论文标题
部分可观测时空混沌系统的无模型预测
Learning Continuous Depth Representation via Geometric Spatial Aggregator
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Depth map super-resolution (DSR) has been a fundamental task for 3D computer vision. While arbitrary scale DSR is a more realistic setting in this scenario, previous approaches predominantly suffer from the issue of inefficient real-numbered scale upsampling. To explicitly address this issue, we propose a novel continuous depth representation for DSR. The heart of this representation is our proposed Geometric Spatial Aggregator (GSA), which exploits a distance field modulated by arbitrarily upsampled target gridding, through which the geometric information is explicitly introduced into feature aggregation and target generation. Furthermore, bricking with GSA, we present a transformer-style backbone named GeoDSR, which possesses a principled way to construct the functional mapping between local coordinates and the high-resolution output results, empowering our model with the advantage of arbitrary shape transformation ready to help diverse zooming demand. Extensive experimental results on standard depth map benchmarks, e.g., NYU v2, have demonstrated that the proposed framework achieves significant restoration gain in arbitrary scale depth map super-resolution compared with the prior art. Our codes are available at https://github.com/nana01219/GeoDSR.