{"id":"07ff503e-5f8a-4490-9916-e074268e6c7b","arxiv_id":"2501.15057","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Augmenting fatigue-life ML models with Basquin-model features and boundary losses is claimed to improve prediction and uncertainty quantification, but key equations and one results table contain errors.","lead":"This paper adds physics-based features and a boundary penalty to machine learning models that predict how many cycles a metal part survives under repeated stress. The authors report better accuracy and uncertainty estimates on titanium and carbon steel fatigue datasets, but several errors in the paper undercut the reported results.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Basquin feature fitting protocol is undisclosed; if fit on full data, test-fold targets leak into training features and the reported PIML gains are not supported.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern: undisclosed Basquin fitting relative to cross-validation could cause target leakage and explain the PIML gains. I agree with that assessment. The physics-informed loss in Eq. (10) is also written backwards relative to its stated purpose—ReLU(y*) penalizes positive predictions and ReLU(10,000,000 - y*) penalizes predictions below the upper bound—which is a serious mechanical error, but the leakage concern is broader because it affects all models and all datasets, including those that do not use the loss. The paper provides code, which is a real resource for verification, but the manuscript's own text is insufficient to rule out leakage. A leakage-safe rerun is the decisive check.","tokens_in":17441,"tokens_out":2536,"duration_ms":25429,"concrete_test":"Clone the public repository (github.com/avakanski/Fatigue-Life-Prediction) and trace the Basquin feature construction. If the constants are fitted on the entire dataset before KFold splitting, rerun all four dataset experiments with a leakage-free protocol: fit Basquin constants only on the training fold, transform the test fold, and recompute the metrics in Tables 2, 4, 6, and 8. If the PIML improvements over the non-PIML baselines shrink to within noise or reverse, leakage is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.3.1 says the Basquin model is used to estimate fatigue life from experimental data and that these estimates are added as input features, but it never states whether the Basquin constants are fitted inside each cross-validation fold, on training folds only, or on the full dataset. Because the target variable is the experimentally recorded fatigue life, fitting Basquin constants on all data before the 5-fold split means each test fold's target values contribute to the physics-informed feature for that fold. That is target leakage, and it alone could explain the consistent 10–20% PIML improvements reported in Tables 2, 4, 6, and 8, including for GPR and NGBoost, which do not use the physics-informed loss. The central claim that physics-informed features improve fatigue-life prediction and UQ is therefore not established by the experiments as described.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a physics-informed machine learning (PIML) framework for fatigue-life prediction with uncertainty quantification. The framework augments experimental fatigue datasets with a Basquin-model estimate of fatigue life as an additional input feature, and adds two boundary penalty terms to the loss function of neural-network models (non-negativity and an upper bound of 10,000,000 cycles). Experiments on one titanium-alloy dataset and three carbon-steel datasets (uniaxial, bending, torsion) compare seven regression models with and without the PIML additions, reporting point-estimate metrics (R2, PCC, RMSE, MAE) and uncertainty metrics (coverage, interval width, composite). The central claim is that the PIML additions improve both point estimates and uncertainty intervals across all four datasets.","tokens_in":17531,"tokens_out":4921,"duration_ms":42769,"significance":"If the reported improvements were valid, the approach would be a useful contribution to data-driven fatigue-life prediction with calibrated uncertainty, especially in small-data materials settings. The paper is strong in breadth: it compares several uncertainty-aware models (QR, NGBoost, GPR, Deep Ensemble, MC Dropout, BNN-VI, BNN-MCMC) on four datasets and makes code available. However, the significance is severely compromised because the core experimental evidence is undermined by an incorrect loss-term derivation, an undisclosed and potentially leaky feature-fitting protocol, a duplicated table, and internally inconsistent metric values. The current manuscript does not establish the claimed superiority of the PIML framework.","major_comments":[{"comment":"The physics-informed loss terms enforce the opposite of the stated constraints. ReLU(y*) is zero for negative y* and penalizes positive predictions, thus driving predicted fatigue life toward zero or negative values rather than enforcing non-negativity; the correct term for a non-negativity constraint is ReLU(-y*). Similarly, ReLU(10,000,000 - y*) penalizes predictions below 10,000,000 and pushes predictions above the bound, whereas the intended upper-bound constraint requires ReLU(y* - 10,000,000). Additionally, the text states that fatigue-life values are log-transformed before training, so the bound of 10,000,000 cycles should also be transformed to the logarithmic scale if the loss is computed on log-transformed outputs. As written, Eq. (10) does not implement the claimed boundary constraints, and all NN-based PIML results that rely on this loss term are questionable.","section":"§3.3.2, Eq. (10)"},{"comment":"The procedure for fitting the Basquin constants c and m in Eq. (2) is not specified. The Basquin model is used to estimate fatigue life from experimental fatigue tests, which makes the resulting physics-informed feature a fitted function of the target variable. The paper does not state whether the constants are fitted inside each cross-validation fold, on the training folds only, or on the full dataset before the 5-fold split. If the fit uses the full dataset, the test-fold target values indirectly contribute to the training features, which is target leakage and could by itself explain the consistent 10-20% improvements across all models, including GPR and NGBoost that do not use the physics-informed loss. This must be clarified and the experiments must be rerun with fold-disciplined fitting before the central claim can be assessed.","section":"§3.3.1, §4.2"},{"comment":"Table 8, labeled as the PIML results for the torsion fatigue test dataset of Carbon steel alloys, is numerically identical to Table 4, which reports the PIML results for the uniaxial fatigue test dataset. Every row and entry matches, including the standard deviations. This means the torsion-dataset PIML results are not actually presented, and the claim that the PIML approach improves results on all four datasets is not supported by the tables as published. This duplication must be corrected and the torsion experiments fully reported.","section":"Tables 4 and 8"},{"comment":"The reported mean absolute error (MAE) for the standard NN model is systematically larger than its root-mean-squared error (RMSE), e.g., Table 1 NN: MAE 2.0463 vs RMSE 0.6443; Table 3 NN: MAE 0.5999 vs RMSE 0.3982; Table 5 NN: MAE 0.5831 vs RMSE 0.3589. Since RMSE >= MAE for any fixed set of errors, these entries cannot be correct on the same scale. The NN metrics are therefore internally inconsistent, and the reported performance of the NN baseline (and its PIML variant) is not credible. These values must be recomputed and corrected, or the errors explained.","section":"Tables 1-8, NN rows"}],"minor_comments":[{"comment":"The definition of the composite metric is ambiguous in the text: '0.75 ∙ coverage + 0.25 mean interval width⁄' should be written as 0.75 * coverage + 0.25 / mean_interval_width, with the division made explicit.","section":"§4.1"},{"comment":"The material constants in the S-N relation are called A and B in Eq. (1), while the Basquin relation in Eq. (2) uses c and m; the relationship between these parameters is not stated, which may confuse readers.","section":"Eqs. (1) and (2)"},{"comment":"The composite metric for BNN-VI is reported as 0.7773±0.30; the large standard deviation relative to the mean is atypical for a bounded metric and may indicate an error in the reported aggregate.","section":"Table 1, BNN-VI row"},{"comment":"There are several typographical issues, including 'Deep Ensemple' for 'Deep Ensemble' in the Table 1 discussion, and 'Mechanichs' for 'Mechanics' in reference titles. These should be corrected.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The duplicated Table 8 and the impossible MAE/RMSE ratios in the NN rows suggest that the experimental data pipeline has not been checked carefully. Combined with the incorrect sign in the physics-informed loss and the undisclosed Basquin fitting protocol, the manuscript's experimental evidence for the central claim is invalid as it stands. The authors would need to rerun all experiments with a corrected loss, fold-disciplined Basquin fitting, and corrected metrics, and then verify the torsion dataset results, which is a substantial revision rather than a local fix. I therefore recommend rejection, but I would consider a resubmission if the corrected experiments still support the method."