Incorporating Data

MrHyDE is designed to enable data-informed physics-based predictions by combining inference with modeling and simulation. There are several ways to incorporate experimental (or synthetic) data into a simulation, but these can be broken down into two classes:

1. Input data: information that can be defined as parameters, coefficients, forcing functions, etc. This is often used along with the forward analysis mode.
2. Output data: information that the simulation will try to predict and then try to find the parameters that best match the data. This is usually used in PDE-constrained optimization, stochastic inversion, data-assimilation, etc.

Incorporating output data in a simulation is described in the Optimization and Data-Consistent Inversion pages. We focus the rest of this page on incorporating input data.

Obviously if the data is simply a scalar, then one can simply define a scalar parameter as described in Optimization. If one has a set of samples for a particular parameter, e.g., the parameter is stochastic and set of samples have been generated elsewhere, one can perform a UQ study using a user-defined set of parameters as described in Optimization.

It is a bit more complicated to incorporate data from a spatially varying field. MrHyDE assumes that this data is given at seed locations in physical space and the values for each element are computed using a nearest neighbor algorithm in Compadre. The seeds are not assumed to be associated with the mesh and can be completely unstructured.