Head-to-head against a standard PBE screening baseline (GPAW, plane-wave 200 eV, 6³ k-points) on 15 canonical materials. Three-layer scoring — engine vs experiment, DFT vs experiment, engine vs DFT — on the same fixed set. The engine takes only the chemical formula; the DFT side requires explicit crystal structure, pseudopotentials, and SCF settings.
Each property scored against both DFT and experiment on the same 15 materials, lattice fixed at experimental input
| Property | N | Engine vs experiment | DFT (PBE) vs experiment | Verdict |
|---|---|---|---|---|
| Lattice constant a (Å) | 15 | MAPE 0.2% · median 0.1% | 0.0% by construction (Tier 1 fixes DFT lattice to experiment; only Tier 2 relaxes) | Engine predicts composition-only; DFT given exp |
| Band gap (eV) | 10 | MAPE 7.6% · median 1.2% | MAPE 45.1% · median 50.7% | Engine beats PBE |
| Magnetic moment (μB) — Fe and Ni only, n=2 | 2 | MAPE 3.6% · median 3.6% | MAPE 9.0% · median 9.0% | Engine beats PBE on Fe/Ni |
DFT runs use plane-wave PBE (200 eV cutoff, 6³ k-points, no relaxation). The full settings are in the methodology section below.
All 15 materials, raw numbers, sorted by family
| Material | Family | Exp. a (Å) | FLUX a (Å) | a error | Exp. Eg (eV) | FLUX Eg (eV) | DFT Eg (eV) | Status |
|---|---|---|---|---|---|---|---|---|
| Si | Group IV (diamond) | 5.431 | 5.431 | −0.0% | 1.12 | 1.12 | 0.92 | PASS |
| Ge | Group IV (diamond) | 5.658 | 5.655 | −0.1% | 0.66 | 0.66 | 0.43 | PASS |
| GaAs | III–V (zincblende) | 5.653 | 5.647 | −0.1% | 1.43 | 1.43 | 1.22 | PASS |
| GaN | III–V (wurtzite) | 3.189 | 3.183 | −0.2% | 3.40 | 3.44 | 1.83 | PASS |
| ZnO | II–VI (wurtzite) | 3.249 | 3.230 | −0.6% | 3.37 | 3.40 | 0.93 | PASS |
| MgO | Oxide (rocksalt) | 4.211 | 4.208 | −0.1% | 7.83 | 6.16 | 3.13 | FAIR |
| TiO2 | Oxide (rutile) | 4.594 | 4.545 | −1.1% | 3.05 | 3.39 | 1.78 | PASS |
| NaCl | Ionic (rocksalt) | 5.640 | 5.630 | −0.2% | 8.60 | 9.17 | 5.38 | PASS |
| Al | Metal (fcc) | 4.046 | 4.049 | +0.1% | 0 | 0 | 0 | PASS |
| Cu | Metal (fcc) | 3.615 | 3.621 | +0.2% | 0 | 0 | 0 | PASS |
| Fe | Magnetic metal (bcc) | 2.866 | 2.864 | −0.1% | moment 2.22 μB → engine 2.26 (+1.9%), DFT 2.20 (−1.0%) | PASS | ||
| Ni | Magnetic metal (fcc) | 3.524 | 3.521 | −0.1% | moment 0.62 μB → engine 0.65 (+5.4%), DFT 0.72 (+16.8%) | PASS | ||
| Graphite (C) | Layered | 2.461 | 2.461 | +0.0% | 0 | 5.73 | 1.28 | FAIR |
| h-BN | Layered | 2.504 | 2.507 | +0.1% | 5.96 | 3.97 | 3.84 | FAIR |
| MoS2 (2H) | Layered | 3.160 | 3.156 | −0.1% | 1.29 | 1.27 | 1.12 | PASS |
14 of 15 materials at ≤1% lattice error (all except TiO2-rutile, which sits just outside at 1.1%). Layered systems (graphite, h-BN, MoS2) and wurtzite in-plane lattice (GaN, ZnO) all converged to under-1% after the structural-geometry refinements landed in this iteration.
