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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, Yunxin Liu, Kun Li

arXiv:2610.11527v1cs.AIcond-mat.mtrl-sci

TL;DR

Conventional atomistic simulation spends substantial computation on low-impact microscopic updates before structurally consequential states. AtomWorld-Mirror distills short simulator segments into physically reachable macro transitions that jointly predict sparse edits and accumulated time. Across five atomic systems, it reports 103–104× speedups over event-by-event simulation while preserving structural and temporal accuracy.

  • Problem

    Conventional atomistic simulators advance through microscopic updates despite persistent structural progress occurring sparsely, creating an evolutionary-resolution bottleneck for long-horizon simulation.

    Source: §1 · pp. 1–2

  • Method

    AtomWorld-Mirror distills atomistic simulator trajectories into macro-step predictions of reachable sparse edits and path-conditioned physical duration, constrained by reachability and inventory conservation.

    Source: §1 · p. 2

  • Results

    103–104× speedups over event-by-event simulation are reported across five atomic systems with KMC and MD teachers, alongside physically valid rollouts and structural and temporal accuracy.

    Source: §1 · p. 2, §6 · p. 9

  • Takeaways & Limitations

    The framework provides physically constrained macro evolution that replaces microscopic replay without discarding structural or temporal information.

    Source: §1 · p. 2

    The current operating range reaches k = 1024; extending support to larger species inventories and continuously evolving structures remains future work.

    Source: K Limitations and future work · p. 19

Abstract

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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.

1 Introduction

Conventional atomistic simulators spend computation on low-impact updates even though persistent structural progress occurs sparsely. AtomWorld-Mirror compresses microscopic trajectories into physically constrained macro transitions that retain structural and temporal information, with reported speedups of 103–104× across five atomic systems.

1 Introduction

  • Conventional simulators treat state changes uniformly, although transient fluctuations and sparse, seed-dependent events contribute differently to persistent structural progress.The introduction calls the resulting computation spent on low-impact intermediate states an evolutionary-resolution bottleneck.Source: §1 · p. 1, Figure 1 · p. 2
  • AtomWorld-Mirror distills simulator trajectories into reachable sparse edits and accumulated physical duration, advancing structure and clock without replaying intervening events.Local reachability, inventory conservation, and continuous-time consistency constrain transitions.Source: §1 · p. 2
  • 103–104× speedups over event-by-event simulation are reported across five atomic systems with KMC and MD teachers.The rollouts are described as physically valid while preserving structural and temporal accuracy.Source: §1 · p. 2

2 Related work

Prior work describes atomistic dynamics through distinct microscopic representations and has developed several ways to accelerate trajectory traversal or amortize local calculations.

Fine-Grained Atomistic Dynamics

  • MD integrates atomic coordinates through short time steps, while KMC samples state-dependent events and advances a residence-time clock.Vacancy-mediated KMC represents RPV steel aging through local events, transition rates, and physical-time labels.Source: §2 · p. 3

Accelerated Atomistic Dynamics

  • Superbasin KMC aggregates recurrent low-barrier events, rate-scaling KMC reduces fast-event rates, and adaptive KMC discovers mechanisms and constructs event tables during simulation.These approaches reduce trajectory-traversal costs in different ways.Source: §2 · p. 3
  • Learned potentials, graph and equivariant simulators, and physics-informed models amortize local force and interaction calculations across atoms.The related work also notes high-performance OpenKMC implementations for very large systems.Source: §2 · p. 3

3 Problem Setup

The problem setup frames long-horizon atomistic modeling as selecting structurally consequential states from fine-grained simulator trajectories while retaining the progress and physical time between them.

