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When introducing physics-constrained deep learning solutions to thevolumetric super-resolution of scientific data, the training is challenging toconverge and always time-consuming. We propose a new hierarchical samplingmethod based on octree to solve these difficulties. In our approach, scientificdata is preprocessed before training, and a hierarchical octree-based datastructure is built to guide sampling on the latent context grid. Each leaf nodein the octree corresponds to an indivisible subblock of the volumetric data.The dimensions of the subblocks are different, making the number of samplepoints in each randomly cropped training data block to be adaptive. Wereconstruct the octree at intervals according to loss distribution to performthe multi-stage training. With the Rayleigh-B\'enard convection problem, wedeploy our method to state-of-the-art models. We constructed adequateexperiments to evaluate the training performance and model accuracy of ourmethod. Experiments indicate that our sampling optimization improves theconvergence performance of physics-constrained deep learning super-resolutionsolutions. Furthermore, the sample points and training time are significantlyreduced with no drop in model accuracy. We also test our method in trainingtasks of other deep neural networks, and the results show our samplingoptimization has extensive effectiveness and applicability. The code ispublicly available at https://github.com/xinjiewang/octree-based_sampling.

Octree-based hierarchical sampling optimization for the volumetric super-resolution of scientific data