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.
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