Calibration and Parameter Estimation

Calibration tunes a model's fixed parameters so its predictions match data, turning a generic model into a twin of one specific unit.

Fitting the model to the machine

Every model carries parameters that are known only approximately: heat-transfer coefficients, friction factors, effective transport rates. Calibration is the process of estimating these parameters from measured data so the model reproduces the behavior of one specific machine. It is distinct from state estimation: state changes moment to moment, while calibrated parameters are fixed or slowly varying properties of the unit.

The Bayesian view

Calibration is naturally posed as Bayesian inference: start from a prior belief about each parameter, based on physics and prior experience, then update it with data to a posterior that is narrower and better centered. The output is not a single tuned value but a distribution, capturing how well the data actually pins each parameter down. Poorly identified parameters stay wide, honestly signaling what the data cannot resolve.

Identifiability

Not every parameter can be recovered from the available data; some affect the measurements too weakly, and some trade off against each other so only a combination is determined. Identifiability analysis reveals this before calibration, guiding either better experiments or acceptance that a parameter must be fixed from independent knowledge.

Guard against overfitting

A model with many free parameters can be tuned to match any dataset while predicting poorly on new data. Calibration must be validated on data held out from the fitting, and priors must be kept physically meaningful so the fit does not wander into unphysical territory. This connects calibration directly to validation.

In the Kronos program

Until hardware exists, calibration targets are the component experiments and reference simulations that underpin the design, and the machinery is proven on synthetic data. After the Hyperion breeder operates near 2030, calibration will tune each unit's twin to its own construction and behavior. For the burner fleet in Aegis and MetroVolt housings, calibration on one unit provides informed priors for the next while each keeps its own posterior. See real-time model updating and Bayesian filtering.