Neural Stochastic Forecasting for Lateral Molecular Diffusion Simulations

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

Molecular dynamics (MD) simulation is computationally demanding, particularly for large-scale systems requiring long-term analysis. Accurate forecast of the outcomes of a MD simulation is not only an attractive scientific challenge but also has substantial practical value. In this work, we developed a data-driven framework, termed ASTEROID (Advanced Spatiotemporal TransformER fOr Inferring Dynamics), that can directly predict multi-step atomic coordinates, avoiding conventional iterative integration. For this purpose, our ASTEROID reformulates MD trajectories as high-dimensional spatiotemporal sequences and integrates the Spatiotemporal Information (STI) Transformation equation into a Transformer architecture. The core innovation of ASTEROID lies in its ability to model multiscale spatiotemporal dependencies. In particular, for spatial dependencies, a local-global self-attention mechanism captures both short- and long-range interactions. For temporal dependencies, an encoder-decoder structure integrates global context with autoregressive forecasting. ASTEROID was evaluated on several quantum-mechanics derived molecular datasets. Our results indicate that ASTEROID achieved not only a higher level of accuracy in multi-step prediction than existing methods on various benchmarks, but also significantly reduced computational cost of conventional MD simulation. Moreover, the model supports iterative multi-step forecasting over an extended time scale. This work establishes a robust and generalizable data-driven paradigm for accelerating MD simulations.