Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation

Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they require the user to build coarse models to handle the unavoidable serial transport of information in time. This is a time-consuming and difficult process since there is still limited theoretical insight into what constitutes a good and efficient coarse model. Novel approaches from machine learning to solve differential equations could provide a more generic way to find coarse-level models for multi-level parallel-in-time algorithms. This paper demonstrates that a physics-informed Fourier Neural Operator (PINO) is an effective coarse model for the parallelization in time of the two-asset Black-Scholes equation using Parareal. We demonstrate that PINO-Parareal converges as fast as a bespoke numerical coarse model and that, in combination with spatial parallelization by domain decomposition, it provides better overall speedup than both purely spatial parallelization and space-time parallelization with a numerical coarse propagator.

Subjects

Black-Scholes equation

machine learning

parallel-in-time integration

Parareal

physics-informed neural operator

space-time parallelization

DDC Class

518: Numerical Analysis

004: Computer Sciences

Funding(s)

NeuralPinT

Publication version

publishedVersion

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

3732775.3733574.pdf

Size

965.38 KB

Format

Adobe PDF

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Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation