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000905463 005__ 20240712112904.0
000905463 0247_ $$2arXiv$$aarXiv:2105.01303
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000905463 037__ $$aFZJ-2022-00704
000905463 1001_ $$0P:(DE-HGF)0$$aGuo, Yue$$b0
000905463 245__ $$aPersonalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators
000905463 260__ $$c2021
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000905463 520__ $$aWe study the meta-learning of numerical algorithms for scientific computing, which combines the mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a departure from the classical approaches in numerical analysis, which typically do not feature such learning-based adaptations. As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture. By combining neural network approximations and meta-learning, we show that we can obtain high-order integrators for targeted families of differential equations without the need for computing integrator coefficients by hand. Moreover, we demonstrate that in certain cases we can obtain superior performance to classical RK methods. This can be attributed to certain properties of the ODE families being identified and exploited by the approach. Overall, this work demonstrates an effective, learning-based approach to the design of algorithms for the numerical solution of differential equations, an approach that can be readily extended to other numerical tasks.
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000905463 7001_ $$0P:(DE-HGF)0$$aDietrich, Felix$$b1
000905463 7001_ $$0P:(DE-HGF)0$$aBertalan, Tom$$b2
000905463 7001_ $$0P:(DE-Juel1)180221$$aDoncevic, Danimir$$b3$$ufzj
000905463 7001_ $$0P:(DE-Juel1)172097$$aDahmen, Manuel$$b4$$ufzj
000905463 7001_ $$0P:(DE-HGF)0$$aKevrekidis, Ioannis G.$$b5
000905463 7001_ $$0P:(DE-HGF)0$$aLi, Qianxiao$$b6$$eCorresponding author
000905463 8564_ $$uhttps://juser.fz-juelich.de/record/905463/files/2105.01303.pdf$$yOpenAccess
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