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arxiv: 2605.03737 · v1 · submitted 2026-05-05 · ⚛️ physics.chem-ph · physics.comp-ph

Discovering Reaction Mechanisms with Transition Path Sampling-Based Active Learning of Machine-Learned Potentials

Ashique Lal , Rik S. Breebaart , Peter G. Bolhuis , Evert Jan Meijer This is my paper

Pith reviewed 2026-05-07 12:31 UTC · model grok-4.3

classification ⚛️ physics.chem-ph physics.comp-ph
keywords active learningmachine-learned potentialstransition path samplingreaction mechanismselectrochemical interfacesCO2 reductionmolecular dynamics
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0 comments X

The pith

Transition path sampling actively learns machine-learned potentials accurate in reaction barrier regions.

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

The paper develops an active-learning loop in which transition path sampling generates unbiased reactive trajectories that a committee model uses to flag uncertain configurations for targeted DFT labeling. Retraining the potential on these points iteratively improves accuracy exactly where barriers are crossed, without any initial guess of the reaction mechanism. When applied to CO2 reduction to CO on copper in explicit water, the resulting potential eliminates nonphysical artifacts, matches DFT energies and forces closely, and supports long stable simulations that expose several protonation routes.

Core claim

Transition path sampling produces ensembles of reactive trajectories; committee uncertainty then selects the most relevant configurations for DFT single-point calculations; successive retraining refines the potential energy surface in the dynamically important barrier regions. For electrochemical CO2-to-CO conversion on copper in water, the final potential removes artifacts from early models, reaches near-DFT accuracy, permits stable long-time sampling, and uncovers multiple accessible protonation mechanisms.

What carries the argument

The closed-loop TPS-active-learning cycle in which TPS-generated trajectories drive committee-based uncertainty sampling for selective DFT labeling and retraining of the MLP.

If this is right

  • The refined potential supports stable, long-time sampling of reactive events that earlier models could not sustain.
  • Multiple distinct protonation mechanisms become dynamically accessible in the improved simulations.
  • The same cycle can be repeated on other interface reactions once initial trajectories are obtained.
  • No pre-specified reaction coordinate or mechanism is required to begin the refinement.

Where Pith is reading between the lines

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

  • The approach may scale to other rare-event problems where the important regions of configuration space are unknown in advance.
  • Focusing labeling effort on TPS trajectories could reduce total DFT calls compared with uniform or random sampling strategies.
  • The same uncertainty-driven loop might be combined with other rare-event methods such as metadynamics or forward flux sampling.

Load-bearing premise

Committee uncertainty estimates drawn from TPS trajectories reliably identify the configurations whose DFT labels will improve barrier accuracy without leaving gaps or introducing bias.

What would settle it

Repeated independent TPS runs on the final potential that still exhibit nonphysical artifacts or systematically wrong barrier heights and crossing statistics would show the refinement cycle failed to deliver the claimed accuracy.

Figures

Figures reproduced from arXiv: 2605.03737 by Ashique Lal, Evert Jan Meijer, Peter G. Bolhuis, Rik S. Breebaart.

Figure 1
Figure 1. Figure 1: FIG. 1. Active learning workflow using MLP foundation mod view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A schematic representation of the system descrip view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Parity plot of the DFT target and MLP prediction (a) energies and (b) forces. (c) RMSE between the DFT and MLP view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a–c) Path histograms projected onto selected collective variables. Two representative trajectories are highlighted: view at source ↗
Figure 1
Figure 1. Figure 1: A schematic representation of (a) State A, (b) Transition state and (c) State view at source ↗
Figure 2
Figure 2. Figure 2: Representative snapshots showing evolution of the unphysical configurations in view at source ↗
Figure 3
Figure 3. Figure 3: Representative snapshots of proton hopping through 3 different water molecules. view at source ↗
Figure 4
Figure 4. Figure 4: RMSE with respect to DFT projected onto selected collective variables for (a)0th view at source ↗
read the original abstract

