Spatio-Temporal Surrogates for Interaction of a Jet with High
  Explosives: Part I -- Analysis with a Small Sample Size
Chandrika Kamath Juliette S. Franzman Brian H. Daub
Computer simulations, especially of complex phenomena, can be expensive,
requiring high-performance computing resources. Often, to understand a
phenomenon, multiple simulations are run, each with a different set of
simulation input parameters. These data are then used to create an interpolant,
or surrogate, relating the simulation outputs to the corresponding inputs. When
the inputs and outputs are scalars, a simple machine learning model can
suffice. However, when the simulation outputs are vector valued, available at
locations in two or three spatial dimensions, often with a temporal component,
creating a surrogate is more challenging. In this report, we use a
two-dimensional problem of a jet interacting with high explosives to understand
how we can build high-quality surrogates. The characteristics of our data set
are unique - the vector-valued outputs from each simulation are available at
over two million spatial locations; each simulation is run for a relatively
small number of time steps; the size of the computational domain varies with
each simulation; and resource constraints limit the number of simulations we
can run. We show how we analyze these extremely large data-sets, set the
parameters for the algorithms used in the analysis, and use simple ways to
improve the accuracy of the spatio-temporal surrogates without substantially
increasing the number of simulations required.