  Historical experimental testing of high-altitude nuclear explosions (HANEs)
are known to cause severe and detrimental effects to radio frequency signals
and communications infrastructure. In order to study and predict the impact of
HANEs, tractable computational approaches are required to model the complex
physical processes involved in the detonation wave physics. Modern
reduced-order models (ROMs) can enable long-time and many-parameter simulations
with minimal computational cost. However, translational and scale invariances
inherent to this type of wave propagation problem are known to limit
traditional ROM approaches. Specifically, dimensionality reduction methods are
typically ineffective in producing low-rank models when invariances are present
in the data. In this work, an unsupervised machine learning method is used to
discover coordinate systems that make such invariances amenable to traditional
dimensionality reduction methods. The method, which has previously been
demonstrated on one-dimensional translations, is extended to higher dimensions
and additional invariances. A surrogate HANE system, i.e. a HANE-ROM, with one
detonation wave is captured well at extremely low-rank. Two detonation-waves
are also considered with various amounts of interaction between the waves, with
improvements to low-rank models for multiple wave quantities with limited
interaction.
