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arxiv: 2605.31144 · v1 · pith:UW3S6WM4new · submitted 2026-05-29 · ❄️ cond-mat.mtrl-sci

A Self-Evolving Machine-Learning-Based Kinetic Monte Carlo Method for Modelling Thin-Film Growth

Jyri Kimari , Flyura Djurabekova , Kostas Sarakinos This is my paper

Pith reviewed 2026-06-28 21:58 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords kinetic Monte Carlomachine learningthin film growthdiffusion rateslocal atomic environmentsnudged elastic bandsilver on silverself-evolving model
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The pith

A kinetic Monte Carlo method builds a machine-learning model on the fly to predict diffusion rates from local atomic environments and gradually replaces expensive nudged elastic band calculations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a kinetic Monte Carlo framework for thin-film growth that constructs an ML regression model for rate parameters during the simulation itself. The model trains on local atomic environments sampled from the evolving system and adds new training points wherever its uncertainty estimate is high. This setup lets quick ML predictions increasingly replace nudged elastic band calculations while the underlying interatomic potential remains the source of truth. The approach is shown for sub-monolayer silver growth on silver {111}, where the resulting adatom islands match the shapes and densities expected from the interaction model and from experiment. A sympathetic reader cares because the method promises to make atom-by-atom growth simulations cheaper without losing the fidelity needed to capture realistic diffusion kinetics.

Core claim

The central claim is that a self-evolving ML-based regression model for rate parameters, trained on local atomic environments encountered during the system evolution, enables efficient KMC simulations of thin-film growth by increasingly using quick ML estimations instead of nudged elastic band calculations, as demonstrated for Ag on Ag{111} where adatom islands form in accordance with the interaction model, the theoretical framework, and available experimental results.

What carries the argument

The self-evolving ML regression model that predicts rate parameters from local atomic environments, with uncertainty estimates used to decide when to perform new nudged elastic band calculations and add those results to the training set.

If this is right

  • Computational cost decreases as the simulation advances because ML rate estimates replace most nudged elastic band calculations.
  • The description of atomic diffusion kinetics stays consistent with the input interatomic potential.
  • The test case of sub-monolayer Ag growth on Ag{111} produces island shapes and densities that agree with theory and experiment.
  • The framework applies to any thin-film system for which an interatomic potential is available.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the uncertainty measure proves reliable across many systems, the method could support simulations over much longer times or larger areas than conventional KMC allows.
  • The same on-the-fly sampling idea might transfer to other kinetic Monte Carlo problems that currently rely on pre-tabulated rates.
  • The approach could be paired with existing acceleration techniques in KMC to further extend accessible time scales.

Load-bearing premise

That diffusion rates depend only on the local atomic environment and that the ML uncertainty estimate will catch every configuration that would produce a materially different rate.

What would settle it

A direct comparison run of the same Ag on Ag{111} system using only nudged elastic band calculations throughout, showing a difference in final island morphology or density from the self-evolving ML version.

Figures

Figures reproduced from arXiv: 2605.31144 by Flyura Djurabekova, Jyri Kimari, Kostas Sarakinos.

Figure 1
Figure 1. Figure 1: Simplified flowchart of the ML-KMC program. The termination condition is [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top view of the Ag {1 1 1} surface slab with eleven adatoms deposited on top. Substrate atoms are silver colour, adsorption sites are small spheres. Deposited atoms and the adsorption sites are coloured green if they conform to the underlying fcc structure, and purple if they are at off-lattice hcp stacking fault locations. New adsorption sites have been generated to three- and four-coordinated sites above… view at source ↗
Figure 3
Figure 3. Figure 3: The different jump lengths allowed in the system. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Local atomic environment (LAE) of the jump of the blue-coloured atom to the [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Key processes chosen to be evaluated after the initial training pipeline. Notation: [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Correlation between selected NEB calculated and ML estimated barriers from [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Corner-A-edge motion with barriers predicted by the ML model. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of adatom island number vs. simulated time in five simulations at [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Representative examples of island shapes as a function of temperature at the [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Island density as a function of inverse temperature. The solid line corresponds [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
read the original abstract

We present a kinetic Monte Carlo (KMC) simulation framework parameterized by automatically sampling machine-learning (ML) for modeling thin-film growth atom by atom. Given an interatomic potential energy function, the KMC algorithm builds an ML-based regression model for rate parameters on runtime, being trained on the local atomic environments encountered during the system evolution. New environments are continuously added to the training set in a self-evolving manner at points where the ML model estimates high uncertainty. As the simulation progresses, the ML model gains confidence, and the quick estimation of rates increasingly overtakes the relatively-expensive nudged elastic band calculations, promoting computational efficiency while retaining high fidelity description of the atomic diffusion kinetics. As a test case, we simulate the sub-monolayer growth of Ag on Ag {111}, where we demonstrate adatom islands forming in shapes and densities in accordance with the underlying atomistic interaction model, the theoretical framework, and available experimental results related to thin-film nucleation and growth.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper presents a kinetic Monte Carlo (KMC) framework that builds an ML regression model on-the-fly for atomic diffusion rates based on local environments encountered during thin-film growth. New training points are added where the ML model reports high uncertainty, allowing NEB calculations to be progressively replaced by fast ML estimates. The method is demonstrated for sub-monolayer Ag growth on Ag{111}, with the claim that resulting island shapes and densities match the underlying interatomic potential, theoretical expectations, and experimental results while gaining computational efficiency.