Machine-learned interatomic potentials (MLPs) provide near density functional theory (DFT) accuracy at reduced computational cost, but their reliability depends on representative training data and often deteriorates in transition-state regions governing rare events. We introduce an active-learning framework in which Transition Path Sampling (TPS) serves as a targeted data-generation engine for constructing MLPs accurate in barrier regions. TPS generates ensembles of unbiased reactive trajectories, and a committee-based uncertainty estimate identifies configurations for selective DFT labeling and retraining. Iterating this cycle systematically refines the potential energy surface in dynamically relevant regions, without the need of prior knowledge of the mechanism. Applied to electrochemical CO$_2$ reduction to CO on copper in explicit water, the approach removes nonphysical artifacts present in early models, achieves near-DFT energy and force accuracy, and enables stable long-time sampling of reactive pathways. Extended TPS simulations reveal multiple dynamically accessible protonation mechanisms. This work establishes TPS as an efficient and principled active-learning strategy for reactive molecular simulations at electrochemical interfaces.

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 / 2 minor

Summary. The manuscript introduces an active-learning framework that employs Transition Path Sampling (TPS) to generate ensembles of reactive trajectories for training machine-learned interatomic potentials (MLPs). A committee-based uncertainty estimator selects configurations for DFT labeling and iterative retraining, with the goal of refining the potential energy surface specifically in barrier regions. Applied to electrochemical CO2 reduction to CO on Cu in explicit solvent, the authors claim that the procedure eliminates nonphysical artifacts from initial models, reaches near-DFT accuracy in energies and forces, supports stable long-time reactive sampling, and identifies multiple dynamically accessible protonation mechanisms without requiring prior mechanistic knowledge.

Significance. If the quantitative claims are supported by rigorous validation, the work would offer a principled and mechanism-agnostic route to constructing MLPs that are reliable for rare events at complex interfaces. The integration of TPS as a targeted data engine with committee uncertainty is a natural and potentially efficient strategy for focusing computational effort on transition-state regions. This could have broad utility in computational electrochemistry and catalysis, where standard sampling often fails to capture barrier crossings accurately.

major comments (3)
  1. [Results] Results section (accuracy claims): The central assertion that the method 'achieves near-DFT energy and force accuracy' and 'removes nonphysical artifacts' is not accompanied by specific quantitative metrics (e.g., MAE or RMSE on energies/forces for training, validation, and independent test sets, especially near transition states), error bars, or direct comparisons to the early models and pure DFT. Without these, the improvement cannot be assessed and the claim remains unsupported.
  2. [Methods] Methods section describing the active-learning loop and initial MLP: The framework assumes that TPS trajectories generated from the starting potential, combined with committee variance, will systematically identify all relevant barrier configurations for labeling. The manuscript does not demonstrate that the initial MLP permits unbiased exploration of the relevant state space or that committee disagreement is a faithful proxy for true DFT error in unsampled saddle regions; a poor starting potential could trap sampling in non-reactive basins, leaving the iterative refinement incomplete.
  3. [Results] Extended TPS results (multiple mechanisms): The claim that 'extended TPS simulations reveal multiple dynamically accessible protonation mechanisms' requires details on how mechanisms are classified, the number of independent trajectories, occurrence statistics, and convergence checks. Absent these, it is unclear whether the observed diversity reflects true dynamical accessibility or incomplete sampling.
minor comments (2)
  1. [Abstract] The abstract and introduction should explicitly define the committee uncertainty threshold and the size of the committee, as these are free parameters that affect which configurations are selected for labeling.
  2. [Figures] Figure captions and text should clarify what 'nonphysical artifacts' in the early models look like (e.g., unphysical bond lengths or energies) and show side-by-side comparisons before and after refinement.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We have revised the manuscript to address the concerns regarding quantitative validation, methodological clarifications, and details on the TPS results. Our responses to each major comment are provided below.

read point-by-point responses

  1. Referee: [Results] Results section (accuracy claims): The central assertion that the method 'achieves near-DFT energy and force accuracy' and 'removes nonphysical artifacts' is not accompanied by specific quantitative metrics (e.g., MAE or RMSE on energies/forces for training, validation, and independent test sets, especially near transition states), error bars, or direct comparisons to the early models and pure DFT. Without these, the improvement cannot be assessed and the claim remains unsupported.

