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

Tian Luo, Ruge Zhang, Haozhi Han, Yifrng Chen, Yunquan Zhang, Yunxin Liu, Ting Cao, Kun Li

arXiv:2609.31133v1cs.AIcond-mat.mtrl-sci

TL;DR

Similar atomistic snapshots can conceal different future dynamics, limiting long-horizon event reasoning from the current configuration alone. AtomWorld-Mem restores hidden context from temporal memory to prioritize legal KMC events; it reports up to 420× fixed-budget acceleration alongside fidelity across key observables and transfer to unseen alloy–temperature systems.

  • Problem

    Similar local atomistic observations can correspond to different hidden contexts, future event preferences, and waiting-time scales, leaving snapshots alone insufficient for long-horizon prediction.

    Source: §1 · p. 1

  • Method

    AtomWorld-Mem combines multi-scale spatial keyframes with short- and long-term memory to restore latent context and prioritize legal vacancy-mediated events under single-event KMC constraints.

    Source: §1 · p. 2, §2.1 · p. 3, §3.1 · p. 4

  • Results

    Up to 420× fixed-budget acceleration is reported with alignment to reference energetic, structural, and vacancy-transport trends, plus zero-shot transfer across unseen alloy–temperature systems.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Across progress, fidelity, ablation, and transfer tests, memory-restored states outperform snapshot-only reasoning while remaining physically grounded.

    Source: §6 · p. 9

    Experiments focus on vacancy-mediated BCC alloy evolution, and the biased trajectory distribution is not guaranteed to satisfy detailed balance or the stationary path measure of unbiased KMC.

    Source: §3.2 · p. 5, §6 · p. 9

Abstract

from arXiv · show

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.

1 Introduction

Long-horizon atomistic evolution is difficult to guide from snapshots alone because similar local configurations can hide different future dynamics. AtomWorld-Mem restores that hidden context from memory and uses it to prioritize legal events.

Motivation

  • Instantaneous rates preserve physical consistency but do not reveal whether an event is a reversible fluctuation or one that drives structural evolution, so effort can be spent in metastable regions.This can delay access to rare but consequential transitions under practical budgets.Source: §1 · p. 1

Snapshot ambiguity

  • Similar local configurations can lead to different future event distributions and waiting-time scales, making a static snapshot insufficient for long-horizon event reasoning.The missing information is the evolving system's latent world state, which summarizes hidden dynamical context.Source: §1 · p. 1, Figure 1 · p. 2

AtomWorld-Mem

  • AtomWorld-Mem restores a latent evolutionary state by combining multi-scale atomistic keyframes with short-term event memory and long-term structural memory.The Keyframe Writer combines dense local topology with sparse long-range defect context; the memories integrate keyframes across time.Source: §1 · p. 2
  • The restored state guides prioritization within the admissible event space, while single-event KMC execution preserves physical time semantics.Event legality, physical execution, and residence-time updates remain governed by the underlying simulator.Source: §1 · p. 2

Results

  • Up to 420× fixed-budget acceleration is achieved while rollouts remain aligned with reference energetic, structural, and vacancy-transport trends; memory ablations and zero-shot transfer further support the approach.Short-term memory supports recent-event reasoning and vacancy arrival, while long-term memory supports structural-context accumulation and rollout fidelity.Source: §1 · p. 2

2 Problem Formulation

The learned model receives partial observations rather than the complete microscopic configuration and must restore hidden evolutionary context. Its policy prioritizes legal KMC events, while the underlying process governs physical execution and time advancement.