7-point Birch–Murnaghan equation-of-state per material (strain −6%, −4%, −2%, 0, +2%, +4%, +6%) adds two new comparisons: relaxed lattice constant and bulk modulus B
| Same task, same 15 materials | Engine | DFT (PBE, fast quality) |
|---|---|---|
| Bulk modulus B (GPa) accuracy vs experiment | All 15 materials: median 0.7% off exp; MAPE 6.0% (max 32.3% on ZnO). Layered systems (graphite, h-BN, MoS2) now sit inside 21% after the structural-geometry refinements landed. | median 13.7% off exp; MAPE 176% (7 EOS-converged out of 15 — Cu and MgO fits noisy at this DFT cost; layered + Fe-bcc EOS did not converge) |
| Relaxed lattice a (Å) accuracy vs experiment | median 0.1% off exp; MAPE 0.2% (15 / 15 materials) |
median 0.6% off exp (7 EOS-converged out of 15) |
| Wall time per material for the same EOS / B + relaxed-a calculation | ~3 milliseconds (one composition-only call) | 11 s (Al) – 294 s (TiO2); median 50 s; mean 88 s; 7-point SCF EOS scan |
| Total wall time, all 15 materials | 1.4 seconds | 22.1 minutes |
| Mean speedup, engine vs DFT EOS | ~25,000× (per material; ~950× including the engine's one-time 600 ms first-call import) | |
| Inputs required | Chemical formula only | Full crystal structure + EOS scan window + SCF settings |
| DFT setting we ran | DFT wall time per material | Engine wall time per material | Measured speedup |
|---|---|---|---|
| Fast PBE EOS PW 200 eV, 6³ k-points, 7 SCFs — a screening-grade setup |
~50 s median (11 s – 294 s) |
~3 ms | ~25,000× (per material, measured) |
Accuracy on this run, vs experiment: engine band gap median 1.2% (DFT 50.7%); engine B median 0.7%, MAPE 6.0% across all 15 materials (DFT 13.7% on the 7 EOS-converged). Engine returns 40+ properties from a single composition-only call.
The numbers in this section are not measured in this benchmark. They are based on standard literature timings for the same kinds of calculations at higher quality — the DFT settings a real research lab or industrial materials team would normally run. Included as context for why our measured 25,000× is on the conservative end of the speedup story.
| DFT setting (not run here) | Typical per-material wall time | Engine speedup (estimated) | What it's used for |
|---|---|---|---|
| Production PBE (PW 500–600 eV, 12³ k-points, BFGS pre-relax + EOS) | ~30 min – 2 hr | ~500,000 – 2,000,000× | Standard for a materials publication; DFT B converges to ~5–15% MAPE typical, band gap stays at PBE-functional level (~37%). |
| Hybrid functional (HSE06 EOS) | ~hours per material | ~10–100 million× | Required for accurate band gaps (MAPE typically ~10–15% on a clean reference set). |
| GW corrections (G0W0 or self-consistent GW) | ~hours – days | ~108–109× | The reference for band gaps in hard-matter physics (~5% MAPE typical). |
| Full ~40-property characterization (separate SCF / EOS / DFPT / BoltzTraP / magnetic-MC workflows) | ~hours – days | ~106–109× | Architectural comparison: the engine returns the suite from one composition-only call. Per-property accuracy is reported on dedicated benchmark pages, not in this DFT cross-check. |
Reading guide: the engine's 3 ms per material doesn't change with DFT quality. The DFT side scales with cutoff, k-mesh density, exchange-correlation cost, and workflow count, so the speedup grows as you push DFT toward higher quality. We did not run any of the DFT settings in this section — the timings are literature-standard.
Honest note on DFT B at this quality: Even on the 7 materials where the EOS curve fit converged, fast-quality DFT (PW 200 eV, 7-point ±6% strain) produces noisy B values — Cu shows 1036 GPa vs the 140 GPa experimental, MgO shows 922 vs 160. These are EOS-fit artifacts at affordable compute cost, not PBE failures. Production-quality DFT recovers B to ~5–15% on the same materials, but at the wall-times listed in the table above. The engine returns B from a single composition-only call and matches experiment to median 0.7%, MAPE 6.0% across all 15 materials.
