Validation

Checked against measured, reference, and analytical results

Terra Multiphysics is cross-validated three ways: against COMSOL Multiphysics (an independent commercial simulator), against instrumented field data, and against closed-form analytical theory. The numbers below are the evidence.

985,000×
vs a full FEM solve
0.08–0.38 °C
vs COMSOL
R² 0.9997
held-out surrogate accuracy
0.30–0.42 °C
vs instrumented field data
Surrogate vs full physics

The AI surrogate reproduces the full FEM result

On 200 held-out coupled-physics runs the surrogate matches the full finite-element solver almost exactly, while returning the answer roughly 985,000× faster.

Surrogate predictions vs full FEM on 200 held-out runs: R² 0.9997, mean error 0.009 °C, ~985,000× faster.
In-situ field validation

Against an instrumented energy pile

Daily outlet temperature against the published field record of an instrumented three-loop energy pile, across three operating modes.

Measured Faizal 2016 outlet temperature versus Terra computed over 20 operating days
In-situ field validation. Daily outlet temperature against the instrumented three-loop energy pile of Faizal et al. (2016), across three operating modes (8 h, 16 h, 24 h continuous) over 20 days: 0.30 to 0.42 °C mean absolute error, with a consistent cold bias. Measured points digitized from the published field record.
Thermo-mechanical response

Field-scale coupling, captured

A full-scale heating test captures the coupled thermo-mechanical signature that temperature-only models leave out: the pile temperature is tracked and the heave-and-recovery character is reproduced, though the peak heave is over-predicted.

Terra simulation of a full-scale energy-pile heating test: pile temperature and pile-head heave across a 28-day test with a 12-day heating phase and recovery
Field-scale thermo-mechanical response. Terra simulation of the EPFL Lausanne in-situ energy-pile heating test (Laloui et al., 2006, Test 1): a 0.88 m, 25.8 m instrumented pile over a 28-day heat-and-recovery cycle. The simulated pile temperature tracks the measurement (peak +20.7 vs +22.0 °C, RMS 1.4 °C) and the head reproduces the heave-and-recovery signature, but the model over-predicts the peak heave (+5.96 vs +3.58 mm measured). Measured data digitized from the published Test-1 record.
Global sensitivity

Which inputs drive the result

Sobol indices decompose the variance in each output, showing which design inputs matter most.

Sobol global sensitivity indices for the surrogate outputs
Global sensitivity. Sobol indices: pile length drives the outlet temperature, while flow rate governs heat and pressure drop.

See the validated models in the gallery

Every model in the gallery is checked against measured or reference results.

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