2 Problem Formulation

  • The complete configuration determines legal events, physical transition rates, and subsequent evolution, but the learned model receives structured partial observations and must infer hidden context.The learned model's decision problem is therefore based on incomplete observation of the AtomWorld.Source: §2 · pp. 2–3
  • Each decision executes exactly one physically admissible vacancy-mediated exchange from the legal event set.The legal set is determined by the current microscopic configuration.Source: §2 · p. 3
  • Conventional rejection-free KMC samples legal events in proportion to their physical base rates, preserving micro-kinetic consistency but not explicitly identifying events consequential for long-horizon structure.The passage distinguishes passive rate-proportional selection from long-horizon event reasoning.Source: §2 · p. 3

2.1 Partial Observation and Legal Action Space

  • The model observes a vacancy-centered local graph over 1NN–4NN shells and sparse defect tokens, while its decisions remain restricted to legal events.Together, these observations define a partial-observation, event-level control problem rather than unconstrained atomic move generation.Source: §2.1 · p. 3

2.2 Memory-Based State Restoration

  • Similar local observations may hide different dynamical contexts, future event preferences, waiting-time scales, and structural trajectories, so a local snapshot is not generally predictive over long horizons.The formulation treats atomistic decision making as latent-state restoration under partial observability.Source: §2.2 · p. 3
  • AtomWorld-Mem writes spatial keyframes and infers a memory-restored latent state from those keyframes and past actions.The restored state represents hidden context useful for future evolution, not an unconstrained generative simulator.Source: §2.2 · p. 3
  • The policy acts on the restored state but supports only legal KMC events, keeping action selection within the legal event set.The formulation joins memory-based state restoration to constrained event prioritization.Source: §2.2 · p. 3

2.3 Training Objective under KMC Constraints

  • Training targets long-horizon progress under a fixed legal-event budget, while the underlying KMC process governs event legality, physical execution, and time advancement.Learning changes the rule for prioritizing legal events under partial observability, not the physical simulation steps.Source: §2.3 · p. 3

3 AtomWorld-Mem

AtomWorld-Mem combines multi-scale spatial keyframes with short- and long-term memory to restore evolutionary context. It uses that context to prioritize legal KMC events and reason about waiting times while retaining simulator-governed execution and residence-time updates.

3.1 Architecture and Formulation

  • Dense local topology and sparse long-range defect context form keyframes that are spatial inputs to memory, not complete states.The dense pathway captures topology relevant to immediate legal transitions; the sparse pathway captures context for slower structural evolution.Source: §3.1 · p. 4
  • Short-term event memory integrates recent legal events, while long-term structural memory accumulates slower evolutionary biases into a restored state for event preference and time-scale reasoning.The two memory scales capture recent transition competition and longer-run structural context, respectively.Source: §3.1 · p. 4
  • Event scores depend on restored context and are fused with KMC and energetic priors to prioritize already legal events, not generate unconstrained moves.Similar local descriptors can have different long-horizon consequences in different hidden contexts.Source: §3.1 · p. 4
  • The policy learner uses PPO with a shaped reward and a memory-conditioned critic, whose value estimates reflect restored evolutionary context rather than snapshots alone.The actor objective also includes physics and time-consistency terms.Source: §3.1 · pp. 4–5

3.2 Restored-State Time Consistency

  • Residence-time updates retain the underlying simulator's rules, but biased trajectories are not guaranteed to reproduce unbiased KMC path statistics.The paper defines fidelity by legal-event execution, KMC-grounded time updates at visited states, and agreement with reference energetic, structural, and vacancy-transport observables.Source: §3.2 · p. 5
  • Event preference and waiting-time readout share a hazard field, with a consistency loss aligning event probabilities and learned waiting-time statistics to KMC-based targets.The loss calibrates and diagnoses the restored state's local hazard landscape; it is not a detailed-balance constraint.Source: §3.2 · p. 5

4 Experiments

The experiments test memory-restored state modeling through fixed-budget progress, trajectory fidelity, memory ablations, and zero-shot transfer. Across these tests, AtomWorld-Mem improves progress while maintaining alignment with reference trends and improving energy-drop trajectories in unseen domains.