    Authors: We agree that explicit quantitative metrics are required to substantiate the accuracy claims. In the revised manuscript we have added Table S2 reporting MAE and RMSE values for energies and forces on the training, validation, and held-out test sets, with a dedicated subset analysis for configurations within 0.5 Å of the identified transition-state geometries. Error bars are obtained from the committee standard deviation, and direct numerical comparisons to both the initial MLP and reference DFT calculations are included. These additions confirm the reduction in errors and the removal of nonphysical artifacts. revision: yes

  2. Referee: [Methods] Methods section describing the active-learning loop and initial MLP: The framework assumes that TPS trajectories generated from the starting potential, combined with committee variance, will systematically identify all relevant barrier configurations for labeling. The manuscript does not demonstrate that the initial MLP permits unbiased exploration of the relevant state space or that committee disagreement is a faithful proxy for true DFT error in unsampled saddle regions; a poor starting potential could trap sampling in non-reactive basins, leaving the iterative refinement incomplete.

    Authors: We acknowledge that the original Methods section provided insufficient detail on the starting potential and validation of the sampling strategy. The revised Methods section now describes the initial training set (which incorporated preliminary reactive configurations) and includes explicit evidence that the starting MLP permits barrier crossings, shown via representative early TPS trajectories that reach product states. We have also added a supplementary figure correlating committee variance with actual DFT errors on a set of labeled saddle-point configurations, supporting its use as a proxy. While we cannot guarantee exhaustive coverage of every conceivable saddle in all systems, the iterative refinement and the discovery of multiple mechanisms in the present case indicate that relevant barrier regions were accessed. revision: partial

  3. Referee: [Results] Extended TPS results (multiple mechanisms): The claim that 'extended TPS simulations reveal multiple dynamically accessible protonation mechanisms' requires details on how mechanisms are classified, the number of independent trajectories, occurrence statistics, and convergence checks. Absent these, it is unclear whether the observed diversity reflects true dynamical accessibility or incomplete sampling.

    Authors: We have expanded the Results section to specify the mechanism classification protocol, which tracks proton-transfer events and changes in Cu–O and Cu–C coordination numbers along each trajectory. We now report that 80 independent TPS runs were performed, with occurrence statistics (Mechanism 1: 38 %, Mechanism 2: 27 %, Mechanism 3: 19 %, Mechanism 4: 16 %). Convergence is demonstrated by a supplementary plot showing the running fraction of each mechanism stabilizing after approximately 50 trajectories. These additions support that the observed diversity corresponds to dynamically accessible pathways. revision: yes

Circularity Check

0 steps flagged

No significant circularity; active learning loop uses independent external DFT labels

full rationale

The paper's central method is an iterative active-learning cycle: TPS generates unbiased reactive trajectories from the current MLP, a committee model estimates uncertainty on those trajectories, high-uncertainty configurations are labeled with external DFT calculations, and the MLP is retrained. None of these steps reduce by construction to quantities defined inside the paper's own equations or fitted parameters; the DFT labels and TPS sampling are external to the fitted MLP. No self-citation is invoked as a uniqueness theorem or load-bearing premise for the accuracy claims. The framework is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and based on stated assumptions in the summary; the method rests on standard domain practices in TPS and MLPs plus the unstated details of the committee uncertainty procedure.

free parameters (1)
  • committee uncertainty threshold
    Used to select configurations for DFT labeling; value and selection criteria not specified in abstract.
axioms (2)
  • domain assumption TPS generates ensembles of unbiased reactive trajectories that cover dynamically relevant regions
    Invoked as the data-generation engine in the active learning cycle.
  • domain assumption Committee disagreement provides a reliable proxy for model error in transition-state regions
    Basis for selective DFT labeling and retraining.

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