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper compares eight ML models for fatigue life prediction with a physics-informed feature (Basquin-estimated life) and a boundary loss, on four datasets. That's a useful benchmark, and the idea of adding a classical S-N curve estimate as an input is a reasonable thing to try. The code is available, which is good.\n\nWhat the paper does well: it runs a broad, systematic comparison of UQ methods (QR, NGBoost, GPR, Deep Ensembles, MC Dropout, BNN-VI, BNN-MCMC) and reports standard metrics plus coverage and interval width. The results are consistent across datasets, and the authors are transparent about the limitations of BNN computational cost.\n\nBut there are load-bearing problems. First, Eq. (10) is written backwards. The second term ReLU(y*) penalizes positive predictions, so it pushes predictions negative, not non-negative. The third term ReLU(10,000,000 - y*) penalizes predictions below the upper bound, pushing them above it. If the code actually uses this loss, the boundary constraints are doing the opposite of what's claimed. If the code uses a corrected loss, then the paper misstates it. Either way, the physics-informed loss as described cannot be what improves results.\n\nSecond, Table 8 is identical to Table 4. Table 8 is supposed to be the torsion dataset PIML results, but the numbers match the uniaxial dataset. That's not a rounding coincidence; every metric matches. So either the tables are swapped or the experiment wasn't run properly.\n\nThird, several NN rows have MAE > RMSE (e.g., Table 1 NN: RMSE 0.6443, MAE 2.0463). That's impossible for the same set of errors. It indicates the reported metrics don't come from the same predictions, or the errors were computed incorrectly.\n\nFourth, and most concerning, the Basquin feature is fit to the target data. The paper doesn't say whether the Basquin constants are fit on the training fold only or on the full dataset. Since the target is the experimentally recorded fatigue life, fitting on all data before the CV split means test-fold targets contribute to the features for that fold. That's target leakage, and it could explain the consistent 10–20% improvements across all models, including GPR and NGBoost which don't use the physics-informed loss. The stress-test note is right: the central claim is not established by the experiments as described.\n\nThe idea is still worth pursuing. A corrected version with a properly stated loss, a leakage-safe feature fitting procedure (fit Basquin constants inside each fold on training data only, and state it), and repaired tables could be a solid contribution. But as it stands, the paper doesn't support its headline claim.\n\nMy recommendation: if this lands on your desk, don't desk-reject it outright — send it to peer review with a clear request to verify the loss, the leakage protocol, and the tables. But warn the reviewers that the current version has serious inconsistencies, and the authors need to fix them before the paper can be accepted.","headline":"Useful UQ benchmark with a plausible PIML idea, but the loss is reversed, Table 8 duplicates Table 4, and the Basquin feature may leak the target, so the central claim is unproven.","tokens_in":18140,"tokens_out":3214,"would_cite":false,"duration_ms":26898,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Augmenting machine learning with a Basquin-estimated fatigue-life feature and a boundary-enforcing physics-informed loss yields more accurate and better-calibrated predictions on all four alloy datasets tested.","keywords":["fatigue life prediction","physics-informed machine learning","uncertainty quantification","Bayesian neural networks","Gaussian process regression","metal alloys","Basquin model","boundary constraints"],"falsifier":"Refit the Basquin constants separately inside each of the five cross-validation training folds, recompute the physics-informed feature for the test fold only, and rerun all reported models; if the roughly ten-to-twenty-percent improvements in $R^2$, RMSE, and coverage shrink or disappear, the central claim fails.","tokens_in":17185,"feed_emoji":"🔩","tokens_out":8257,"duration_ms":70423,"temperature":0.7,"pith_summary":"Fatigue life of metal alloys is expensive to measure, and purely data-driven models often give point estimates without trustworthy confidence intervals. The paper proposes a physics-informed machine learning approach that adds a fatigue-life estimate from the Basquin stress-life relation as an extra input feature and trains neural