When working with PDEs the reconstruction of a previous state often proves difficult. Good prior knowledge and fast computational methods are crucial to build a working reconstruction. We want to identify the heat sources on a three dimensional domain from later measurements under the assumption of small, distinct sources, such as hot chippings from a milling tool. This leads us to the need for a Prior reflecting this a priori information. Sparsity-inducing hyperpriors have proven useful for similar problems with sparse signal or image reconstruction. We combine the method of using a hierarchical Bayesian model with gamma hyperpriors to promote sparsity with low-rank computations for PDE systems in tensor train format.

翻译：与 PDEs 合作重建先前状态时, 通常会证明很难。 良好的前科和快速计算方法对于重建工作至关重要。 我们希望在小的、独特的来源(如磨机工具的热芯片)的假设下,从后来的测量中找出三维域的热源。 这导致我们需要一个先验的反映这一先验信息。 分化诱导超位元对于信号稀少或图像重建等类似问题非常有用。 我们把使用Bayesian 等级模型的方法与伽马超精度模型的方法结合起来,以促进高压列车模式的PDE系统低级计算。