论文标题
部分可观测时空混沌系统的无模型预测
Hamiltonian transformation for accurate and efficient band structure interpolation
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。
Electronic band structure is a cornerstone of condensed matter physics and materials science. Conventional methods like Wannier interpolation (WI), which are commonly used to interpolate band structures onto dense k-point grids, often encounter difficulties with complex systems, such as those involving entangled bands or topological obstructions. We introduce the Hamiltonian transformation (HT) method, a novel framework that enhances interpolation accuracy by localizing the Hamiltonian. Using a pre-optimized transformation, HT produces a far more localized Hamiltonian than WI-SCDM (where Wannier functions are generated via the selected columns of the density matrix projection), achieving up to two orders of magnitude greater accuracy for entangled bands. Although HT utilizes a slightly larger, nonlocal numerical basis set, its construction is rapid and requires no optimization, resulting in significant computational speedups. These features make HT a more precise, efficient, and robust alternative to WI-SCDM for band structure interpolation, as verified by high-throughput calculations.