Significance. If the uncertainty-driven replacement of NEB calculations preserves per-event rate accuracy, the framework could enable KMC simulations of thin-film growth at substantially larger length and time scales than conventional NEB-based KMC. The on-the-fly, self-evolving training without a precomputed dataset is a methodological strength that avoids the usual separation between training and production phases.

major comments (3)
  1. [Abstract] Abstract: the central claim that the method 'retains high fidelity description of the atomic diffusion kinetics' while the ML model 'increasingly overtakes' NEB calculations is unsupported by any quantitative metrics, error analysis, rate-comparison tables, or plots of ML vs. NEB barrier distributions for low-uncertainty configurations.
  2. [Results (Ag on Ag{111} demonstration)] Results (Ag on Ag{111} demonstration): the reported agreement in 'shapes and densities' is an integrated morphological outcome; no per-configuration validation is shown that ML-predicted rates match NEB results once uncertainty falls below the acceptance threshold, leaving open the possibility that undetected errors accumulate in the morphology.
  3. [Method (self-evolving training procedure)] Method (self-evolving training procedure): the assumption that the chosen environment descriptor plus uncertainty estimator flags every configuration that would produce a materially different rate is load-bearing for the fidelity claim, yet no calibration of uncertainty against actual prediction error, no tests for descriptor collisions (distinct barriers mapped to similar feature vectors), and no coverage analysis of the rate surface are provided.
minor comments (1)
  1. [Figures] Figure captions should explicitly state the coverage range, temperature, and number of independent runs used for the morphology statistics.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions. We address each of the major comments below and will incorporate revisions to strengthen the quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the method 'retains high fidelity description of the atomic diffusion kinetics' while the ML model 'increasingly overtakes' NEB calculations is unsupported by any quantitative metrics, error analysis, rate-comparison tables, or plots of ML vs. NEB barrier distributions for low-uncertainty configurations.

    Authors: We agree with this observation. The current manuscript relies on the morphological outcomes to infer fidelity, but direct quantitative validation is indeed valuable. In the revised manuscript, we will add quantitative metrics such as mean absolute error between ML and NEB barriers for low-uncertainty configurations, along with a table or plot comparing the distributions. This will be included in a new subsection on model validation. revision: yes

  2. Referee: [Results (Ag on Ag{111} demonstration)] Results (Ag on Ag{111} demonstration): the reported agreement in 'shapes and densities' is an integrated morphological outcome; no per-configuration validation is shown that ML-predicted rates match NEB results once uncertainty falls below the acceptance threshold, leaving open the possibility that undetected errors accumulate in the morphology.

    Authors: The referee correctly notes that integrated outcomes do not guarantee per-event accuracy. To address this, we will include in the results section additional analysis showing per-configuration comparisons for a representative set of environments where the uncertainty threshold is met. This will help rule out accumulation of errors and strengthen the demonstration. revision: yes

  3. Referee: [Method (self-evolving training procedure)] Method (self-evolving training procedure): the assumption that the chosen environment descriptor plus uncertainty estimator flags every configuration that would produce a materially different rate is load-bearing for the fidelity claim, yet no calibration of uncertainty against actual prediction error, no tests for descriptor collisions (distinct barriers mapped to similar feature vectors), and no coverage analysis of the rate surface are provided.

    Authors: This is a valid point regarding the robustness of the uncertainty-driven approach. We will revise the methods section to include a calibration study correlating the uncertainty estimates with actual errors on a validation set. Additionally, we will provide an analysis of the descriptor's resolution by checking for potential collisions and include a discussion or plot on the coverage of the configuration space sampled during the simulation. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation anchored in external ground truth

full rationale

The paper describes a self-evolving ML-KMC framework that samples local atomic environments during growth, performs NEB calculations on an external interatomic potential to obtain rates, and trains an ML regressor on those data, adding points only at high ML uncertainty. No equation or step reduces a claimed prediction or result to a fitted parameter defined by the same simulation; the morphology outcomes are direct consequences of the underlying potential and NEB ground truth rather than tautological re-use of fitted quantities. No self-citation chains, uniqueness theorems, or ansatzes imported from prior author work are invoked as load-bearing premises. The method is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard domain assumptions of KMC and ML regression without explicit new free parameters or invented entities stated in the abstract.

axioms (2)
  • domain assumption Diffusion rates are determined by local atomic environment
    ML regression is trained exclusively on local environments encountered during evolution.
  • standard math Nudged elastic band calculations supply accurate ground-truth rates
    Used to label training data when uncertainty is high.

pith-pipeline@v0.9.1-grok · 5709 in / 1215 out tokens · 29962 ms · 2026-06-28T21:58:43.572884+00:00 · methodology

discussion (0)

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