3.1 Micro-event resolution and key-state evolution

  • Long-term behavior concentrates in a small set of structurally decisive states, so the learning problem is to identify and retain their structural progress.The setup contrasts these key states with trajectories composed of many local integration steps or atom-vacancy events.Source: §3.1 · p. 3, §3 · p. 3
  • The critical evolution backbone retains system-dependent milestones, with macro horizons ranging from 1 to 1024 micro-events and ending at the next important state.Examples include Cu-cluster growth and connectivity milestones in RPV steel and topology-change signatures in MD cage-swap systems.Source: §3.1 · p. 3

3.2 Macro-step state-time objective

  • The macro-step objective jointly predicts sparse edits over physically reachable candidate sites and the physical duration of the teacher segment.Most lattice sites remain unchanged, making full-state prediction inefficient; endpoint edits and path duration together define a macro transition.Source: §3.2 · p. 3

3.3 KMC supervision of continuous time

  • KMC supervision models expected macro time as path-conditioned because similar endpoints can accumulate different durations along different rate environments.The expected waiting time at a state is 1/R(Xt); realized duration records one stochastic draw and serves as an uncertainty diagnostic.Source: §3.3 · p. 4

4 AtomWorld-Mirror

AtomWorld-Mirror distills teacher-simulated atomistic segments into macro-step predictions of reachable sparse edits, accumulated duration, and next latent state. Reachability, inventory conservation, and path-conditioned timing constrain the transitions used in rollout.

4 AtomWorld-Mirror

  • AtomWorld supplies teacher trajectories, local transition rules, and physical-time labels for Mirror, a student world model of backbone state-time transitions.The primary instantiation uses atomistic KMC; other Step-Wise simulators with sparse structural states and physical-time supervision can use the same teacher interface.Source: §4 · p. 4

4.1 Teacher supervision

  • Each teacher segment supervises endpoint edits, path summaries, reachable supports, and expected and realized duration; expected CTMC time is the primary duration target.The supervised sample also includes the start state and horizon.Source: §4.1 · pp. 4–5

4.2 Mirror macro-step world model

  • Mirror uses horizon-conditioned path latents to represent distinct admissible paths from the same state, then predicts a next latent for macro-step dynamics.Training conditions the posterior path latent on the endpoint and teacher path summary; rollout uses a prior.Source: §4.2 · p. 5

4.3 Reachability-constrained sparse edits

  • The edit decoder predicts changes only on teacher-reachable candidate sites, while projection preserves material counts and copies sites outside the patch unchanged.Paired vacancy–atom transport implements the projection, which is applied before latent, reward, and duration losses.Source: §4.3 · pp. 5–6

4.4 Continuous-time duration modeling and loss

  • Expected macro duration is predicted in log space with a residual that corrects the start-state estimate for rate changes along the teacher path.Realized duration remains stochastic and is modeled as an auxiliary conditional lognormal target.Source: §4.4 · p. 6
  • At each step, Mirror filters candidate horizons for reachability and inventory legality, ranks survivors by predicted structural progress per physical time, and advances state and clock.The horizon is selected independently from 1 to 1024 micro steps.Source: §4.4 · p. 6
  • Backbone persistence stays above 0.98 across horizons, while largest-Cu-cluster identity reaches 0.9066 across trajectory seeds.The sensitivity analysis spans 1 to 1024 micro steps on 16 held-out trajectories.Source: §4.4 · p. 6

5 Experimental design

The experiments evaluate AtomWorld-Mirror across five atomic systems, using KMC and MD teachers to test projected validity, time alignment, closed-loop behavior, and efficiency. Macro-step inference is compared with event-by-event simulation and tested across system sizes, temperatures, and material systems.

5.1 Experimental scope

  • Across five systems, Mirror maintains zero reachability and inventory violations; the evaluation spans RPV steels, Cu–Zr metallic glass, and Li3N-based electrolyte.The RPV systems use a KMC teacher, while Cu–Zr and Li3N use MD teachers and cage-swap topology events as macro-step boundaries.Source: §5.1 · pp. 6–7
  • The system set tests state-time macro modeling across composition, structural order, and simulator type, including alloy aging, amorphous-alloy relaxation, and ionic migration.The systems include Cu-rich precipitate formation in RPV steel, cage-swap dynamics in Cu–Zr, and ionic migration in Li3N-based solid electrolyte.Source: §5.1 · p. 7
  • Mirror distills simulator segments into sparse reachable edits, next latent states, and accumulated physical duration while retaining local-support and inventory conditions.The teacher interface is applied to event-driven KMC and MD-generated topology-change segments.Source: §5.1 · p. 7