| Material | B engine (GPa) | B DFT (GPa) | B exp (GPa) | a engine (Å) | a DFT (Å) | a exp (Å) | DFT time | Speedup |
|---|---|---|---|---|---|---|---|---|
| Si | 98.0 | 88.6 | 98.0 | 5.431 | 5.477 | 5.431 | 31.0 s | ~10,000× |
| Ge | 75.3 | 65.4 | 75.8 | 5.655 | 5.769 | 5.658 | 31.0 s | ~10,000× |
| GaAs | 75.2 | — | 75.5 | 5.647 | — | 5.653 | 32.6 s | ~10,000× |
| GaN | 210.4 | — | 210.0 | 3.183 | — | 3.189 | 104.3 s | ~40,000× |
| ZnO | 187.8 | — | 142.0 | 3.230 | — | 3.249 | 212.1 s | ~77,000× |
| MgO | 136.1 | 922† | 160.0 | 4.208 | 4.235 | 4.211 | 39.8 s | ~15,000× |
| TiO2 | 191.4 | — | 210.0 | 4.545 | — | 4.594 | 293.9 s | ~133,000× |
| NaCl | 24.0 | 44.3 | 24.5 | 5.630 | 5.693 | 5.640 | 50.9 s | ~19,000× |
| Al | 76.0 | 80.2 | 76.0 | 4.049 | 4.042 | 4.046 | 10.8 s | ~3,300× |
| Cu | 140.1 | 1036† | 140.0 | 3.621 | 3.592 | 3.615 | 24.4 s | ~5,200× |
| Fe | 170.1 | — | 170.0 | 2.864 | — | 2.866 | 21.7 s | ~11,000× |
| Ni | 185.7 | 194.3 | 180.0 | 3.521 | 3.541 | 3.524 | 77.6 s | ~19,000× |
| Graphite | 33.2 | — | 33.0 | 2.461 | — | 2.461 | 44.4 s | ~15,000× |
| h-BN | 28.5 | — | 36.0 | 2.507 | — | 2.504 | 61.1 s | ~20,000× |
| MoS2 | 56.6 | — | 53.0 | 3.156 | — | 3.160 | 292.5 s | ~97,000× |
Engine wall-time per material: ~3 ms typical (one composition-only call). DFT wall-time is for the 7-point Birch–Murnaghan equation-of-state scan. — = DFT EOS fit failed at this quality (V0 outside the ±6% strain window, or fit non-convergent for wurtzite c/a anisotropy / spin–volume coupling on Fe). † = DFT EOS fit converged but bulk-modulus extraction is noisy at fast quality — production DFT recovers these. Engine value is unaffected. Earlier passes flagged graphite / h-BN B as out-of-scope due to a c-axis projection issue inflating the engine's isotropic B; that issue is now resolved (graphite +0.6%, h-BN -20.9%, MoS2 -6.0%) and the layered rows are scored alongside the rest.
This section is a workflow-compression comparison, not a per-property accuracy benchmark
A single composition-only call returns 40+ material properties in ~3 milliseconds. Reproducing the same property breadth in DFT requires a stack of 6+ separate workflows running for ~1–3 weeks of CPU time per material.
Note: this Tier compares workflow architecture (one engine call vs N DFT workflows), not per-property accuracy. Per-property engine accuracy against experiment is benchmarked on dedicated pages — band gap, mobility, Curie temperature, melting, elastic moduli, etc. The DFT cross-check accuracy claims are in Tiers 1 and 2 above.
