Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations

Chuhao Sun, Asaf Cohen, James Stokes and Shravan Veerapaneni

Papers from arXiv.org

Abstract: Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of time-dependent PDEs, the dominant paradigm involves casting the approximate solution in terms of stochastic minimization of an objective function given by the norm of the PDE residual, viewed as a function of the neural network parameters. Recently, advancements have been made in the direction of an alternative approach which shares aspects of nonlinearly parametrized Galerkin methods and variational quantum Monte Carlo, especially for high-dimensional, time-dependent PDEs that extend beyond the usual scope of quantum physics. This paper is inspired by the potential of solving Hamilton-Jacobi-Bellman (HJB) PDEs using Neural Galerkin methods and commences the exploration of nonlinearly parametrized trial functions for which the evolution equations are analytically tractable. As a precursor to the Neural Galerkin scheme, we present trial functions with evolution equations that admit closed-form solutions, focusing on time-dependent HJB equations relevant to finance.

Date: 2023-11
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2311.12239 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2311.12239

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().