Organizations: Yonsei University, Seoul, Republic of Korea · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · School of Computer Science, Peking University, Beijing, China · Economics & Technology Research Institute, China National Petroleum Corporation, Beijing, China · Shenzhen Research Institute of Big Data, Shenzhen, China
Atomistic simulation is a fundamental tool for studying long-term materials evolution, from diffusion and defect dynamics to interfacial reactions and fracture. Yet conventional simulators typically advance at microscopic resolution, spending substantial computation on low-impact local updates before reaching structurally consequential states, an evolutionary-resolution bottleneck that limits long-horizon simulation. We propose AtomWorld-Mirror, a time-aware macro-step world model for the critical evolution backbone of atomic systems. For Step-Wise atomistic simulation, AtomWorld-Mirror distills short micro-event segments into physically reachable transitions between key states, jointly predicting sparse structural edits and accumulated physical time through latent macro-step dynamics. Local reachability, inventory conservation, and continuous-time consistency constrain each transition. By amortizing local atomic physics into a reusable latent macro model and replacing explicit micro-event replay with macro-step inference, this formulation provides a path toward substantially faster prediction of long-term materials evolution while preserving structural validity and time semantics. Across five atomic systems, spanning Cu-rich RPV steel irradiation aging, Cu-Zr metallic glass, and Li3N-based anti-perovskite solid electrolyte, macro-step inference delivers a speed up of 103 to 104 times over event-by-event simulation.
Figures & tables
Figure 1: Random timing of key structural evolution within a fixed kinetic simulator replay budget. Each row is one kinetic simulator trajectory at a specified Cu density and random seed; ticks mark Cu-vacancy exchange events within a 1000 -micro-event budget, and the cumulative curves show how these events accumulate across the budget.
Figure 2: Controlled macro-step validation against the teacher simulator. The panels show (a) cumulative structural edits, (b) single-segment expected-time alignment across temperatures, (c) long-trajectory cumulative expected time, and (d) cumulative correctly typed edits for Teacher and Mirror.
Figure 3: Cu-density and temperature ablation matrices for Multi-K teacher-probe rollout. Darker cells denote larger values of the corresponding failure metric.
Figure 4: End-to-end timing diagnostic across lattice sizes and temperatures.
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
Data / Teacher
Value
Student / Optim.
Value
Teacher
atom-vacancy KMC
Student
Mirror macro-step world model
Lattice
403 BCC
Candidates
Ck(Xt) ; 8 V seeds
Cu / V density
0.0134 / 0.0002
Path input
teacher path summary
Temperature
300 K
Latents
global 32×16 ; patch/path 64/32
Event support
2NN hops
Epochs / batch
120 / 32
Train / val
2000 / 400 segments per k
Optimizer
Adam, lr 10−4
Appendix
Table 1: Training and evaluation configuration.
Figure 5: AtomWorld-Mirror architecture. The teacher supplies segments with reachable candidate supports, path summaries, and continuous-time labels. Mirror encodes the configuration and active patch, draws a horizon-conditioned path latent from the posterior during training and the prior during rollout, predicts the macro latent, and decodes a sparse edit, accumulated duration, and reward/energy quantity. Inventory projection precedes the downstream losses, so the projected state consumed during rollout is also the state used for optimization.
Component
Input
Output
Rollout-time
Graph encoder
Xt , global context gt
global latent zt ( 32×16 ), site embeddings ui
yes
Candidate builder
Xt , 2NN event support, k
Ck(Xt) from 8 vacancy seeds
yes
Path posterior qϕ
zt , zt+k , spath , k
path latent ht (dim 32)
no (training only)
Path prior pθ
zt , gt , k
path latent ht (dim 32)
yes
Macro dynamics Fθ
zt , ht , k
residual to z^t+k
yes
Edit decoder Dθ
ui , patch context (dim 64), z^t+k , ht , k
change logit ℓi , type distribution πi over {Fe, Cu, Vac}
yes
Appendix
Table 2: Component-level implementation details. Rollout-time availability marks whether a component’s inputs are computable from Xt and k alone.
