{"id":"87133f24-9291-42fc-9b03-1b7bec6051e2","arxiv_id":"2509.06525","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A machine learning tight-binding framework reconstructs DFT-level Hamiltonians and computes electronic properties for systems with up to 100 million atoms, including graphene mobility versus carrier concentration.","lead":"GPUTB is a GPU-accelerated machine learning tight-binding method that predicts electronic structure from atomic positions, and then uses linear-scaling transport to compute density of states and mobility in systems with up to 100 million atoms. It is significant because it brings near-DFT accuracy to device-scale electronic property simulations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Training on high-symmetry k-path eigenvalues may underdetermine the Hamiltonian, leaving DOS and mobility predictions unvalidated off-path.","rationale":"The central claim is that GPUTB produces Hamiltonians that yield accurate DOS and mobility for systems up to 100M atoms. For that to hold, the learned real-space Hamiltonian must be correct over the entire Brillouin zone and across environments not seen in the small training cells. The manuscript only reports fitting to eigenvalues along high-symmetry k-paths (Sec. 2.3) and does not provide a uniform-k-grid test. DOS and LSQT transport depend on the full BZ; the velocity operator in particular samples off-path regions. Thus the underdetermination of SK parameters from a path-only loss is a concrete, load-bearing gap. The paper partially mitigates this for pristine graphene by comparing to DFT tetrahedron DOS, but that comparison is for a perfect lattice and does not test disordered or heterojunction environments. A uniform-k-grid validation would settle whether the model generalizes off-path. This does not change the conditional verdict but sharpens the condition.","tokens_in":11265,"tokens_out":4753,"duration_ms":52281,"concrete_test":"Take the trained 8-atom SiGe model and compute band eigenvalues on a dense uniform k-grid (e.g., 6×6×6) for the 8-, 64-, and 216-atom cells; compare to DFT eigenvalues on the same k-grid, reporting the off-path MAE separately from the high-symmetry path. If the uniform-grid MAE is comparable to the reported 13–20 meV, the concern is alleviated; if it is significantly larger, the Hamiltonian is not validated for full-BZ properties.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The loss function (Eq. 3) is evaluated only at 'high-symmetry k-path' eigenvalues (Sec. 2.3). GPUTB's real-space SK parameters are therefore fit to a low-dimensional slice of the Brillouin zone. But DOS and LSQT conductivity (Sec. 2.4) integrate over the full BZ, and the velocity operator, which controls transport, depends on off-path Hamiltonian matrix elements. No uniform-k-grid validation is reported: Fig. 4(a) compares a 100M-atom finite-temperature DOS to a unit-cell DFT tetrahedron DOS, which is not a stringent check for disordered, polycrystalline, or heterojunction systems. The environment-dependent parameters may be underdetermined by the path-only training, so the claimed transferability to 100M-atom and heterojunction systems is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents GPUTB, a machine-learning tight-binding framework that constructs environment-dependent Slater-Koster Hamiltonians from DFT band structures. The Hamiltonians are used with the linear-scaling quantum transport (LSQT) method to compute density of states, conductivity, and carrier mobility for large systems. Reported band-structure MAEs are 13.0–25.8 meV for SiGe, graphene, diamond, GaP, and AlAs, with transfer from an 8-atom training cell to 64- and 216-atom supercells. The method is applied to graphene DOS with over 100 million atoms, to 2.4–3.0 million atom SiGe single-crystal and polycrystalline systems, and to h-BN/graphene heterojunctions. The room-temperature graphene mobility versus carrier concentration is compared with experimental data. The central claim is that GPUTB provides an accurate and efficient bridge from DFT accuracy to device-scale electronic property calculations.","tokens_in":11561,"tokens_out":5732,"duration_ms":67454,"significance":"If the accuracy and transferability claims are substantiated, GPUTB would be a practically useful tool for device-scale electronic-structure calculations. The strongest evidence is the external experimental benchmark for graphene mobility and the demonstration of DOS calculations on 100-million-atom systems. The paper also shows flexibility with respect to basis sets, exchange-correlation functionals, allotropes, and heterojunctions, and it offers an efficiency comparison against DeePTB. However, the validation has important gaps: training is performed only on high-symmetry k-path eigenvalues, and the large-scale DOS comparisons are made against 0 K DFT tetrahedron DOS, so the claims about off-path Hamiltonian accuracy and finite-temperature DOS are not yet established at the reported level of precision.","major_comments":[{"comment":"The training loss in Eq. (3) is evaluated only on high-symmetry k-path eigenvalues ('High-symmetry k-path selections were made for band structure