Evidence scope for calibrated and learned fluid models

For this remark, a computational fluid-dynamics model is the specified fluid equations together with a numerical algorithm and its code, mapping initial data, boundary data, parameters, and time to calculated fields or quantities of interest. A context of use is the stated set of geometries, initial and boundary conditions, parameter ranges, time interval, output quantities, and required accuracy for which a prediction is intended. A benchmark is a finite set of specified input cases, reference outputs, target quantities, comparison metric, and scoring procedure. Calibration is the selection of adjustable model parameters to fit identified data; training is the corresponding parameter-fitting process for a learned component. A held-out evaluation set is not used to fit those parameters, although it may still be generated by the same numerical reference model.

Code verification checks that the code implements the stated mathematical model; solution verification estimates numerical error for a particular calculation. Physical-model validation assesses agreement with relevant observations of the physical system for the stated context of use, with experimental and computational uncertainty accounted for. These are different claims: a numerical verification benchmark does not establish physical realism, and an algorithmic held-out score is not, by itself, physical-model validation.

Accordingly, a calibrated or learned model’s reported score supports only the specified cases, reference outputs, quantities, metric, and evaluation protocol. If the reference outputs are themselves computed by a fluid solver, agreement with them is evidence about the learned component relative to that solver and its assumptions, not direct evidence about an actual fluid. Extrapolation to other geometries, boundary conditions, forcing, parameter ranges, time horizons, or measured flows is a separate claim that requires its own evidence. Reports should identify the intended use, training and evaluation data, reference source, comparison metric, baselines, and relevant numerical, input, and measurement uncertainties; a fit to calibration data alone does not establish accuracy for other uses.

Duraisamy, Iaccarino, and Xiao, Turbulence Modeling in the Age of Data, §§3.1–3.4, 5.1–5.2, 6

Yeo, A Summary of Industrial Verification, Validation, and Uncertainty Quantification Procedures in Computational Fluid Dynamics, NIST IR 8298, §§3–6

Selin, ESD.864 Lecture 3: Verification and Validation, MIT OpenCourseWare, slides 10, 15–22, 26–29