Plenary talk of Reinhold Schneider (TU Berlin)

Optimization in Tensor-Networks and Fock Space Discretization for the Electronic Schrödinger Equation
Recently tensor product approximation has made substantial progress in highdimensional approximation. Some recent tensor formats fit into the framework of tensor networks, like the TT-format as welll as the hierarchical format. These techniques allow to approximate wavefunctions in the fermionic Fock space as tensor ≅ &otimesi=1k R2 with a storage requirement formally scaling linearly in k. In this representation the formalism of second quantization could be used numerically. The Schrödinger equations leads to a tensor optimization problem with additional constraints given in terms the particle number operator. With increasing tensor ranks this solution can approximate the full CI wave function up to any required precision. We present a local optimzation calculus numerical for solving optimization problems in these tensor formats.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)