calculations'). DOS and LSQT conductivity, Eqs. (3)–(4) in §2.4, depend on the full Brillouin zone and on off-path Hamiltonian matrix elements through the velocity operator. Fitting a low-dimensional k-path slice may leave parts of the environment-dependent Hamiltonian underdetermined. No uniform-k-grid validation is reported. I recommend adding a validation set on uniform k-meshes for small cells and reporting band-structure and DOS errors over the full BZ.","section":"§2.3, Eq. (3)"},{"comment":"The finite-temperature DOS for SiGe (Fig. 3a) and for 100-million-atom graphene (Fig. 4a) is compared to a 0 K DFT tetrahedron DOS. This comparison conflates thermal broadening with model error and cannot discriminate between temperature effects and Hamiltonian inaccuracy. A direct comparison of GPUTB DOS against DFT DOS at the same temperature and k-point sampling for small supercells is needed to validate the method quantitatively.","section":"Fig. 3(a), Fig. 4(a)"},{"comment":"The polycrystalline SiGe DOS/conductivity and the h-BN/graphene heterojunction DOS are presented without quantitative reference DFT calculations for the same disordered or interface geometries. The mid-gap defect states and the heterojunction bandgap opening are discussed only qualitatively. Since GPUTB uses a fixed orthogonal TB Hamiltonian with no charge self-consistency or explicit long-range electrostatics, it is not obvious that these effects are captured reliably. I request benchmarks on small grain-boundary and heterojunction supercells with quantitative error metrics.","section":"§3, polycrystalline and heterojunction results"},{"comment":"No code or training/test data are provided; the Data Availability statement only says 'Data will be made available on request.' For a machine-learning method paper, this hampers independent verification of the central claims. I encourage the authors to release the code, trained models, and representative training/testing datasets.","section":"Reproducibility / Data availability"}],"minor_comments":[{"comment":"The table header appears garbled (repeated 'c/c', 'm/c', and 'Average' entries). Please clarify the columns and define how the 'Average' values are computed.","section":"Table 1"},{"comment":"Two equations are labeled (3): the conductivity equation in §2.4 and the loss function in §3. Please renumber.","section":"Equation numbering"},{"comment":"The caption reads 'Band structure of unit-cell h-BN/graphene heterojunction with 1 million atoms,' which is self-contradictory. Clarify whether the band structure is for a small unit cell and the DOS for the 1-million-atom system.","section":"Fig. 4(c) caption"},{"comment":"MAEs and mobility curves are reported without uncertainties. Please provide error bars or standard deviations over multiple model initializations and/or MD frames to assess statistical significance.","section":"Fig. 2 and Fig. 4(b)"}],"recommendation":"major_revision","confidential_remarks":"The experimental graphene mobility comparison is the strongest point in favor of the method. The k-path-only training and temperature-mismatched DOS validation are the main technical concerns; both are addressable with additional uniform-grid and same-condition benchmarks. I would also strongly encourage code/data release for reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nKey takeaway: this is a real piece of work. GPUTB is an environment-dependent Slater-Koster tight-binding model trained on DFT band structures, and the authors use it with a GPU LSQT implementation to push DOS and conductivity to 100 million atoms. The graphene room-temperature mobility versus carrier concentration matches experiment at low carrier density, which is the strongest external evidence that the Hamiltonians are physically meaningful. The MAEs on SiGe (13–19 meV from 8 to 216 atoms) beat DeePTB in their Table 1 across several systems, and the single-model graphene/diamond transfer is a nice demonstration of environmental descriptors.\n\nThe conceptual core already exists in DeePTB, but the engineering is new: Chebyshev descriptors, GPU implementation, and integration with NEP-MD and LSQT. That is worth something, provided the code ships.\n\nNow the soft spots. Most serious: the loss function in Eq. (3) is evaluated only on eigenvalues along high-symmetry k-paths. The real-space hopping parameters are therefore fit to a low-dimensional slice of the BZ, while DOS and conductivity integrate over the full BZ and depend on off-path matrix elements. No uniform-k-grid validation is reported. The comparison in Fig. 4(a) is a 100M-atom finite-temperature DOS against a 0 K unit-cell tetrahedron DOS, which is not a stringent test for the disordered or heterojunction systems where transferability is claimed. That concern stands after reading the paper; it is not manufactured.\n\nSecond, there is no code, no data, and the supplemental material is referenced but absent. “Data will be made available on request” is not enough for a methods paper of this type. Third, the h-BN/graphene heterojunction section is thin: no detail on whether the model was trained on heterojunction configurations or extrapolated, and the DOS comparison near the Fermi level is qualitative. Given the claim of heterojunction capability, that needs numbers. Minor: the finite-temp DOS comparison in Fig. 3 is also against 0 K DFT, and there are no error bars anywhere.