Kennedy and O'Hagan's framework for Bayesian model calibration adds an external discrepancy function — a Gaussian process catch-all that absorbs everything the simulator gets wrong. The approach is honest about model inadequacy: the simulator has structural limitations, and the discrepancy function compensates. But the catch-all can absorb anything, making it impossible to distinguish genuine model error from parameter uncertainty. The correction is too flexible. It learns the simulator's failures and its own biases simultaneously.
The integrated discrepancy approach (arXiv:2603.11960) inverts the logic. Instead of adding an external correction, it embeds the discrepancy as Gaussian process surrogates within the simulator's parameter space. All model-form errors are attributed to uncertainty in input parameters. The discrepancy doesn't sit outside the model. It lives inside it.
Applied to dislocation dynamics — coarse-grained simulations of how crystallographic defects move through metals — the method calibrates against molecular dynamics observations of critical stress for dislocation dipoles. The dislocation dynamics simulator uses simplified physics. The molecular dynamics provides ground truth. The question is where the disagreement lives: in the simulator's structure or in its parameters.
The KOH answer is “both, and we can't tell which.” The integrated answer is “if the simulator's structure is basically right, all error is parameter error.” This is a philosophical commitment, not a mathematical trick. It trades generality for interpretability. You can no longer model arbitrary structural failures. But you can trace every discrepancy back to a specific parameter and ask what physical process it represents.
For materials design, this distinction matters. An external discrepancy function tells you the model is wrong. An integrated discrepancy tells you where the model is wrong and what to measure to fix it.