{"id":"e793e670-dd19-4e7d-946b-32f4520a5da9","arxiv_id":"2411.19617","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"MALA predicts electron densities and energies from local atomic environments using trained neural networks, reaching system sizes beyond standard DFT.","lead":"MALA is an open-source software package that trains neural networks to predict local electronic structure, electron density, and total energy from atomic positions, replacing expensive density functional theory calculations. It is demonstrated on boron, aluminum near its melting point, and a 131,072-atom beryllium slab, with computational cost that grows roughly linearly with system size.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stacking-fault slab validation is missing: surfaces and the fault are out-of-distribution environments for the bulk-trained model, and no DFT reference or Rcutoff convergence test is given at the 131k-atom scale.","rationale":"The paper is a solid software/methods description with credible benchmarks: the Be transferability up to 2048 atoms (Fig. 14) has DFT reference and shows errors below 10 meV/atom, the scaling analysis in Sec. 5.2 is thorough, and the code is publicly available. The reader's CONDITIONAL verdict reflects that the central claim is plausible but not airtight. The most load-bearing gap is the 131k-atom stacking-fault demonstration: it is the flagship example of 'scales far beyond standard DFT', yet it lacks any DFT validation and introduces surface environments that are entirely outside the training distribution. The paper itself honestly states that no DFT reference is available (Sec. 5.1.1), so the limitation is acknowledged; however, the abstract and introduction still assert predictive capability at such scales, which overstates what the evidence shows. My proposed test - a smaller slab with DFT reference plus an Rcutoff convergence check - directly addresses whether the nearsightedness/transferability assumption holds for surfaces and defects, and would either validate or invalidate the large-scale demonstration. This does not change the reader's verdict (CONDITIONAL remains appropriate until such validation is provided), but it sharpens the condition that needs to be met: the model must be shown to generalize to the specific environments in the slab, not just to larger periodic bulk cells.","tokens_in":43773,"tokens_out":4254,"duration_ms":40147,"concrete_test":"Apply the same bulk-trained beryllium MALA model (256-atom training data) to a smaller slab containing both free surfaces and a stacking fault at a DFT-accessible size, e.g., 2048 atoms, and compare against Quantum ESPRESSO reference calculations: (1) total free energy per atom for faulted and perfect slabs, (2) the stacking-fault energy (difference between faulted and perfect slab), and (3) the electronic density profile across the slab, particularly near surfaces and the fault. In addition, rerun the MALA inference with the bispectrum cutoff Rcutoff increased by 20% (and, if feasible, a second increase) to check that the fault energy changes by less than the 10 meV/atom target. If the errors exceed target accuracy or the result depends strongly on Rcutoff, the 131k-atom transferability claim is not supported without additional training or descriptor refinement.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of transferability to the 131,072-atom beryllium slab (Sec. 5.1.1) rests on the assumption that the local descriptor-to-LDOS mapping learned from 256-atom bulk hcp snapshots generalizes to every environment in the slab. The slab contains two environments absent from the training data: free surfaces and the stacking-fault region. Nearsightedness (Refs. 91,92) justifies using a finite descriptor cutoff, but it does not ensure that the model has learned the correct mapping for descriptor vectors that never occur in bulk training data - a surface grid point has a half-empty neighborhood, which is structurally different from any bulk configuration. The paper provides no DFT reference for any slab system, no convergence test with respect to the bispectrum cutoff Rcutoff for the slab, and no check of predicted density or LDOS at the surfaces. The only quantitative check is the total-free-energy scaling with N^{-1/3}, which is compared to an empirical interatomic potential and is only qualitative (the paper states this explicitly). Consequently, the large-scale demonstration shows that MALA can be executed at 131k atoms and yields plausible energy trends, but it does not establish that the predicted electronic structure is accurate at that scale. The reader's weakest assumption points at the same unresolved locality/transferability issue, but the more precise failure mode is out-of-distribution descriptor environments (surfaces) rather than only long-range electronic effects. This matters because the abstract and introduction claim predictive capability 'at scales far beyond standard DFT'; without validation on a slab at a DFT-accessible size, that claim is under-supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper describes the Materials Learning Algorithms (MALA) package, a machine-learning framework that predicts the local density of states (LDOS) from local atomic descriptors and derives electronic density, DOS, band energy, and total free energy via an exact reformulation of Kohn-Sham DFT. It presents the theoretical basis, software architecture, data-generation and training workflows, and three numerical demonstrations: a boron tutorial example, aluminum