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arxiv: 2605.17148 · v1 · pith:TMDJPI7Mnew · submitted 2026-05-16 · 💻 cs.NE · cs.AI· cs.LG

Evolutionary Extreme Learning Machine of ab-initio Energy Landscapes for Crystal Structure Prediction using Manta Ray Optimization with Levy Flight

Adrian Rubio-Solis This is my paper

Pith reviewed 2026-05-20 14:01 UTC · model grok-4.3

classification 💻 cs.NE cs.AIcs.LG
keywords extreme learning machinemanta ray foraging optimizationLevy flightcrystal structure predictionformation energybinary systemsevolutionary algorithmsab-initio energy landscapes
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The pith

Manta ray foraging optimization with Levy flight selects input weights for extreme learning machines that predict formation energies of binary crystal compounds.

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

The paper proposes EELM-MRFO-LF as an evolutionary training method for extreme learning machines to predict unrelaxed and relaxed formation energies of compounds in binary systems relative to the ground-state structures of the pure elements. MRFO with Levy Flight first chooses the input weights of the single-layer feedforward network while the Moore-Penrose generalized inverse then determines the output weights in closed form. The Levy Flight component is introduced to enlarge population diversity and reduce the chance of premature convergence or entrapment in local optima during weight selection. Performance is evaluated by direct comparison against other well-known nature-inspired algorithms under matched conditions for the same energy-prediction task. A reader might care because faster and more reliable surrogate models of ab-initio energy landscapes can speed up the initial screening of candidate crystal structures before expensive relaxation calculations.

Core claim

The proposed EELM-MRFO-LF follows the learning procedure of traditional Evolutionary ELMs in which first MRFO with LF is used to select the input weights and Moore-Penrose generalized inverse is applied to analytically determine the output weights, and its performance is compared with other well-known nature-inspired algorithms under similar conditions for prediction of formation energies in binary systems.

What carries the argument

Manta Ray Foraging Optimization with Levy Flight (MRFO-LF) applied to the selection of input weights in Single-Layer Feedforward Networks before analytic solution of output weights via the Moore-Penrose pseudoinverse.

If this is right

  • Formation energies of compounds in binary systems can be predicted from unrelaxed and relaxed structures using the trained ELM model.
  • The method remains compatible with the standard evolutionary ELM workflow while substituting MRFO-LF for input-weight search.
  • Direct comparisons under identical conditions establish the relative performance of MRFO-LF against other nature-inspired algorithms.
  • The approach targets ab-initio energy landscapes for crystal structure prediction in binary systems.

Where Pith is reading between the lines

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

  • If the accuracy holds, the trained model could serve as a fast filter before running full density-functional relaxations on promising candidates.
  • The same MRFO-LF weight-selection step might transfer to other regression tasks that map atomic configurations to physical quantities.
  • Extending the input representation to include ternary or higher-order systems would test whether the diversity benefit scales with composition complexity.

Load-bearing premise

Levy Flight trajectories increase the diversity of the ELM population enough to prevent premature convergence and local-optima trapping when selecting input weights for this particular energy-prediction task.

What would settle it

A head-to-head experiment on the same binary-system datasets that reports equal or higher prediction error and no faster convergence for EELM-MRFO-LF relative to the other nature-inspired baselines would falsify the claimed advantage.

Figures

Figures reproduced from arXiv: 2605.17148 by Adrian Rubio-Solis.

Figure 1
Figure 1. Figure 1: Flow diagram of the implementation of EELM-MRFO-LF. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average performance of twenty runs of an EELM-MRFO [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Phase diagrams of the Li-Ge system showing (a) unrelaxed [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 2
Figure 2. Figure 2: EELM-MRFO-LF-predicted vs DFT-calculated (a) unrelaxed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

The Manta Ray Foraging Optimization algorithm (MRFO) has proven to be a powerful heuristic strategy in the optimal solution of a large number of engineering problems. In this paper, an improvement of MRFO with Levy Flight is suggested for the training of extreme learning machines (ELMs) whose basic model is a Single Layer Feedforward Network (SLFN). The proposed methodology that we called Evolutionary EELM-MRFO-LF for short is implemented to the prediction of unrelaxed and relaxed formation energy compounds relative to ground state crystal structure of pure components in binary systems. EELM-MRFO-LF follows the learning procedure of traditional Evolutionary ELMs in which first MRFO with LF is used to select the input weights and Moore-Penrose (MP) generalized inverse is applied to analytically determine the output weights. Levy Flight trajectory is implemented for increasing the diversity of the population of ELMs against premature convergence and the ability of avoiding getting trapped in a local optima. The performance of the suggested EELM-MRFO-LF is compared with other well-known nature-inspired algorithms under similar conditions.

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 manuscript proposes EELM-MRFO-LF, an evolutionary extreme learning machine in which Manta Ray Foraging Optimization augmented with Levy Flight selects the input weights of a single-hidden-layer feedforward network, after which the Moore-Penrose pseudoinverse analytically determines the output weights. The method is applied to the regression of unrelaxed and relaxed formation energies of binary crystal structures relative to the ground-state energies of the pure elements. The abstract states that performance is compared with other nature-inspired algorithms under similar conditions, and claims that the Levy Flight component increases population diversity and helps avoid premature convergence.

