AtomWorld-Mirror: Macro-Step World Modeling of Critical Evolution Backbones for Materials Dynamics

Ziming Pan; Ruge Zhang; Haozhi Han; Junkai Zhou; Xingyuan Chen; Yifeng Chen; Yunquan Zhang; Ting Cao

cs.AIOct 8, 2026

AtomWorld-Mirror: Macro-Step World Modeling of Critical Evolution Backbones for Materials Dynamics

Authors: Ziming Pan, Ruge Zhang, Haozhi Han, Junkai Zhou, Xingyuan Chen, Yifeng Chen, Yunquan Zhang, Ting Cao, +2 more

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

Abstract

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 Li $_3$ N-based anti-perovskite solid electrolyte, macro-step inference delivers a speed up of $10^3$ to $10^4$ 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	$40^{3}$ BCC	Candidates	$\mathcal{C}_{k}(X_{t})$ ; 8 V seeds
Cu / V density	0.0134 / 0.0002	Path input	teacher path summary
Temperature	300 K	Latents	global $32{\times}16$ ; 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.

Panel of Figure 5 — 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	$X_{t}$ , global context $g_{t}$	global latent $z_{t}$ ( $32{\times}16$ ), site embeddings $u_{i}$	yes
Candidate builder	$X_{t}$ , 2NN event support, $k$	$\mathcal{C}_{k}(X_{t})$ from 8 vacancy seeds	yes
Path posterior $q_{\phi}$	$z_{t}$ , $z_{t+k}$ , $s_{\mathrm{path}}$ , $k$	path latent $h_{t}$ (dim 32)	no (training only)
Path prior $p_{\theta}$	$z_{t}$ , $g_{t}$ , $k$	path latent $h_{t}$ (dim 32)	yes
Macro dynamics $F_{\theta}$	$z_{t}$ , $h_{t}$ , $k$	residual to $\hat{z}_{t+k}$	yes
Edit decoder $D_{\theta}$	$u_{i}$ , patch context (dim 64), $\hat{z}_{t+k}$ , $h_{t}$ , $k$	change logit $\ell_{i}$ , type distribution $\pi_{i}$ over {Fe, Cu, Vac}	yes

Appendix

Table 2: Component-level implementation details. Rollout-time availability marks whether a component’s inputs are computable from

X_{t}

and

k

alone.

System	Model	violation% $\cdot$ F1	log-MAE $\cdot$ scale
RPV 3-element	KMC	0% $\cdot$ 1.00	0.00 $\cdot$ 1.00
	Mirror	0% $\cdot$ 0.77	0.21 $\cdot$ 1.05
RPV 10-element	KMC	0% $\cdot$ 1.00	0.00 $\cdot$ 1.00
	Mirror	0% $\cdot$ 0.78	0.32 $\cdot$ 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% $\cdot$ F1	log-MAE $\cdot$ scale
MD teacher	0% $\cdot$ 1.00	0.00 $\cdot$ 1.00
Mirror	0% $\cdot$ 0.84	0.26 $\cdot$ 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% $\cdot$ F1	log-MAE $\cdot$ scale
MD teacher	0% $\cdot$ 1.00	0.00 $\cdot$ 1.00
Mirror	0% $\cdot$ 0.71	0.27 $\cdot$ 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 $\cdot$ scale	$\rho_{T}$
Teacher KMC	violation 0% $\cdot$ F1 1.00	0.00 $\cdot$ 1.00	1.00
Dreamer-style (no constraints)	reach 45.2% $\cdot$ inv 59.2%	4.08 $\cdot$ 0.35	0.35
Endpoint regression	change-F1 0.42 $\cdot$ type-acc 0.45	N/A	N/A
AtomWorld-Mirror	violation 0% $\cdot$ F1 0.91	0.13 $\cdot$ 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\in\{1,\ldots,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\in\{1,\ldots,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% $\cdot$ F1 1.00	log-MAE 0.00 $\cdot$ scale 1.00	$\rho_{T}$ 1.00
Mirror	violation 0% $\cdot$ F1 0.91	log-MAE 0.27 $\cdot$ scale 1.17	$\rho_{T}$ 0.89

Appendix

Table 8: Physical validity and time alignment at the

5.4\times 10^{10}

-atom scale in the RPV steel aging benchmark.

Figure 9: End-to-end speed up of Mirror over OpenKMC for the

5.4\times 10^{10}

-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 $C_{i}$ , 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.

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AtomWorld-Mem: Memory-Restored World States for Long-Horizon Atomistic Evolution

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Open paper AskPDF arXiv

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.

Abstract

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