Accelerating Long-Term Molecular Dynamics with Physics-Informed Time-Series Forecasting

TL;DR

This work tackles the prohibitive cost and reliability issues of long-horizon ab initio MD by reframing MD as displacement-based time-series forecasting. It introduces PhysTimeMD, which predicts future atomic displacements with any time-series backbone while enforcing physical plausibility via a Morse-potential loss (PIT) during training and a real-time physics-informed correction (PII) during inference. Key contributions include the displacement-based formulation, DFT-informed Morse potential parametrization, and extensive AIMD-based benchmarking showing improved accuracy and near-zero physical violations across diverse materials, with substantial speedups over DFT: thousands of steps can be generated in minutes rather than hours. The method delivers stable, physically meaningful trajectories and provides a scalable, transferable approach for long-term MD simulations applicable to materials science and biophysics.

Abstract

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.

Figures (5)

• Figure 1: Overview of the PhysTimeMD framework. The framework takes as input a sequence of atomic positions over the past $H$ timesteps and converts them into relative displacements for each atom (e.g., $\Delta_{i,t}$ and $\Delta_{j,t+1}$ represent the movement vectors of atoms $i$ and $j$ between consecutive steps). Then, it uses a time-series forecaster to predict $L$-step future displacements. These predictions are then integrated to reconstruct future atomic positions (see Sec. \ref{['sec:framework']}). A physics-informed mechanism, guided by the Morse potential based on the distance between 2 atoms (e.g, $d^{i,j}$), refines the predicted configurations through a physics-based loss during training (see Sec. \ref{['sec:pit']}) and a physics-based correction during inference (see Sec. \ref{['sec:pii']}), ensuring adherence to physical constraints.
• Figure 2: Radar plot comparing forecasting error ($\text{MAE}_\Delta$) and normalized physical violation rate $V_r$ (%) across datasets G (left) and F (right). The lower the metrics the better the results. Each axis represents one of the four baseline architectures—TimeMixer, ITransformer, Mamba, and TSMixer—with and without the PhysTimeMD framework, highlighting improvements in both accuracy and physical consistency.
• Figure 3: Effect of $\lambda$ on $\text{MAE}_\Delta$ performance for TimeMixer and Mamba on Dataset A. Each curve illustrates how careful tuning of this hyperparameter can positively influence prediction accuracy.
• Figure 4: Diffusivity computed from ground-truth trajectories (left), PhysTimeMD-generated trajectories (middle), and TimeMixer-generated trajectories (right).
• Figure 5: Comparison of TSMixer and PhysTimeMD-enhanced TSMixer on Dataset E. We visualize the predicted positions of an atom (the same observation was observed for other atoms), each along the three Cartesian axes. The model TSMixer without physics-informed regularization ($\lambda=0$) exhibits divergence (after 200 timesteps), while incorporating the PhysTimeMD term stabilizes rollout and significantly reduces error.