networks with a loss that penalizes predictions outside the physically plausible range of zero to ten million cycles. Across four experimental datasets — a titanium alloy set and three carbon steel sets from uniaxial, bending, and torsion fatigue tests — the physics-informed versions improve accuracy and uncertainty metrics relative to the same models without physics. The paper reports that single-point metric improvements are on the order of ten to twenty percent, with the strongest overall point-and-interval performance from Markov chain Monte Carlo Bayesian neural networks and Gaussian process regression.","feed_headline":"Physics features lift fatigue-life prediction on four alloy datasets","feed_subtitle":"Adding a Basquin-derived feature and boundary-aware loss improved accuracy and interval coverage in every tested alloy.","key_machinery":"Two ingredients carry the argument. The first is the Basquin stress-life relation, a power law $\\sigma = c N_f^m$ relating stress amplitude to cycles to failure; fitted to each dataset, it supplies a physics-informed fatigue-life feature that is concatenated with the measured alloy, processing, and test-condition features. The second is a physics-informed loss function for the neural networks, $\\mathcal{L} = \\frac{1}{N}\\sum_i [(y_i - y_i^*)^2 + \\lambda_1 \\mathrm{ReLU}(y_i^*) + \\lambda_2 \\mathrm{ReLU}(10{,}000{,}000 - y_i^*)]$, which penalizes negative predicted lives and predictions beyond the ten-million-cycle endurance-limit boundary. Together they embed the known monotone stress-life trend and its physical bounds into models that would otherwise fit only the measured samples.","core_discovery":"The central claim is that combining physics-based feature engineering with physics-informed regularization makes data-driven fatigue-life prediction both more accurate and more reliable in its uncertainty estimates. In the proposed framework, the Basquin relation $\\sigma = c N_f^m$ is fitted to experimental stress-life data to produce a physics-informed estimate of fatigue life, and this estimate is appended to the measured input features. For neural-network models, the training loss adds ReLU penalty terms that force predicted fatigue life to stay non-negative and below $10{,}000{,}000$ cycles, the conventional endurance-limit boundary. Validated on four fatigue-test datasets, the method consistently improves $R^2$, RMSE, MAE, coverage, and a composite uncertainty metric compared with the identical models trained without the physics-informed feature and loss; the largest gains appear where the data-only baseline is weakest, such as the uniaxial carbon steel dataset.","pith_inferences":["If the Basquin feature is fitted strictly inside each training fold, the framework should transfer to any property governed by a simple power law, such as creep or tensile strength; the paper does not test this transfer explicitly.","The largest gains appear exactly where the data-only baseline is weakest, suggesting the physics feature acts most as a regularizer when data are sparse or noisy; one could test this by applying the method to deliberately downsampled versions of the four datasets.","A model with a randomly permuted or shuffled physics feature would separate the feature's information content from its mere presence, and would clarify how much of the gain is due to the physics itself versus added model capacity.","The upper-bound penalty at ten million cycles may mask run-out behavior; the paper does not report how predictions near the boundary behave, so it would be informative to evaluate performance on specimens whose measured lives exceed the cutoff."],"forward_implications":["On all four datasets, every evaluated model improves when the physics-informed feature and loss are added, with single-point metrics such as $R^2$, RMSE, and MAE improving by roughly ten to twenty percent.","The boundary-aware loss keeps predicted fatigue lives within the physically meaningful interval from zero to ten million cycles, eliminating predictions that are negative or beyond the endurance-limit cutoff.","Markov chain Monte Carlo Bayesian neural networks and Gaussian process regression produce the most reliable point estimates and uncertainty intervals, while deep ensembles and MC dropout tend to under-cover the true values.","The resulting point predictions plus confidence intervals can be used to plan fatigue tests for new alloys, potentially reducing the number of tests and cycles needed for material qualification."],"supporting_citations":[{"why":"supplies the template for the physics-informed loss with boundary constraints used here.","marker":"[19]"},{"why":"provides the