Journal of Scientific Computing· 2026Q1
Using Machine Learning to Design Time Step Size Controllers for Stable Time Integrators
- 1citations
- Q1SCImago
- 2026year
Short summary
Bayesian optimization with a novel objective function designs time step controllers for stable integrators with embedded error estimates, achieving performance comparable to state-of-the-art methods.
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Key points
- A machine learning method using Bayesian optimization is proposed for designing time step controllers.
- A novel objective function is introduced to capture tolerance convergence and computational stability.
- The method is applied to MPRK and Rosenbrock-type schemes, extending classical PI/PID controllers.
- Optimized controllers demonstrate performance comparable to state-of-the-art methods across various ODEs and PDEs.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that provide a local error estimate similar to Runge–Kutta pairs. To design good time step size controllers using these error estimates, we propose to use Bayesian optimization. In particular, we design a novel objective function that captures important properties such as tolerance convergence and computational stability. We apply our new approach to several modified Patankar–Runge–Kutta (MPRK) schemes and a Rosenbrock-type scheme, equipping them with controllers based on digital signal processing which extend classical PI and PID controllers. We demonstrate that the optimization process yields controllers that are at least as good as the best controllers chosen from a wide range of suggestions available for classical explicit and implicit time integration methods by providing work-precision diagrams for a variety of ordinary and partial differential equations.
The authors' abstract, as published at the source. Journal of Scientific Computing, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics