Scalable and Efficient Linear and Eigenvalue Solvers Using Tensor Decompositions – SELESTE

Tensor methods have witnessed a remarkable recent progress in theory, algorithms, and applications in many domains including signal processing, big data analysis, artificial intelligence, and scientific computing. Among these advancements is the introduction of tensor-based solver frameworks based on low-rank tensor arithmetic for efficiently representing large-scale and potentially high dimensional systems. These solvers provide tremendous gains in terms of computational and memory costs by effectively compressing operators/matrices as well as vectors representing the problem at hand. They are capable of surpassing the gains obtained by their matrix-based counterparts using hierarchical matrices or reduced bases. However, applying such tensor methods to large scale problems still requires a substantial computational power, hence calls for efficient parallel algorithms and software. The goal of the SELESTE project is precisely addressing this need by developing a scalable tensor-based solver framework harnessing all compute capabilities offered by modern HPC architectures. This software library will be tested and validated using two existing applications in quantum chemistry and electromagnetics, and will be complemented with Python wrappers for rapid development of parallel code by researchers from many different application domains.