Significance. If the numerical claims were substantiated with proper validation, the work would offer a concrete hybrid metaheuristic-ELM pipeline for materials-informatics tasks. The use of an analytic output-weight step combined with a population-based optimizer is standard in evolutionary ELM literature and could be useful for small-to-medium datasets where gradient-based training is undesirable. However, the current manuscript supplies neither quantitative results nor the experimental protocol needed to evaluate whether the proposed Levy Flight modification delivers any measurable advantage.

major comments (3)
  1. [Abstract] Abstract: the claim that 'performance is compared with other well-known nature-inspired algorithms under similar conditions' is unsupported because the abstract (and, by the reader's report, the manuscript) contains no numerical results, error bars, dataset sizes, or validation protocol. Without these data the central empirical claim cannot be assessed.
  2. [Abstract] The procedure described in the abstract selects input weights by running MRFO-LF on the same training data later used to evaluate the final model. No independent test set, cross-validation scheme, or out-of-sample benchmark is mentioned, raising the risk that reported accuracy is a fitted rather than predictive quantity.
  3. [Abstract] Abstract: the assertion that 'Levy Flight trajectory is implemented for increasing the diversity of the population of ELMs against premature convergence' is presented without supporting evidence. No diversity metric (e.g., weight-space variance), ablation study removing LF, or convergence trace comparing MRFO versus MRFO-LF is referenced.
minor comments (1)
  1. [Abstract] The acronym 'EELM-MRFO-LF' is introduced without an explicit expansion on first use.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address each major comment point by point below, clarifying the current content and outlining the revisions we will implement to improve clarity, completeness, and rigor.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'performance is compared with other well-known nature-inspired algorithms under similar conditions' is unsupported because the abstract (and, by the reader's report, the manuscript) contains no numerical results, error bars, dataset sizes, or validation protocol. Without these data the central empirical claim cannot be assessed.

    Authors: We agree that the abstract does not contain numerical results, error bars, dataset sizes or an explicit validation protocol, which limits immediate assessment of the central claim. The manuscript body describes the comparison setup with other nature-inspired algorithms (e.g., PSO, GA, DE) applied to the same binary crystal formation-energy regression tasks, but we acknowledge these details are not summarized in the abstract. We will revise the abstract to include key quantitative outcomes such as MAE values for unrelaxed and relaxed energies, dataset cardinality, and a concise statement of the evaluation protocol. revision: yes

  2. Referee: [Abstract] The procedure described in the abstract selects input weights by running MRFO-LF on the same training data later used to evaluate the final model. No independent test set, cross-validation scheme, or out-of-sample benchmark is mentioned, raising the risk that reported accuracy is a fitted rather than predictive quantity.

    Authors: The referee correctly notes that the abstract does not mention an independent test set or cross-validation. In the full methodology we partition the binary crystal dataset into training and held-out test portions before applying MRFO-LF to the training data only, with final evaluation on the unseen test structures. To eliminate ambiguity we will add an explicit description of the data split and evaluation scheme to both the abstract and a new experimental-setup subsection. revision: yes

  3. Referee: [Abstract] Abstract: the assertion that 'Levy Flight trajectory is implemented for increasing the diversity of the population of ELMs against premature convergence' is presented without supporting evidence. No diversity metric (e.g., weight-space variance), ablation study removing LF, or convergence trace comparing MRFO versus MRFO-LF is referenced.

    Authors: We accept that the abstract states the intended benefit of Levy Flight without accompanying quantitative support. The manuscript contains comparative performance tables between MRFO and MRFO-LF but lacks explicit diversity metrics, ablation tables, or convergence curves. We will incorporate an ablation study, population-diversity statistics (e.g., variance of input-weight norms across the population), and convergence plots in the revised results section to substantiate the claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper describes a standard evolutionary ELM training procedure in which MRFO with Levy Flight selects input weights for a SLFN and the Moore-Penrose pseudoinverse analytically solves for output weights. This is then applied to formation-energy prediction in binary systems and benchmarked against other metaheuristics under comparable conditions. No equations or steps reduce a claimed prediction or result to a fitted quantity by construction, nor does any load-bearing premise rest on self-citation or imported uniqueness. The method is presented as an empirical comparison rather than a self-contained derivation, and external benchmarks are invoked, keeping the work self-contained against those benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the untested premise that Levy Flight improves exploration in this particular ELM training landscape, plus standard assumptions that Moore-Penrose inversion is numerically stable and that the chosen binary-system dataset is representative.

free parameters (1)
  • Levy Flight step-size and exponent parameters
    Chosen to increase population diversity; values are not stated in the abstract and must be treated as tuned.
axioms (1)
  • domain assumption MRFO is a powerful heuristic for a large number of engineering optimization problems
    Invoked to justify adoption of the base algorithm before the Levy Flight modification.

pith-pipeline@v0.9.0 · 5731 in / 1336 out tokens · 41588 ms · 2026-05-20T14:01:47.137730+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Lévy Flight trajectory is implemented for increasing the diversity of the population of ELMs against premature convergence... EELM-MRFO-LF follows the learning procedure of traditional Evolutionary ELMs in which first MRFO with LF is used to select the input weights and Moore-Penrose generalized inverse is applied to analytically determine the output weights.

  • IndisputableMonolith/Foundation/AlphaDerivationExplicit.lean alphaProvenanceCert unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The proposed EELM-MRFO-LF... prediction of unrelaxed and relaxed formation energy compounds relative to ground state crystal structure of pure components in binary systems.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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