Theory Seminar: Solving high-dimensional parabolic PDEs using the tensor train format

Lorenz Richter, Leon Sallandt, Nikolas Nüsken:
In the 1990s the quantum physics community discovered tensor networks - in particular matrix product states and Stephen White's DMRG algorithm.

March 23, 2022

Lorenz Richter, Leon Sallandt, Nikolas Nüsken
Group seminar (hybrid format: B2.46/online)
Wed, 23 March 2022, 10:30 am (MEZ)

Abstract:


In the 1990s the quantum physics community discovered tensor networks - in particular matrix product states and Stephen White's DMRG algorithm. At the end of the 2000s the mathematical community rediscovered these tensor networks under the name tensor trains and has since then analyzed them mathematically, while discovering further applications. In this talk we represent high-dimensional functions using matrix product states and perform high-dimensional regression. We apply this machinery in order to solve high-dimensional parabolic PDEs, which can be reformulated using stochastic calculus to backward stochastic differential equations. After a discretization, this problem can be reduced to a sequence of regression problems. We compare the performance of the matrix product states with prominent neural network approaches.

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