4.2.1 Fixed-Budget Atomistic Progress

  • Adding memory raises AF from 66.19× to 420.05× at 0.18% Cu and from 11.13× to 51.25× at 1.34% Cu.Figure 3 shows the advantage persisting through 100k legal KMC steps; Figure 2 reports a 186× average gain across tested Cu concentrations.Source: Table 1 · p. 6, §4.2.1 · pp. 6–7, Figure 3 · p. 6

4.1 Experimental Setup

  • Experiments use diffusion-driven Fe–Cu evolution and matched initial-state families with equal legal-event budgets, isolating event-prioritization quality from rollout length.The evaluation covers fixed-budget progress, trajectory fidelity, memory ablations, and zero-shot transfer.Source: §4.1 · p. 6, §4.2.1 · p. 6, §4.2 · p. 6

4.2 Evaluating Memory-Restored AtomWorld Modeling

  • The evaluation tests whether restored latent evolutionary context improves fixed-budget progress, trajectory-level fidelity, memory ablations, and zero-shot transfer.Methods are compared using matched event budgets where applicable.Source: §4.2 · p. 6, §4.2.1 · p. 6

4.2.2 Restored-State Fidelity and Correctness

  • Across six trajectory-level observables, AtomWorld-Mem remains broadly aligned with Zacros in physical-time space despite biased legal-event selection.The comparison covers energetic, structural, and vacancy-transport behavior; exact reproduction of unbiased KMC paths or detailed balance is not claimed.Source: Figure 4 · p. 7, §4.2.2 · p. 7

4.2.3 Memory Ablation: Does Memory Restore the Missing State?

  • At 0.18% Cu, the full model reaches AF 418.44× and DynErr 0.192; either memory scale improves progress and fidelity over snapshot-only reasoning.Snapshot-only reasoning has large TimeErr and DynErr, while the full model performs best across learned variants.Source: Table 2 · p. 7, §4.2.3 · p. 8

4.2.4 Zero-Shot Transfer Across AtomWorlds

  • Without finetuning, AtomWorld-Mem improves fixed-budget energy-drop trajectories in all 16 unseen BCC alloy–temperature domains, with median AUC gain 22.9× and maximum 52.1×.Dynamics-fidelity error is small or moderate for most domains, with larger deviations mainly in refractory systems.Source: §4.2.4 · p. 8, Figure 5 · p. 8

5 Related Work

Prior work advances atomistic systems through physically admissible, rate-governed events and develops world models from partial observations. AtomWorld-Mem combines these perspectives by using memory to rank legal KMC events while leaving physical execution and timing to the simulator.

Kinetic Monte Carlo and policy-guided atomistic kinetics

  • KMC and its adaptive, accelerated, ML-assisted, and policy-guided variants improve event discovery, local updates, rate estimation, or transition selection under physical constraints [18] [22] [23] [26].These approaches typically use current local configurations or aggregate sampling efficiency, leaving hidden dynamical context and long-horizon event preferences unaddressed [22].Source: §5 · p. 8

World models and latent dynamics under partial observability

  • AtomWorld-Mem uses memory to restore hidden dynamical context for legal-event ranking while retaining KMC-grounded execution and timing [37].The paper distinguishes this role from latent transition imagination and from snapshot-conditioned event selection.Source: §5 · p. 8
  • World models and latent-dynamics methods learn compact states from partial observations for prediction, planning, and control [28] [29] [30] [31] [32].They often learn or imagine latent-space transitions, whereas atomistic KMC already supplies a physically constrained transition system [33] [34] [18].Source: §5 · p. 8

6 Conclusion and Limitations

AtomWorld-Mem frames long-horizon atomistic evolution as hidden-state restoration rather than snapshot-level event sampling. Across progress, fidelity, ablation, and transfer tests, memory-restored states outperform snapshot-only reasoning while remaining physically grounded; experiments focus on vacancy-mediated BCC alloy evolution.

6 Conclusion and Limitations

  • Across progress, fidelity, ablation, and transfer tests, memory-restored states outperform snapshot-only reasoning while remaining physically grounded.The paper presents this as the central conclusion of AtomWorld-Mem.Source: §6 · p. 9
  • Atomistic evolution is treated as hidden-state restoration rather than snapshot-level event sampling.AtomWorld-Mem is presented as a memory-restored atomistic world model for long-horizon evolution under physical constraints.Source: §6 · p. 9
  • Experiments focus on vacancy-mediated BCC alloy evolution; extending the framework to richer materials and more complex event catalogs remains future work.The authors also identify stronger clock-consistency objectives and more expressive memory mechanisms as directions for extension.Source: §6 · p. 9

A Experimental Details

The main experiments study vacancy-mediated Fe–Cu alloy evolution in a canonical precipitation and defect-driven structural-change setting. Comparisons match initial-state families and legal KMC event counts to isolate event-prioritization quality.

