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| Home > Publications database > AlphaNumerics Zero: First Steps, First Results, First Mysteries |
| Poster (After Call) | FZJ-2022-00888 |
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2021
Abstract: The spectral deferred correction method is an iterative solver for time-dependent partial differential equations. It can be interpreted as a preconditioned Picard iteration for the so-called collocation problem. The key to an efficient method is the choice of the preconditioner: It defines the speed of convergence and the level of parallelism. While the de-facto standard is a fast-converging, serial preconditioner, our goal is to use reinforcement learning techniques to find a fast-converging, parallel one. We look at a simple test equation and train a phasic policy gradient (PPG) agent to pick favorable, diagonal preconditioners depending on the parameter of the equation. For small dimensions of the collocation problem, PPG is indeed able to yield very promising results. This does not hold for larger dimensions, though. When successful, however, the trained network can be used directly to pick parallel preconditioners for more complex problems, where the parameters describe stiffness, largest eigenvalue or other characteristics of the differential equation. This work is a prototype problem for the Helmholtz AI AlphaNumerics Zero project, where reinforcement learning is used to learn on-average optimal numerical solutions for a given simulation problem.
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