A hybrid Alternating Least Squares -- TT Cross algorithm for parametric PDEs

Understand

We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition.

• Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications.
• We propose an algorithm that is a hybrid of the alternating least squares and the TT cross methods.
• It computes a TT approximation of the whole solution, which is beneficial when multiple quantities of interest are sought.