stress-life/Basquin relation used to generate the physics-informed input feature.","marker":"[30]"},{"why":"defines natural gradient boosting, one of the conventional uncertainty-quantification baselines.","marker":"[42]"},{"why":"defines Gaussian process regression, a baseline and a strong performer in the comparison.","marker":"[44]"},{"why":"defines deep ensembles, a neural-network uncertainty-quantification baseline.","marker":"[45]"},{"why":"defines MC dropout, a neural-network uncertainty-quantification baseline.","marker":"[46]"},{"why":"supplies the titanium alloy fatigue dataset used in the first experiment.","marker":"[53]"},{"why":"supplies the three carbon steel fatigue datasets (uniaxial, bending, torsion).","marker":"[54]"},{"why":"provides hyperparameters adopted for the conventional uncertainty-quantification models.","marker":"[55]"}],"fun_headline_variants":["Physics feature sharpens fatigue-life ML forecasts","Basquin physics tightens ML fatigue-life intervals","Physics-informed loss improves ML fatigue-life confidence","Alloy fatigue-life predictions: physics helps ML","ML fatigue-life accuracy boosted by Basquin input"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported improvements assume that the Basquin material constants are fitted in a way that does not let test-fold fatigue lives leak into the training features; if the constants are fit on the full dataset, the physics-informed feature carries information from the held-out samples and the gains would be inflated by leakage.","fun_headline_variants_meta":{"raw":{"variants":["Physics feature sharpens fatigue-life ML forecasts","Basquin physics tightens ML fatigue-life intervals","Physics-informed loss improves ML fatigue-life confidence","Alloy fatigue-life predictions: physics helps ML","ML fatigue-life accuracy boosted by Basquin input"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000225,"raw_usage":{"total_tokens":1426,"prompt_tokens":872,"completion_tokens":554,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":488,"completion_tokens_details":{"reasoning_tokens":485}},"tokens_in":488,"tokens_out":554,"duration_ms":5064,"temperature":1.0,"reasoning_tokens":485,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:39:25.724672+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refit the Basquin constants separately inside each of the five cross-validation training folds, recompute the physics-informed feature for the test fold only, and rerun all reported models; if the roughly ten-to-twenty-percent improvements in $R^2$, RMSE, and coverage shrink or disappear, the central claim fails.","supporting_citations":[{"cited_title":"A physics -informed neural network for creep -fatigue life prediction of components at elevated temperatures","cited_arxiv_id":null,"evidence_quote":"supplies the template for the physics-informed loss with boundary constraints used here."},{"cited_title":"Essential structure of SN curve: Prediction of fatigue life and fatigue limit of defective materials and nature of scatter","cited_arxiv_id":null,"evidence_quote":"provides the stress-life/Basquin relation used to generate the physics-informed input feature."},{"cited_title":"Ngboost: Natural gradient boosting for probabilistic prediction","cited_arxiv_id":null,"evidence_quote":"defines natural gradient boosting, one of the conventional uncertainty-quantification baselines."},{"cited_title":"Gaussian processes for regression","cited_arxiv_id":null,"evidence_quote":"defines Gaussian process regression, a baseline and a strong performer in the comparison."},{"cited_title":"Simple and scalable predictive uncertainty estimation using deep ensembles","cited_arxiv_id":null,"evidence_quote":"defines deep ensembles, a neural-network uncertainty-quantification baseline."},{"cited_title":"Dropout as a Bayesian approximation: Representing model uncertainty in deep learning","cited_arxiv_id":null,"evidence_quote":"defines MC dropout, a neural-network uncertainty-quantification baseline."},{"cited_title":"Machine learning assisted interpretation of creep and fatigue life in titanium alloys","cited_arxiv_id":null,"evidence_quote":"supplies the titanium alloy fatigue dataset used in the first experiment."},{"cited_title":"Mits.nims.go.jp (Accessed March 16, 2024)","cited_arxiv_id":null,"evidence_quote":"supplies the three carbon steel fatigue datasets (uniaxial, bending, torsion)."},{"cited_title":"Uncertainty quantification for Bayesian active learning in rupture life prediction of ferritic steels","cited_arxiv_id":null,"evidence_quote":"provides hyperparameters adopted for the conventional uncertainty-quantification models."}],"review_version":1}