5.2 Event-driven instantiation

  • The KMC instantiation evaluates projected edit validity, expected-duration alignment, closed-loop consistency, and timed macro-inference efficiency.Structural quality uses edit F1 and type accuracy; expected time is evaluated against a path-conditioned CTMC target with log-MAE, log-RMSE, log-correlation, and scale ratio.Source: §5.2 · pp. 7–8

5.3 Closed-loop validity and ablations

  • Closed-loop teacher-probe ablations vary Cu concentration and temperature and assess candidate-support validity, inventory preservation, and path-conditioned duration.The comparisons include a KMC teacher, a fixed-state copy baseline, removal of reachability or inventory constraints, and a start-state CTMC duration baseline.Source: Figure 3 · p. 7, §5.3 · p. 8

5.4 Long-horizon diagnostics and efficiency

  • A 10^3–10^4× speedup over event-by-event simulation is reported across lattice size, temperature, and material system.The timing includes candidate construction, projection, benchmark orchestration, and batched neural inference for one adaptive macro transition.Source: §5.4 · p. 8, Figure 4 · p. 8
  • One macro step replaces an average of 480 teacher micro-events and advances expected time by 12.98 seconds; inference cost stays near-constant with system size.A model trained on 403 runs is reported to run on larger configurations without retraining.Source: §5.4 · p. 8
  • A 50-year autonomous closed-loop rollout is evaluated on the 5.4 × 10^10-atom RPV steel aging system across four temperatures.The rollout is reported in Appendix I.Source: §5.4 · p. 8

6 Conclusion

The paper presents AtomWorld-Mirror as a simulator-to-world-model distillation method for time-aware macro-step modeling over critical evolution backbones. Across five atomic systems, it reports physically valid rollouts and 103–104× speedups over event-by-event simulation.

6 Conclusion

  • AtomWorld-Mirror converts step-wise atomistic teachers into time-aware macro-step models over critical evolution backbones.The method predicts reachable sparse edits and path-conditioned physical time while preserving material inventory.Source: §6 · p. 9
  • Across five atomic systems with KMC and MD teachers, AtomWorld-Mirror achieves physically valid rollouts and 103–104× speedups over event-by-event simulation.The conclusion characterizes the rollouts as preserving structural and temporal accuracy.Source: §6 · p. 9
  • The reported framework combines reachable sparse edits, path-conditioned physical time, and material-inventory preservation in its macro-step predictions.These properties are presented as part of the method's conclusion.Source: §6 · p. 9

A Training details and parameters

The appendix identifies a training and evaluation configuration table and reports the hardware and source of timing values.

A Training details and parameters

B Implementation details by component

AtomWorld-Mirror implements macro-step prediction through projected, physically constrained transitions and evaluates the formulation across KMC and MD systems. The section also compares its constraints with alternative formulations and describes teacher-forced evaluation and adaptive horizon selection.

B Implementation details by component

  • The architecture encodes configuration and active-patch context, predicts horizon-conditioned macro dynamics, and decodes sparse edits, duration, and reward or energy after inventory projection.Training samples the path latent from the posterior; rollout samples it from the prior, and the projected state also feeds downstream losses.Source: Figure 5 · p. 14, C Macro-step pseudocode · pp. 14–15

D Generality across material systems and teacher types

  • The evaluation extends the state-time interface across KMC and MD teachers, with MD macro steps ending at cage-swap topology events and timed by elapsed MD time.The MD systems have no vacancy species; snap-to-lattice mapping conserves inventory, with species edits represented as paired swaps.Source: D Generality across material systems… · p. 15

D.1 RPV steel, multi-component (KMC teacher)