System
Model
violation% ⋅ F1
log-MAE ⋅ scale
RPV 3-element
KMC
0% ⋅ 1.00
0.00 ⋅ 1.00
Mirror
0% ⋅ 0.77
0.21 ⋅ 1.05
RPV 10-element
KMC
0% ⋅ 1.00
0.00 ⋅ 1.00
Mirror
0% ⋅ 0.78
0.32 ⋅ 1.06
Appendix
Table 3: RPV steel: physical validity and time calibration at 3 and 10 elements.
Figure 6: End-to-end speed up over the KMC teacher for the RPV steel systems at 263, 293, 333, and 373 K. Bars show runtime and the line shows speed up.
Model
violation% ⋅ F1
log-MAE ⋅ scale
MD teacher
0% ⋅ 1.00
0.00 ⋅ 1.00
Mirror
0% ⋅ 0.84
0.26 ⋅ 1.10
Appendix
Table 4: Cu–Zr metallic glass: physical validity and time calibration.
Figure 7: End-to-end speed up over the MD teacher for the Cu–Zr metallic glass across temperature and system size.
Model
violation% ⋅ F1
log-MAE ⋅ scale
MD teacher
0% ⋅ 1.00
0.00 ⋅ 1.00
Mirror
0% ⋅ 0.71
0.27 ⋅ 1.07
Appendix
Table 5: Li 3 N-based anti-perovskite solid electrolyte: physical validity and time calibration.
Figure 8: End-to-end speed up over the MD teacher for the Li 3 N-based anti-perovskite solid electrolyte across temperature and system size.
Model
Physically valid sparse edits
log-MAE ⋅ scale
ρT
Teacher KMC
violation 0% ⋅ F1 1.00
0.00 ⋅ 1.00
1.00
Dreamer-style (no constraints)
reach 45.2% ⋅ inv 59.2%
4.08 ⋅ 0.35
0.35
Endpoint regression
change-F1 0.42 ⋅ type-acc 0.45
N/A
N/A
AtomWorld-Mirror
violation 0% ⋅ F1 0.91
0.13 ⋅ 1.00
1.01
Appendix
Table 6: Constraint and formulation baselines against AtomWorld-Mirror on the shared RPV steel aging held-out split (Cu 0.0134 , 300 K, k∈{1,…,1024} ). The table quantifies the contributions of reachability, inventory conservation, and duration modeling.
Horizon k
128
256
512
1024
Coverage
0.889
0.906
0.780
0.649
Appendix
Table 7: Measured macro-step inference within the operating range k∈{1,…,1024} on NVIDIA A100 GPUs. The table reports representative horizons; coverage is the fraction of attempted segments that yield a usable macro sample after terminal and no-op filtering.
Model
Physically valid edits
Single-segment time
Cumulative clock
OpenKMC
violation 0% ⋅ F1 1.00
log-MAE 0.00 ⋅ scale 1.00
ρT 1.00
Mirror
violation 0% ⋅ F1 0.91
log-MAE 0.27 ⋅ scale 1.17
ρT 0.89
Appendix
Table 8: Physical validity and time alignment at the 5.4×1010 -atom scale in the RPV steel aging benchmark.
Figure 9: End-to-end speed up of Mirror over OpenKMC for the 5.4×1010 -atom RPV steel aging benchmark over a 50 -year physical timescale. Bars show runtime and the line shows speed up.
Figure 10: Cu-cluster visual evolution from initial to final states in an RPV steel aging simulation. Each point denotes a Cu atom in the teacher-simulated lattice. Colors use a shared red–pink-purple–blue scale for the actual 1NN/2NN-connected Cu cluster size Ci , with red denoting single-Cu clusters and blue denoting the maximum cluster size in this trajectory.