\n\nNone of this sinks the central claim that a well-fitted environment-dependent TB Hamiltonian, combined with LSQT, can reproduce device-scale transport. The graphene mobility check is a genuinely independent benchmark. But the abstract overstates what is established: transferability to 100M-atom disordered and heterojunction systems is plausible, not proven.\n\nWho is this for? Anyone working on ML Hamiltonians, linear-scaling transport, or large-scale electronic structure. It deserves a serious referee, but the authors should be asked to provide code/data or at least a uniform-k-grid DOS validation and error bars. I would not cite it in my own work until the code is available, but I would watch for it.\n\nBest,\n[Your name]","headline":"GPUTB is a credible ML-TB framework with an impressive scale demonstration and a convincing experimental mobility check, but the Hamiltonian is fit only to high-symmetry k-path eigenvalues, leaving off-path DOS and heterojunction transfer claims under-validated, and the missing code/data blocks independent verification.","tokens_in":11989,"tokens_out":3017,"would_cite":false,"duration_ms":35954,"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 machine-learned tight-binding model computes electronic properties for 100 million atoms, matching graphene's room-temperature mobility.","keywords":["machine learning tight-binding","GPU acceleration","Slater-Koster","linear-scaling quantum transport","electronic structure","graphene mobility","heterojunction","large-scale simulation"],"falsifier":"Take a graphene/h-BN heterojunction with a moiré period not sampled during training, compute its density of states with GPUTB, and compare against a converged DFT band-structure calculation on the same geometry; if the band-gap opening or the DOS near the Fermi level deviates by much more than the claimed 13-26 meV band MAE, the environmental-transfer premise is falsified.","tokens_in":11215,"feed_emoji":"⚛️","tokens_out":7123,"duration_ms":77229,"temperature":0.7,"pith_summary":"GPUTB claims that a machine-learned, environment-dependent tight-binding model can deliver density-functional-theory-quality electronic properties at device scale. It trains neural networks to output Slater-Koster hopping integrals and onsite energies from local atomic environments, using DFT band structures as reference, reaching band mean absolute errors of 13-26 meV across tested materials. With those Hamiltonians, a linear-scaling transport solver computes density of states and carrier mobility for systems up to 100 million atoms, including finite-temperature graphene, polycrystalline SiGe, and h-BN/graphene heterojunctions. The central validation is that graphene's room-temperature mobility versus carrier concentration matches experiment, suggesting that device-scale electronic simulations no longer need direct ab-initio calculation of the full system.","feed_headline":"Electronic properties computed for 100 million atoms","feed_subtitle":"A machine-learned tight-binding model trained on density-functional theory bands reproduces graphene's room-temperature mobility.","key_machinery":"An environment-dependent Slater-Koster Hamiltonian built from message-passing graph neural networks. Hopping integrals between an atom pair are written as the product of geometric Slater-Koster coefficients and a neural-network output whose input is a Chebyshev-polynomial expansion of the pair's local environment; onsite energies come from a separate network on the atomic environment descriptor. This yields an orthogonal sparse Hamiltonian with no overlap matrix, which is precisely what the linear-scaling transport solver needs to keep every step linear in the number of atoms.","core_discovery":"The paper introduces GPUTB, a machine-learning method that maps an atomic structure directly to a sparse orthogonal tight-binding Hamiltonian. The mapping is trained by matching predicted band structures to DFT reference bands on small periodic cells, with band mean absolute errors reported around 13-26 meV across SiGe, graphene, diamond, GaP, AlAs, and h-BN/graphene. The key claim is that the resulting Hamiltonian is accurate enough beyond the training cell: it is used with a linear-scaling quantum transport solver to compute density of states for a 100-million-atom graphene sheet, room-temperature mobility versus carrier concentration for 6.5-million-atom graphene, and the DOS of million-a","pith_inferences":["If the local-environment descriptor is as transferable as claimed, the same trained model should predict defect states and grain-boundary conductance without retraining; a direct test would be a DFT comparison for a single vacancy in graphene.","Because the Hamiltonian is sparse and orthogonal, the sampling of ionic configurations, not the electronic solve, becomes the main remaining cost; combining GPUTB with faster generative sampling would make device-scale workflows routine.","The method's fixed