MOLE project

Description of the project

Today's technologies and connected world provide easy access to vast amounts of data. Fully utilizing this data is essential for the success of modern data-driven scientific computing. As data complexity increases, finding low-dimensional hidden structures becomes important for effective algorithm design. MOLE exploits the representation of high-dimensional data by tensors approximated on a low-dimensional Riemannian manifold, and focuses on the design and analysis of algorithms for supervised learning with neural networks and for tensor least-squares problems.

Aims of the project 

MOLE aims at developing and analyzing new numerical algorithms to solve nonlinear tensor and matrix least-squares problems and to train deep neural networks on low-parametric Riemannian manifolds. The novel computational and mathematical framework sees specific application to data compression, network analysis, and the solution of PDEs using tools of numerical linear algebra, tensor analysis, network science, and numerical optimization.

Expected results 

MOLE will provide key mathematical and algorithmic tools for the analysis and solution of (a) time integration of high-dimensional PDEs, increasing efficiency while preserving relevant physical quantities; (b) high-dimensional data compression problems, such as dictionary learning, thanks to the efficient computation of constrained matrix and tensor factorizations; (c) neural network-based supervised learning, with new efficient and mathematically sound training algorithms.