When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on octree to solve these difficulties. In our approach, scientific data is preprocessed before training, and a hierarchical octree-based data structure is built to guide sampling on the latent context grid. Each leaf node in the octree corresponds to an indivisible subblock of the volumetric data. The dimensions of the subblocks are different, making the number of sample points in each randomly cropped training data block to be adaptive. We reconstruct the octree at intervals according to loss distribution to perform the multi-stage training. With the Rayleigh-B\'enard convection problem, we deploy our method to state-of-the-art models. We constructed adequate experiments to evaluate the training performance and model accuracy of our method. Experiments indicate that our sampling optimization improves the convergence performance of physics-constrained deep learning super-resolution solutions. Furthermore, the sample points and training time are significantly reduced with no drop in model accuracy. We also test our method in training tasks of other deep neural networks, and the results show our sampling optimization has extensive effectiveness and applicability. The code is publicly available at https://github.com/xinjiewang/octree-based_sampling.

翻译：将物理约束深度学习引入科学数据的体超分辨率时，训练难以收敛且耗时巨大。我们提出一种基于八叉树的新型层次化采样方法来解决上述难题。该方法在训练前对科学数据进行预处理，构建基于八叉树的层次数据结构以指导潜在上下文网格上的采样。八叉树中每个叶节点对应体数据的一个不可分割子块，各子块维度不同，使得随机裁剪的每个训练数据块中的采样点数量自适应调整。我们根据损失分布定期重建八叉树以实现多阶段训练。针对瑞利-贝纳德对流问题，我们将该方法部署到最先进模型中，并通过充分实验评估训练性能与模型精度。实验表明，我们的采样优化提升了物理约束深度学习超分辨率解决方案的收敛性能。同时，在模型精度不降低的前提下，采样点数量与训练时间显著减少。我们还在其他深度神经网络的训练任务中测试了该方法，结果表明该采样优化具有广泛有效性和适用性。代码公开于：https://github.com/xinjiewang/octree-based_sampling