transferability across the solid-liquid phase boundary and across temperatures, and beryllium transferability from a 256-atom training cell to systems up to a 131,072-atom slab containing a stacking fault. It also reports scaling benchmarks showing linear inference cost growth, strong-scaling bottlenecks in the observable-calculation step, and weak-scaling efficiency around 0.6-0.7.","tokens_in":44054,"tokens_out":4419,"duration_ms":41865,"significance":"If the transferability claims hold, this is a significant software contribution: the LDOS-to-energy route is an exact reformulation rather than a fitted identity, the package is open source and reproducible, and the 131,072-atom beryllium demonstration would be an electronic-structure prediction at a scale inaccessible to standard DFT. The paper is also careful in several respects: it distinguishes discretization errors from machine-learning errors, provides uncertainty across network initializations, and openly states that no DFT reference exists for the largest system. The strength of the numerical evidence for the smaller beryllium and aluminum benchmarks supports the package's practical value. However, the headline large-scale demonstration and the boron model-selection procedure need additional validation or reframing before the central claims can be fully accepted.","major_comments":[{"comment":"The 131,072-atom beryllium stacking-fault result, presented as the headline demonstration, has no DFT reference and no test of the locality assumption at the surfaces or fault region. The text itself states that \"DFT reference data is not available for this large system,\" and the only quantitative check is an N_i^{-1/3} energy trend compared against an empirical EAM potential. Since the training set contains only bulk 256-atom hcp configurations, the free surfaces and the stacking-fault environment are out-of-distribution descriptor states; nearsightedness alone does not guarantee that the learned mapping is correct there. Please add a DFT reference for a smaller slab containing the same surfaces and stacking fault, or explicitly restrict the claim to feasibility and qualitative trend prediction.","section":"Sec. 5.1.1, Fig. 15"},{"comment":"The boron model is selected from five trained initializations using the test set: the text says \"model #1 is chosen\" based on both low MAE and low MaxAE in Fig. 9, which plots test-set errors. This selection makes the subsequently reported inference errors in Figs. 10-12 optimistic relative to true out-of-sample performance. If test-set-based selection is retained, the selection bias should be explicitly acknowledged and ideally accompanied by test-set statistics for all five models or selection on the validation snapshot.","section":"Sec. 4.2, Fig. 9"},{"comment":"The claim that \"MALA inferences not only scale linearly\" is not directly established by Fig. 20, because both the computational resources and the grid resolution change with system size: the number of GPUs rises from 4 to 30 and grid points per atom drops from 4860 to 2298 at 131,072 atoms (Tables 3 and 4). A constant-resource or constant-grid-points-per-atom scaling curve, or an explicit statement that the observed trend is a weak-scaling efficiency result, is needed before the linear-scaling cost claim can be accepted as demonstrated.","section":"Sec. 5.2, Fig. 20, Tables 3-4"},{"comment":"The paper does not report a convergence test of the bispectrum descriptor cutoff Rcutoff for the slab geometry. Because the slab contains atomic environments far from the training bulk distribution, such a test in a smaller slab or a surface-containing cell is needed to check that the finite descriptor range is sufficient and that the learned descriptor-to-LDOS mapping generalizes to the fault and surface environments.","section":"Secs. 5.1.1 and 5.2"}],"minor_comments":[{"comment":"There is a typo: \"Eii the the ion-ion interaction\" should read \"Eii the ion-ion interaction.\"","section":"Sec. 2.2, Eq. (10)"},{"comment":"The sentence \"Usually on the order of 100 to 10 1\" is garbled; it should presumably read \"100 to 10^1\" or \"100 to 1,000.\"","section":"Sec. 3.6"},{"comment":"The beryllium 256-atom room-temperature model entry appears twice in the table.","section":"Table 2"},{"comment":"The phrase \"The analysis shows that a that a k-grid\" contains a repeated word and should be corrected.","section":"Sec. 4.1.2"},{"comment":"The caption writes \"Ni − 13 fit\"; this should be \"N_i^{-1/3} fit.\"","section":"Fig. 15 caption"},{"comment":"The notation for r' = p - r and the argument of the delta function delta(R_alpha - r') is confusing; please clarify how the auxiliary grid p is used in the descriptor evaluation.","section":"Sec. 3.2.2, Eq. (24)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a software paper for a mature ML-DFT framework, and it is mostly a well-written package description. The genuinely new piece is the boron workflow: a first non-metal MALA model, trained with off-the-shelf hyperparameters from previous work, that reproduces the complex DOS of alpha-rhombohedral boron to a reasonable approximation. The aluminum phase-boundary and temperature-transfer results are updated from earlier papers, and the scaling analysis is thorough—it identifies the observable calculation as the main bottleneck in multi-GPU inference. The exact LDOS-to-energy reformulation is clearly presented and correct, and the package itself appears well-engineered, open-source, and integrated with Quantum ESPRESSO and LAMMPS. The length-scale transfer tests on beryllium (512–2048 atoms) with DFT reference are convincing evidence for the method's locality assumption in bulk environments.