Optimal Coefficients of Runge-Kutta Schemes with Machine Learning

Research Internship at Karlsruhe Institute of Technology (KIT) Advisor: Prof. Martin Frank

This project explored the intersection of numerical analysis and deep learning by using Artificial Neural Networks to discover numerical schemes for Ordinary Differential Equations (ODEs).

Key Contributions:

• Designed neural networks to learn optimal coefficients for Runge-Kutta schemes with a target order of accuracy.
• Successfully rediscovered classical high-order schemes using a data-driven approach.
• Developed new methods to reduce computational cost for stiff problems.
• Implemented architectures in Python, TensorFlow, and Keras.