Materials Atlas · physics workbench

Model. Compare. Investigate.

Work from molecular geometry, crystal structure, processing conditions or a material stack. Inspect the physics, compare calculated results, and turn uncertainty into the next research question.

Research with AI →Metal equations of state →Methods & scientific foundations →

01 Define the system02 Review the method03 Calculate & check04 Compare & decide

Define your calculation

Calibrated multi-fidelity model

Fit a correction to a lower-cost method, calibrate its residual uncertainty and evaluate it on an untouched test set.

Import calculation inputs

Scientific inputsPhysical systemObservableObservable unitLower-cost method and versionReference method and versionFeature namesComma-separated labels, in feature order.Feature unitsComma-separated labels, in feature order.Partitioned observations

h2-00,train,0.5,-1.0429962745400945,-1.0496012657436526
h2-01,calibration,0.5416666666666666,-1.0741343528763903,-1.0800572543039797
h2-02,test,0.5833333333333334,-1.095062993037366,-1.101064208462562
h2-03,pool,0.625,-1.1081499901921301,
h2-04,train,0.6666666666666666,-1.1151728362867335,-1.1234314275750812
h2-05,calibration,0.7083333333333334,-1.1174902304760561,-1.127769225630249
h2-06,test,0.75,-1.1161514489386013,-1.12892185116276
h2-07,pool,0.7916666666666667,-1.111969723761592,
h2-08,train,0.8333333333333333,-1.1055749715023768,-1.1244153491165272
h2-09,calibration,0.875,-1.0974543197010038,-1.1197531350454604
h2-10,test,0.9166666666666667,-1.0879846683289323,-1.113973153803025
h2-11,pool,0.9583333333333333,-1.077459196109015,
h2-12,train,1,-1.0661086493179361,-1.1000888638268593
h2-13,calibration,1.0416666666666665,-1.05411791918494,-1.0923718132036488
h2-14,test,1.0833333333333335,-1.0416384357970403,-1.084332299235084
h2-15,pool,1.125,-1.0287970270214153,
h2-16,train,1.1666666666666665,-1.0157019744326656,-1.0676994932623267
h2-17,calibration,1.2083333333333335,-1.0024469970470669,-1.0592614454348703
h2-18,test,1.25,-0.9891138140908923,-1.0508194495308372
h2-19,pool,1.2916666666666665,-0.9757738103142214,
h2-20,train,1.3333333333333335,-0.9624891850825288,-1.0340859142178995
h2-21,calibration,1.375,-0.9493138354832644,-1.0258548361911761
h2-22,test,1.4166666666666665,-0.9362941185716135,-1.0177441860705478
h2-23,pool,1.4583333333333335,-0.9234695631401909,
h2-24,train,1.5,-0.9108735545943865,-1.0019473809619723

CSV rows: ID, split, feature value(s), low value, reference value. Splits: train, calibration, test, pool. Leave pool reference values blank.Normalized length scaleRegularizationTarget test errorobservable units

Method scope & sources

A bounded Gaussian-process delta model for one system, observable and explicit low/reference method pair.

All samples describe the same observable, units and method pair
Training, calibration and test sets have distinct feature coordinates
Calibration coverage is empirical; a posterior spread alone is not calibrated physical confidence

Delta machine learning ↗

Explore a calculated exampleCompare on the same axes

Edit calculation inputs ↓

Calculated result

Hydrogen · learned basis correction

Model calculation

Low-fidelity test MAE0.038435Hartree

Corrected test MAE7.822E-5Hartree

Eligible test coverage100%

Empirical calibration error bound0.00012672Hartree

Reference training cases7cases

total electronic+nuclear energy (Hartree)

H–H bond length (Å)

Withheld referenceResidual-corrected predictionLow-fidelity baseline

Inspect calculated samples

H–H bond length: 0.58333 Å · total electronic+nuclear energy: -1.1011 Hartree

Interpret the result

All paired observables describe the same system, units, normalization and conditions.
The reference-minus-low discrepancy is smooth within the training envelope.
Splits and hyperparameters were fixed before inspecting test results.

The training envelope is a numerical support check, not proof of chemical transferability.

Posterior scale is a model-based acquisition signal, not calibrated physical uncertainty.

Reference-method error and experimental uncertainty are not estimated by this correction.

Fewer than 19 eligible calibration cases: no finite 95% split-conformal interval is reported. The empirical calibration error bound is descriptive only.

Evaluation: advance

This decision applies to the supplied evaluation cases and declared error target.

Numerical checks & provenance

Residual solve consistency6.1062E-15 ≤ 1E-5 normalized residual

Passing these checks verifies the stated numerical properties. Agreement with experiment requires a separate, condition-matched comparison.

Input SHA-256: a097bfbc25612acce60491dd042324f954cb80287f033452562c8888c255f99d
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1 · baseline_sha256 dfa2749c659f4dec76d4b7a80bc6d79d31152f8817dfdd42215831fbc9d95d1f
Calculated 11/12/2026, 2:21:55 AM · 0.15338 s

Test the explanation

Compare a numerical refinement or a different physical assumption. Agreement within one model does not establish agreement with experiment.

Build the investigation

Bring the observable, conditions and result into a research plan with competing hypotheses and a test that can distinguish them.

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