Kavli Affiliate: Katrin Heitmann
| First 5 Authors: Xiaofeng Dong, Xiaofeng Dong, , ,
| Summary:
The potential of deep learning-based image-to-image translations has recently
attracted significant attention. One possible application of such a framework
is as a fast, approximate alternative to cosmological simulations, which would
be particularly useful in various contexts, including covariance studies,
investigations of systematics, and cosmological parameter inference. To
investigate different aspects of learning-based cosmological mappings, we
choose two approaches for generating suitable cosmological matter fields as
datasets: a simple analytical prescription provided by the Zel’dovich
approximation, and a numerical N-body method using the Particle-Mesh approach.
The evolution of structure formation is modeled using U-Net, a widely employed
convolutional image translation framework. Because of the lack of a controlled
methodology, validation of these learned mappings requires multiple benchmarks
beyond simple visual comparisons and summary statistics. A comprehensive list
of metrics is considered, including higher-order correlation functions,
conservation laws, topological indicators, and statistical independence of
density fields. We find that the U-Net approach performs well only for some of
these physical metrics, and accuracy is worse at increasingly smaller scales,
where the dynamic range in density is large. By introducing a custom
density-weighted loss function during training, we demonstrate a significant
improvement in the U-Net results at smaller scales. This study provides an
example of how a family of physically motivated benchmarks can, in turn, be
used to fine-tune optimization schemes — such as the density-weighted loss
used here — to significantly enhance the accuracy of scientific machine
learning approaches by focusing attention on relevant features.
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