\n\nThe soft spot is exactly where the stress-test note points: the 131,072-atom stacking-fault slab. The model was trained on 256-atom bulk hcp snapshots, and the slab contains free surfaces—environments that never appear in the training data. Nearsightedness justifies using a local descriptor cutoff, but it does not guarantee that the descriptor-to-LDOS mapping is correct for a half-empty surface neighborhood. The paper explicitly states that no DFT reference is available for the slab and only compares energy trends against an N^{-1/3} fit and an interatomic potential. That is qualitative. A DFT reference for a small slab with the same surface orientation and stacking fault, say a few hundred atoms, would have validated the transfer and closed the gap. This is a correctable omission rather than a fatal flaw, but it means the headline claim of predicting electronic structure 'far beyond standard DFT' is under-supported.\n\nTwo smaller issues. The boron model is selected from five initializations by best MAE and MaxAE on the test set; reporting ensemble statistics or a proper validation split would be more honest. Reproducibility is incomplete: no commit hash, no released training data, and 'Supplementary material: None' for a CPC paper.\n\nBottom line: the package is real, the method is sound in outline, and the paper deserves a serious referee. The fixes are straightforward: add a DFT-validated small slab test, report ensemble-averaged boron errors, and release the training data or a documented generation pipeline. I would engage with it.","headline":"Solid package paper with a genuinely new boron demo; the 131k-atom stacking-fault slab is a compelling demo but lacks validation at DFT scale and deserves referee scrutiny.","tokens_in":44711,"tokens_out":3524,"would_cite":true,"duration_ms":33591,"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":"A network trained on a few hundred atoms predicts electronic structure for a 131,072-atom beryllium slab at near-chemical accuracy and linearly scaling cost.","keywords":["machine learning","electronic structure","density functional theory","local density of states","nearsightedness","multi-scale transferability","linear scaling","atomistic simulation"],"falsifier":"Take a metallic system with a charged defect or a bare surface, where long-range electronic effects are expected to matter, and run a MALA model trained with the same descriptor cutoffs used for beryllium; compare the predicted LDOS and total free energy against a DFT reference on a mid-size cell of a few hundred atoms. If the error exceeds the paper's 10 meV/atom threshold once the defect or surface is introduced, the nearsightedness assumption fails for the large-scale application.","tokens_in":1765,"feed_emoji":"⚛️","tokens_out":2131,"duration_ms":55137,"temperature":0.7,"pith_summary":"The paper presents MALA, a machine learning package designed to accelerate density functional theory calculations. The central claim is that a neural network trained on a few hundred DFT snapshots can predict the local density of states, and from it all derived electronic observables, for systems hundreds of times larger than the training cell, with errors at or near the 10 meV/atom threshold commonly used for machine-learning potentials. The featured demonstration is a 131,072-atom beryllium slab containing a stacking fault, whose per-atom free energy follows the expected scaling behavior. If correct, this would extend electronic structure calculations to scales far beyond conventional DFT, at a fraction of the cost.","feed_headline":"ML predicts electronic structure at 131,072 atoms","feed_subtitle":"A network trained on 256 atoms transfers to large beryllium slabs at near-DFT accuracy and linear cost.","key_machinery":"The central object is the local density of states $d(r, \\epsilon) = \\sum_j |\\psi_j(r)|^2 \\delta(\\epsilon - \\epsilon_j)$, which encodes the full electronic structure at each real-space grid point and integrates over energy to yield the electronic density and over space to yield the density of states. The machine learning model maps bispectrum descriptors, rotation-invariant encodings of the ionic environment within a cutoff radius around each grid point, to the LDOS at that point. The physical justification for using a finite local description is the nearsightedness of electronic matter. All downstream observables, including band energy, electronic entropy, and total free energy, are computed by analytically integrating the predicted LDOS, with the Fermi energy determined self-consistently by root-finding on the electron count.","core_discovery":"The paper claims that a feed-forward neural network, trained on the local density of states (LDOS) of only a few hundred atoms, transfers unchanged to systems hundreds of times larger. The key design is learning the LDOS rather than the electronic density, because every observable is derived from the predicted LDOS by quadrature over energy and space. The claim is supported by three demonstration cases: beryllium from 256-atom training cells to 2,048 atoms with total free energy errors below 10 meV/atom and density mean absolute percentage errors below 1%; aluminum across the solid-liquid phase boundary, where the phase gap of roughly 95 meV/atom is easily resolved; and the 131,072-atom beryllium slab with a stacking fault, whose