Family
What it changes
Physical clock
Examples
Trajectory accelerators
the accepted event sequence
not directly traceable once event order is altered
RL/PPO policies for KMC, neural surrogate event samplers ( Schulman et al., 2017 ; Tang et al., 2024 ; Bojesen, 2018 )
Analytical accelerators
rates or grouping of fast events; event-level execution retained
preserved, every effective event still resolved
superbasin KMC, adaptive KMC ( Fichthorn and Lin, 2013 ; Henkelman and Jónsson, 2001 )
Rate-scaling accelerators
fast-event rates; event-level execution retained
sampled from scaled rates; fidelity to original kinetics depends on scaling regime
Rate Scaling KMC ( Lin et al., 2019 )
AtomWorld-Mirror
the prediction unit: sparse macro edit between backbone states
predicted explicitly as path-conditioned accumulated duration
this work
Appendix
Table 9: Where AtomWorld-Mirror sits among KMC acceleration families.
High-fidelity atomistic evolution over long timescales requires more than observing the current crystal configuration. Instantaneous atomistic snapshots are often incomplete: locally similar configurations can correspond to different hidden dynamical contexts, future event preferences, and waiting-time scales. We argue that this snapshot ambiguity makes long-horizon atomistic evolution fundamentally a memory-based world-state restoration problem. To address this, we introduce AtomWorld-Mem, a memory-restored atomistic world model that recovers the latent world state missing from instantaneous crystal snapshots. AtomWorld-Mem treats the evolving alloy as an AtomWorld: spatial encoders write multi-scale atomistic keyframes from dense local topology and sparse long-range defect context, while short-term event memory and long-term structural memory integrate these keyframes across time to restore a future-predictive evolutionary state. The restored state is used to prioritize legal vacancy-mediated events under single-event Kinetic Monte Carlo (KMC) constraints, while event legality, physical execution, and residence-time updates remain governed by the underlying simulator. Empirically, AtomWorld-Mem improves long-horizon atomistic progress under fixed microscopic event budgets while maintaining high-fidelity evolution across energetic, structural, and vacancy-transport observables. It further transfers zero-shot across diverse unseen alloy-temperature AtomWorlds, suggesting that the learned memory-restoration mechanism captures reusable principles of hidden-state inference rather than a system-specific local energy heuristic. These results position memory-restored world-state modeling as a promising route toward efficient, physically grounded, and transferable atomistic evolution.
Tian Luo, Ruge Zhang, Haozhi Han +5
Sichuan University, Chengdu, China · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China +2
Understanding and predicting microstructure evolution is central to materials design, yet purely data-driven spatiotemporal learning models often suffer from limited physical consistency and degraded long-term prediction accuracy. In this work, we introduce a physics-guided fully convolutional spatiotemporal learning framework for microstructure evolution prediction. Unlike prior self-supervised approaches, the proposed method explicitly incorporates governing physical equations into the training objective, thereby encouraging the learned dynamics to remain consistent with known thermodynamic and kinetic laws. This physics-guided formulation improves predictive accuracy, long-horizon stability, and robustness across spatial resolutions and temporal prediction settings. Extensive experiments for spinodal decomposition demonstrate that incorporating physics-guided residual regularization leads to more faithful reproduction of microstructural morphology, statistics, and evolution trends compared with purely data-driven baselines. The proposed framework preserves the scalability and computational efficiency of fully convolutional architectures while bridging the gap between high-fidelity physics-based simulations and data-driven surrogate modeling, offering a reliable and efficient surrogate-modeling step toward digital-twin-enabled microstructure evolution prediction.
Michael Trimboli, Wenxi Liu, Xianqi Li
Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL, 32901, USA
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.
Kexin Wu, Luonan Chen, Renxiao Wang
Department of Medicinal Chemistry, School of Pharmaceutical Sciences, Fudan University, 826 Zhangheng Road, Shanghai 201203, People's Republic of China · School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China