Dimension Reduction Aided Design in History Matching

History matching is a procedure for identifying a collection of points for which the evaluation gives an acceptable match to an observation. This is done by ruling out regions of input space which are deemed implausible given this observation and using a number of model runs. Often history matching is performed on expensive functions meaning only a limited number of model runs are available, therefore requiring an emulator to be constructed to represent this simulator. Here, a Gaussian process (GP) emulator is used, allowing one to ascertain probabilistically whether a specific point in input space is implausible via an implausibility measure using the posterior mean and variance. History matching is done in iterations (commonly called waves) in which the not ruled out yet (NROY) space is sampled, an emulator constructed, and further space ruled out using the implausibility measure forming a new NROY space.

Where these samples are taken from in NROY space is important; with a careless selection of design leading to a negligible amount of space ruled out in that wave. To attempt to counteract this, a rotation of NROY space is done using weighted singular value decomposition (WSVD), which is able to incorporate areas of high uncertainty into the rotation, meaning (ideally) the first principal axes are the ones which represent the areas of NROY which are more favourable to ruling out space. History matching and emulator performance is compared with and without this rotation of NROY space.