Primary challenge for computer simulations is the curse of dimensionality: The exponential increase of the needed resources, memory, speed, etc., with the number of variables/dimensions of the problem. Transformation of the calculations on structures, that is, on tensor formats factorized into product grid, subject to a controlled error, solves this problem and remove the curse of dimensionality. This project develops a new systematic mathematical formalism for tensor-network- based numerical algorithms and high-performance computer applications capable of ultra-fast solving any type of ultra-large partial differential equations and high dimensional integrals, that have been out of reach for the current computer capabilities.

## Papers

**Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation.**,

D. P. Truong, M. I. Ortega, I. Boureima, G. Manzini, K. Ø. Rasmussen, ...

arXiv preprint arXiv:2309.03347: 2023.**The tensor-train mimetic finite difference method for three-dimensional Maxwell’s wave propagation equations.**,

G. Manzini, P. M. D. Truong, R. Vuchkov, B. Alexandrov

Mathematics and Computers in Simulation 210: 2023.**Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format.**,

B. Alexandrov, G. Manzini, E. W. Skau, P. M. D. Truong, R. G. Vuchov

Mathematics 11 (3): 2023.