  • Increasing RPV steel composition from 3 to 10 elements roughly doubles speed up because added chemistry raises teacher per-event cost while macro-step cost remains tied to the candidate patch.The RPV systems retain the atom-vacancy KMC teacher.Source: D Generality across material systems… · p. 15, §D.1 · p. 16

D.2 Cu–Zr metallic glass (MD teacher)

  • Cu–Zr achieves edit F1 0.84 and duration scale 1.10; its MD teacher resolves femtosecond steps between rare cage swaps, while higher temperature shortens each macro step’s covered interval.Cu–Zr provides the largest speed up in the study.Source: §D.2 · p. 16

D.3 Li3N-based anti-perovskite solid electrolyte (MD teacher)

  • The electrolyte reaches edit F1 0.71 and duration scale 1.07, with well-separated ionic-migration topology events keeping the duration target sharp.Source: §D.3 · p. 17

E Separating the macro-step formulation from learned dynamics

  • AtomWorld-Mirror raises reachable edits from 45.2% to 100% and cumulative clock ratio from 0.35 to 1.01, while matching Dreamer-style wall-clock time within 0.5%.It reaches change-F1 0.91 with path-conditioned duration modeling, versus 0.42 for the endpoint regressor, which has no duration output.Source: E Separating the macro-step… · p. 17

F Teacher-forced long-trajectory protocol

  • The teacher-forced protocol feeds teacher states at each segment to isolate duration-scale error, horizon-selection bias, and reward misalignment from autonomous rollout drift.It reports cumulative expected-time curves, selected-horizon histograms, stop reasons, and cumulative energy-error summaries.Source: F Teacher-forced long-trajectory… · p. 18

G Adaptive horizon selection

  • Adaptive horizon selection ranks legal candidates after projection; selected-horizon histograms track local configuration difficulty, while rejected candidates yield recorded stop reasons.Source: G Adaptive horizon selection · p. 18

H Macro-step inference over k ∈{1, . . . , 1024}

Macro-step cost is tied to the local candidate patch rather than total atom count, and a checkpoint trained at 403 applies to larger configurations without retraining.

H Macro-step inference over k ∈{1, . . . , 1024}

  • Macro-step inference cost is set by the event-neighborhood candidate patch, stays near-constant in total atom count, and a checkpoint trained at 403 applies to larger configurations without retraining.Source: H Macro-step inference over k ∈{1, . .… · p. 18
  • One macro step covers 480 teacher micro events on average and advances the physical clock by 12.98 seconds of accumulated expected time.Measurements use the prior forward pass plus inventory projection on held-out active patches over k ∈ {1, . . . , 1024}.Source: H Macro-step inference over k ∈{1, . .… · p. 18
  • Coverage falls from 0.889 at k = 128 to 0.649 at k = 1024, making the efficiency-coverage relationship explicit as longer horizons replace more replay.Source: H Macro-step inference over k ∈{1, . .… · p. 18

I 54-billion-atom RPV steel aging benchmark

The 5.4 × 10^10-atom RPV steel benchmark tests a 50-year autonomous rollout across four temperatures. Mirror retains physically valid edits and substantial cumulative time alignment at that scale.

I 54-billion-atom RPV steel aging benchmark

J RPV steel aging visualization

  • The aging visualization shows Cu-cluster evolution in a vacancy-mediated KMC trajectory, with full-lattice views and enlarged sub-volumes; colors encode cluster size.Cluster sizes are computed on the full periodic BCC lattice from the teacher configuration.Source: J RPV steel aging visualization · p. 19

K Limitations and future work

The paper positions AtomWorld-Mirror as a macro-transition approach for long-horizon evolution and identifies broader teacher coverage, larger species inventories, and continuously evolving structures as future methodological scope.

K Limitations and future work

  • The study evaluates controlled simulator teachers, while broader simulator-teacher combinations and distributed deployment remain future work.Source: K Limitations and future work · p. 19
  • The current operating range reaches k = 1024; larger species inventories and topology criteria for continuously evolving structures remain next methodological steps.Source: K Limitations and future work · p. 19

L Expanded related-work discussion

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