per-atom free energy reproduces the expected $N^{-1/3}$ scaling behavior. The paper explicitly states that DFT reference data at the 131,072-atom scale is unavailable, so the large-scale energetics are validated qualitatively against dimensional analysis and an interatomic potential.","pith_inferences":["A natural extension would be to test whether the nearsightedness assumption holds for systems with charged defects, surfaces, or strong long-range screening, where the LDOS at a point might depend on the environment beyond the descriptor cutoff; the paper does not provide such a convergence study for the stacking-fault system.","Because the LDOS is precisely the quantity measured in scanning tunneling microscopy, the method suggests a direct route to generate STM images for extended systems, which the authors name as a future application.","The paper describes atomic cluster expansion descriptors as a richer alternative to the bispectrum descriptors used in the current benchmarks, so testing transferability across multiple chemical species in alloys would be a natural next step."],"forward_implications":["If the central claim is correct, electronic structure calculations become feasible for systems of hundreds of thousands of atoms at near-DFT accuracy, with a cost that grows linearly in the number of atoms.","For defect systems such as stacking faults, the model reproduces the expected $N^{-1/3}$ total-energy scaling, meaning defect energetics in large systems could be computed without a full DFT treatment of the whole cell.","Because all derived properties come from a single learned quantity, the LDOS, predictions of density, DOS, band energy, and free energy remain mutually consistent by construction.","Training costs are on the order of a few to tens of GPU hours, shifting the practical bottleneck to DFT data generation, which the authors note can take several days of wall time per snapshot.","The demonstrated transferability across length scale, temperature, and the solid-liquid phase boundary implies that a single MALA model can cover a wide region of configuration space for a given element."],"supporting_citations":[{"why":"Establishes the deep neural network approach for accelerating finite-temperature Kohn-Sham DFT and provides the model architecture used throughout the paper.","marker":"[48]"},{"why":"Supplies the hyperparameter optimization method for bispectrum descriptors and network architecture selection that the paper relies on.","marker":"[23]"},{"why":"Demonstrated temperature transferability of MALA models for aluminum, which the paper extends with updated datasets.","marker":"[52]"},{"why":"Introduced the prediction of electronic structures at any length scale and the beryllium stacking-fault slab that the paper presents as its largest-scale result.","marker":"[53]"},{"why":"Kohn's linear-scaling density functional argument provides the nearsightedness principle that justifies local descriptors for the LDOS.","marker":"[91]"},{"why":"Prodan and Kohn's formal analysis of nearsightedness is the theoretical grounding for transferring models trained on small cells to large systems.","marker":"[92]"},{"why":"Provides the detailed trajectory sampling, shuffle handling, and updated datasets that the paper's numerical benchmarks build on.","marker":"[37]"}],"fun_headline_variants":["ML predicts 131k atoms from a 256-atom training set","Scale-up: ML learns from 256 atoms, predicts 131k","MALA: From 256 atoms to 131k atom simulations","ML transfers from 256 atoms to 131k systems","Machine learning scales electronic structure to 131k atoms"],"cache_read_input_tokens":46720,"weakest_assumption_plain":"The entire transfer from small training cells to the 131,072-atom slab rests on the assumption that the LDOS at a grid point depends only on the ionic environment inside the finite descriptor cutoff radius, so no long-range electronic effect such as metallic screening or charged defects contributes significantly at that point.","fun_headline_variants_meta":{"raw":{"variants":["ML predicts 131k atoms from a 256-atom training set","Scale-up: ML learns from 256 atoms, predicts 131k","MALA: From 256 atoms to 131k atom simulations","ML transfers from 256 atoms to 131k systems","Machine learning scales electronic structure to 131k atoms"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001389,"raw_usage":{"total_tokens":5610,"prompt_tokens":924,"completion_tokens":4686,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":4598}},"tokens_in":540,"tokens_out":4686,"duration_ms":27828,"temperature":1.0,"reasoning_tokens":4598,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:59:46.893874+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a metallic system with a charged defect or a bare surface, where long-range electronic effects are expected to matter, and run a MALA model trained with the same descriptor cutoffs used for beryllium; compare the predicted LDOS and total free energy against a DFT reference on a mid-size cell of a few hundred atoms. If the error exceeds the paper's 10 meV/atom threshold once the defect or surface is introduced, the nearsightedness assumption fails for the large-scale application.","supporting_citations":[{"cited_title":"Predicting electronic structures at any length scale with machine learning","cited_arxiv_id":"2210.11343","evidence_quote":"Introduced the prediction of electronic structures at any length scale and the beryllium stacking-fault slab that the paper presents as its largest-scale result."}],"review_version":1}