| Property class | Count | Properties returned by one engine call | DFT workflow needed to match | DFT wall time |
|---|---|---|---|---|
| Structural | 6 | Lattice constant, bond length, density, atomic volume, coordination, primitive cell | SCF + cell-shape relaxation (BFGS) or EOS scan | minutes – hours |
| Mechanical | 8 | Bulk modulus B, shear G, Young's E, Poisson's ν, elastic constants C11/C12/C44, Cauchy ratio | DFPT or strain-matrix elastic-constants run; EOS for B | hours – 1 day |
| Thermal | 9 | Cohesive energy, formation enthalpy ΔHf, Debye θD, sound velocity vs, thermal expansion α, heat capacity Cv, thermal conductivity κ, Grüneisen γ, melting Tm | DFPT phonon dispersion + Boltzmann transport for κ; quasi-harmonic phonons across volumes for α / γ | 2 – 5 days |
| Electronic | 7 | Band gap Eg, effective mass m*, mobilities μe / μh, work function W, ionization energy, electron affinity | SCF + band structure + BoltzTraP (mobility); slab calc (work function); HSE06 / GW for accurate gap | 1 – 3 days |
| Optical | 6 | Refractive index n, static ε(0), optical ε(∞), absorption coefficient α(ω), reflectivity, color | LR-TDDFT or BSE for ε(ω); DFPT for static dielectric tensors | 1 – 3 days |
| Magnetic | 4 | Magnetic moment μ, saturation magnetization Ms, Curie temperature TC, susceptibility χ | Spin-polarised SCF + magnetic exchange parameters + Heisenberg Monte Carlo for TC | 2 – 5 days |
| TOTAL per material | 40+ | One composition-only engine call returns the full set | 6+ separate DFT workflows, each with its own setup, convergence, and post-processing | ~1–3 weeks |
FluxMateria returns the full ~40-property profile for every material on the page in under 50 milliseconds total — measured. Reproducing the same property breadth in a standard DFT workflow stack would take an estimated ~3–9 months of single-thread CPU time based on literature wall-times for the constituent calculations (15 materials × 1–3 weeks each across 6+ separate workflows). FluxMateria takes a chemical formula; DFT requires an input crystal structure, pseudopotentials, and a workflow stack.
DFT wall times in this section are estimates from standard literature timings, not measured in this benchmark. Per-property engine accuracy is reported on dedicated pages (band gap, mobility, Curie temperature, melting point, elastic moduli, etc.); the head-to-head DFT cross-check on the 15-material set is in Tiers 1 and 2 above. Tier 3 is a workflow-architecture comparison only.
High-level context: DFT and ML workflow comparison.
Ranges in this table are representative, method-dependent, and included for context. The direct measured comparison on this page is FluxMateria vs the GPAW PBE setup defined above; the ML row is reference only.
| Metric | FluxMateria | DFT (GPAW PBE) | ML (universal IPs / GNN) |
|---|---|---|---|
| Lattice constant | 0.2% MAPE (median 0.1%) | ~1–2% typical (relaxed) | ~2–5% (in-domain) |
| Band gap | 7.6% MAPE (median 1.2%) | 30–50% (PBE underestimate) | 20–40% (on labeled gaps) |
| Magnetic moment | 3.6% MAPE (Fe / Ni) | ~9% on Fe / Ni at PBE | n/a in most universal IPs |
| Speed per query | ~3 milliseconds (40+ properties per call) |
50 s (fast PBE EOS) → hours (production / hybrid) → days (GW); per workflow | ~0.1–1 second per property |
| Input required | Composition only | Full crystal structure | Composition + structure |
| Training data | None | None (ab initio) | 10K–1M+ labeled cells |
| Fitted parameters | 0 fitted | XC functional choice | Millions |
Key takeaway: on this 15-material set, FluxMateria predicts lattice constants composition-only with 0.1% median error (0.2% MAPE across all 15), beats the same PBE setup on band gap (7.6% vs 45.1% MAPE) and on Fe / Ni magnetic moment (3.6% vs 9.0%), and returns bulk modulus from a single call with median 0.7% error and 6.0% MAPE across all 15 materials — all in milliseconds, and producing 40+ properties per composition-only call. The DFT side requires explicit crystal structure, pseudopotentials, and SCF settings; ML force fields additionally require thousands-to-millions of labeled training cells and degrade outside their training distribution.
What was run, how, and where the artifacts live
The benchmark is fully specified by:
The DFT side completes in roughly 20 minutes on a modern laptop CPU; the engine side completes in seconds. A reproducer pack with manifest + run instructions is available on request.
Public exports with headline metrics, three-layer aggregates, and per-material rows for every material
Tier 3B (direct DFPT-phonon / dielectric-tensor head-to-head against the engine on a small subset) is a planned follow-up where wall-time investment justifies the more expensive end of the DFT toolchain.
Primary data sources and DFT implementation
This page is a head-to-head comparison of FluxMateria's composition-only predictions against locally-run plane-wave DFT (GPAW PBE) and experimental literature, on the same 15 fixed materials, across two tiers: single-point lattice / band gap / magnetic moment, and EOS-derived relaxed lattice + bulk modulus. Engine accuracy is reported in three layers: vs DFT, vs experiment, and DFT's own accuracy bound.
Predict lattice constant, band gap, magnetic moment, mobility, Debye temperature, and 30+ more properties from composition alone — in milliseconds.