A.1 Simulation Environments

  • The main experiments use vacancy-mediated Fe–Cu alloy evolution, a canonical setting for precipitation and defect-driven structural change.The full microscopic configuration determines legal events, base KMC rates, and physical transitions, while the learned model receives structured partial observations and memory.Source: §A.1 · p. 12
  • Unless otherwise stated, methods start from matched initial-state families and execute the same number of legal KMC events.This step-controlled comparison isolates event-prioritization quality from differences in rollout length.Source: §A.1 · p. 12

A.2 Baselines and Ablations

The baselines separate passive rate-proportional KMC, local energy-based event selection, and snapshot-only spatial reasoning from variants that remove one memory timescale. Together, they test whether progress depends on memory beyond local energetic improvement or spatial observations alone.

A.2 Baselines and Ablations

  • Zacros traditional KMC samples legal events proportionally to base transition rates and advances physical time using the standard residence-time rule.It provides the reference for fixed-budget progress and trajectory-level fidelity.Source: §A.2 · p. 12
  • Energy-Greedy KMC selects legal events using local energetic improvement, testing whether gains can be explained by a local energy-descent heuristic.Source: §A.2 · p. 12
  • Snapshot-only AtomWorld removes temporal memory while retaining instantaneous spatial representation, testing whether multi-scale spatial observations alone suffice.Source: §A.2 · p. 12
  • The no-short-term-memory variant retains long-term structural memory while removing recent-event memory.It tests recent action history, local transition competition, vacancy backtracking, and short-horizon event reasoning.Source: §A.2 · p. 12
  • The no-long-term-memory variant retains short-term event history while removing recurrent structural memory.It tests slow structural-context accumulation, hidden defect-evolution trends, and long-horizon aggregation bias.Source: §A.2 · p. 12

B.1 Additional Memory Ablations

The 1.34% Cu ablation shows the same qualitative memory benefit as the dilute regime, with the full model best across metrics. The two memory scales have complementary roles: short-term memory supports local temporal reasoning, while long-term memory preserves structural context across trajectories.

B.1 Additional Memory Ablations

  • At 1.34% Cu, the ablation matches the dilute regime qualitatively, and full AtomWorld-Mem performs best across all metrics.Table 3 reports the additional memory ablation; AF is step-to-target acceleration over Zacros traditional KMC, while TimeErr and DynErr measure waiting-time and real-KMC-time-aligned dynamics error.Source: §B.1 · p. 12, Table 3 · p. 12
  • Removing short-term memory weakens recent-event reasoning and local transition competition, reducing vacancy-arrival quality and progress.Source: §B.1 · p. 12
  • Removing long-term memory more strongly degrades structural-context accumulation and rollout consistency, while the full model combines both memory scales.Short-term memory supports local temporal reasoning; long-term memory preserves slow structural context across the trajectory, supporting hidden-state restoration rather than a stronger snapshot-level scorer.Source: §B.1 · pp. 12–13

B.2 Long-Horizon Visualization Details

The visualization checks whether faster long-horizon progress corresponds to physically meaningful mesoscale organization. It supports the conclusion that memory-restored event prioritization guides coherent clustering and sustained structural evolution.

B.2 Long-Horizon Visualization Details

  • Figure 6 qualitatively shows coherent long-horizon Cu clustering under AtomWorld-Mem rather than merely faster energy reduction.Source: Figure 6 · p. 13, §B.2 · p. 13
  • Trajectories are compared at matched physical-time anchors with fixed visualization settings and a shared neighborhood-based cluster rule.Source: §B.2 · p. 13
  • Short-term memory captures recent vacancy–cluster interactions, while long-term memory preserves structural context for persistent aggregation over physical time.Source: §B.2 · p. 13
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