is adapted for system size using Flory scaling for the radius of gyration, enabling extrapolation to larger molecules.

Training and Evaluation

TITO is trained on the MDQM9-nc dataset (small organic molecules) and the Timewarp dataset (tetra-peptides), with lag times sampled uniformly up to 1–5 ns. The loss function is the conditional flow matching loss, aligning the neural ODE's velocity field with the optimal transport between initial and final configurations over the lag time. Evaluation metrics include Jensen-Shannon divergence (JSD) for equilibrium distributions, VAMP-based metrics for dynamical fidelity, and coverage/precision for conformational space exploration.

Results

Preservation of Boltzmann Statistics and Dynamical Fidelity

TITO-generated trajectories for unseen molecules and peptides accurately reproduce the Boltzmann equilibrium distribution, as quantified by low JSD values relative to reference MD. In cases where TITO samples states not observed in long unbiased MD, these states are validated by replica exchange (RE) MD, confirming that TITO uncovers genuine metastable basins inaccessible to brute-force simulation within practical timeframes.

Figure 3: TITO accurately samples two orders of magnitude slower dynamics than the training data, achieving superior coverage and precision compared to conventional MD.

TITO also recapitulates relaxation transients and implied timescales across three orders of magnitude, demonstrating that the learned transfer operator generalizes to both fast and slow dynamical processes. The model's predictions remain consistent under nested sampling at different time resolutions, indicating that the Chapman–Kolmogorov equation is approximately satisfied and the dynamics are genuinely Markovian.

Figure 2: TITO recapitulates transients, fast vibrations, and potential energies, matching both slow and fast dynamical modes and equilibrium properties.

Extrapolation to Larger Systems

A key result is TITO's ability to extrapolate to peptides up to twice the size of those in the training set. By rescaling the base distribution according to Flory's law, TITO generates physically plausible conformational ensembles and relaxation kinetics for penta-, hexa-, hepta-, and octapeptides. While some compaction and energy drift are observed for the largest systems, the generated structures remain meaningful and can be refined with short MD equilibration.

Figure 4: Extrapolation to larger systems: TITO trained on tetra-peptides generates free energy landscapes and VAMP timescales for longer peptides.

Discovery of Rare and Metastable States

TITO systematically samples metastable states missed by conventional MD but recovered by RE MD, and in some cases predicts novel states that remain stable under subsequent MD refinement. This demonstrates that TITO is not merely interpolating within the training data but is capable of inferring physically valid transitions and basins beyond the reach of brute-force simulation.

Figure 5: Free energy landscape comparison between MD, RE, and TITO for different regions of JSD, illustrating TITO's ability to recover rare states.

Figure 6: TITO recovers states sampled by RE but not accessible by training set-like MD simulations.

Calibration of Accuracy vs. Computational Cost

TITO enables explicit control over the trade-off between simulation fidelity and computational throughput. Equilibrium properties are reproduced at low ODE solver budgets, while accurate kinetics require more solver steps. On a single GPU, TITO achieves up to 10 ms of physical simulation time per day—over four orders of magnitude faster than standard MD for comparable system sizes.

Figure 7: Correlation plot of MD and TITO time-scales for different numbers of ODE steps; error decreases with more ODE steps, enabling calibration of accuracy to compute budget.

Analysis of Generalization and Chemical Similarity

A notable finding is the lack of correlation between TITO's performance (as measured by JSD) and chemical similarity between training and test molecules, both for small molecules (Tanimoto distance) and peptides (Hamming distance). This suggests that generalization is governed more by the diversity of dynamical motifs in the training data than by chemical coverage per se.

Figure 10: TICA JSD vs. chemical similarity for small molecules; no correlation is observed, and test set is well covered by training set.

Figure 12: TICA JSD vs. chemical similarity for tetra-peptides; again, no correlation is observed.

Limitations and Future Directions

TITO currently operates on implicit solvent models and is limited to systems of a few hundred atoms. Extension to explicit solvent, periodic boundary conditions, and larger biomolecular assemblies will require advances in neural architectures (e.g., scalable equivariant GNNs, hierarchical or coarse-grained representations). Thermodynamic transferability (across temperature/pressure) is not yet supported, and generalization to chemically distant systems may require more diverse and mechanistically representative training datasets.

Implications and Outlook

TITO establishes a new paradigm for generative modeling of molecular dynamics, unifying thermodynamic sampling and dynamical prediction in a transferable, data-driven surrogate. By bypassing explicit time integration, TITO enables the paper of slow conformational processes, rare event kinetics, and free energy landscapes at a fraction of the computational cost of traditional MD. The framework is complementary to Boltzmann Generators and machine-learned force fields, offering unique advantages for dynamical observables and transferability.

The lack of dependence on chemical similarity for generalization challenges prevailing assumptions in the field and motivates the design of training datasets that capture the essential physics of molecular dynamics rather than maximizing chemical diversity alone. Hybrid schemes that interleave TITO propagation with short MD refinement, or that combine TITO with coarse-grained or latent space models, are promising avenues for scaling to larger and more complex systems.

Conclusion

TITO demonstrates that deep generative models can learn transferable, physically realistic molecular dynamics across multiple timescales and chemical systems. The approach achieves quantitative agreement with MD for both equilibrium and kinetic observables, uncovers rare and metastable states, and extrapolates to larger molecules with minimal loss of fidelity. By decoupling simulation throughput from the femtosecond time step constraint, TITO paves the way for practical, AI-accelerated molecular simulation and the exploration of processes previously inaccessible to atomistic modeling.