basis and finite cutoff mean long-range electrostatic environments, such as metal-water interfaces, are likely outside its reach; testing on such systems would clarify how much expressivity the network needs."],"forward_implications":["Finite-temperature electronic structure and transport become practical for millions of atoms, not just perfect crystals; polycrystalline and heterojunction samples are within reach.","A single GPUTB model can describe structurally distinct allotropes and heterostructures, so transfer across phases requires no separate training per structure.","The combination with linear-scaling transport means density of states and conductivity are computed in O(N), opening micrometer-scale samples to direct simulation.","Graphene's room-temperature mobility as a function of carrier concentration is reproduced from a Hamiltonian trained on small DFT cells, giving a predictive bridge between ab-initio accuracy and experiment."],"supporting_citations":[{"why":"Supplies the LCAO-basis DFT band structures used as training targets for the tight-binding Hamiltonian.","marker":"[8]"},{"why":"Provides the linear-scaling quantum transport method with GPU implementation that the paper integrates.","marker":"[10]"},{"why":"The LSQT methodology review that the transport calculation follows, including Chebyshev expansion and kernel polynomial techniques.","marker":"[12]"},{"why":"An earlier deep-learning tight-binding approach that GPUTB is compared against for accuracy and training speed.","marker":"[27]"},{"why":"The machine-learned potential used to generate finite-temperature molecular dynamics structures for large systems.","marker":"[28]"},{"why":"Experimental room-temperature graphene mobility at low carrier concentration used as a validation target.","marker":"[29]"},{"why":"Experimental room-temperature graphene mobility on SiO2 used as a validation target at higher carrier concentration.","marker":"[30]"},{"why":"Slater-Koster bond integrals, the geometric parameterization that defines how hopping depends on bond direction.","marker":"[34]"}],"fun_headline_variants":["ML tight-binding computes properties for 100M atoms","GPU-accelerated tight-binding scales to 100M atoms","Tight-binding ML: DFT accuracy at device scale","GPUTB: machine-learned Hamiltonians for huge systems","From DFT bands to 100M atom electronics via ML"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The whole pipeline assumes that a model trained on small perfect cells with finite-temperature snapshots recognizes the same local bonding environments in 100-million-atom, polycrystalline, and heterojunction systems, so the learned parameters transfer without re-fitting and without charge self-consistency.","fun_headline_variants_meta":{"raw":{"variants":["ML tight-binding computes properties for 100M atoms","GPU-accelerated tight-binding scales to 100M atoms","Tight-binding ML: DFT accuracy at device scale","GPUTB: machine-learned Hamiltonians for huge systems","From DFT bands to 100M atom electronics via ML"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000781,"raw_usage":{"total_tokens":3281,"prompt_tokens":734,"completion_tokens":2547,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":478,"completion_tokens_details":{"reasoning_tokens":2466}},"tokens_in":478,"tokens_out":2547,"duration_ms":20932,"temperature":1.0,"reasoning_tokens":2466,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T23:28:20.225225+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a graphene/h-BN heterojunction with a moiré period not sampled during training, compute its density of states with GPUTB, and compare against a converged DFT band-structure calculation on the same geometry; if the band-gap opening or the DOS near the Fermi level deviates by much more than the claimed 13-26 meV band MAE, the environmental-transfer premise is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the LCAO-basis DFT band structures used as training targets for the tight-binding Hamiltonian."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the linear-scaling quantum transport method with GPU implementation that the paper integrates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The LSQT methodology review that the transport calculation follows, including Chebyshev expansion and kernel polynomial techniques."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"An earlier deep-learning tight-binding approach that GPUTB is compared against for accuracy and training speed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The machine-learned potential used to generate finite-temperature molecular dynamics structures for large systems."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Experimental room-temperature graphene mobility at low carrier concentration used as a validation target."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Experimental room-temperature graphene mobility on SiO2 used as a validation target at higher carrier concentration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Slater-Koster bond integrals, the geometric parameterization that defines how hopping depends on bond direction."}],"review_version":1}