Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part I -- Analysis with a Small Sample Size

TL;DR

This paper develops methods for creating accurate spatio-temporal surrogates from limited simulation data of a jet interacting with high explosives, addressing challenges of large-scale, vector-valued outputs with small sample sizes.

Contribution

It introduces techniques for building high-quality surrogates from small samples of large, complex spatio-temporal simulation data with vector outputs.

Findings

Effective analysis of large-scale, vector-valued data sets.

Strategies to improve surrogate accuracy with limited simulations.

Insights into handling variable computational domains.

Abstract

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.