History Matching as Inversion
Matching the Past
A model is trusted only after it reproduces the field's measured history. History matching adjusts the uncertain inputs, permeability, aquifer strength, relative permeability, until the simulated production passes through the observed points.
An Inverse Problem
This is an inverse problem: the objective is the misfit, the sum of squared residuals between simulated and observed, and matching is minimizing it. A good match drives the misfit down to the measurement noise floor and no further; chasing the noise itself is over-fitting.
Match, Then Forecast
Only a model that reproduces the past earns the right to forecast the future. The match is the gate; what comes after the last data point is the prediction the whole exercise is for.