Enhancing Cosmological Simulations with Efficient and Interpretable Machine Learning in the Gabor Wavelet Basis

Accurately simulating the large-scale structure of the universe is critical for understanding fundamental phenomena such as dark matter, the neutrino mass, and the expansion history of the cosmos. While traditional hydrodynamic simulations are essential for resolving small-scale gas dynamics, their computational demands make it impractical to model the vast volumes required by next-generation cosmological surveys. To address this limitation, we present a novel approach that leverages the Gabor (wavelet) transformation in combination with machine learning to enhance low-resolution simulations to resemble higher resolutions. Unlike previous methods that relied on convolutional networks constrained by grid-specific parameters, our architecture decomposes input data into a localized frequency basis in a grid-shape and resolution-agnostic way, allowing for efficient feature sharpening with significantly fewer learned parameters. This flexibility enables the model to generalize across different resolutions and coordinate systems, including non-Cartesian grids, without significant loss of accuracy. Moreover, the reduced complexity of our model enhances interpretability, offering a robust tool for cosmological simulations and other fluid mechanics applications, such as weather forecasting and fusion plasma modeling.