Combining Monte Carlo and Tensor-network Methods for Partial
Differential Equations via Sketching
- URL: http://arxiv.org/abs/2305.17884v6
- Date: Wed, 11 Oct 2023 01:09:11 GMT
- Title: Combining Monte Carlo and Tensor-network Methods for Partial
Differential Equations via Sketching
- Authors: Yian Chen, Yuehaw Khoo
- Abstract summary: We propose a framework for solving high-dimensional partial differential equations with tensor networks.
Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples as a tensor-network.
- Score: 1.3144299362395915
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we propose a general framework for solving high-dimensional
partial differential equations with tensor networks. Our approach uses
Monte-Carlo simulations to update the solution and re-estimates the new
solution from samples as a tensor-network using a recently proposed tensor
train sketching technique. We showcase the versatility and flexibility of our
approach by applying it to two specific scenarios: simulating the Fokker-Planck
equation through Langevin dynamics and quantum imaginary time evolution via
auxiliary-field quantum Monte Carlo. We also provide convergence guarantees and
numerical experiments to demonstrate the efficacy of the proposed method.
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