Efficiently Solving High-Order and Nonlinear ODEs with Rational Fraction Polynomial: the Ratio Net

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient backpropagation algorithms. However, challenges remain in solving complex ODEs, including high-order and nonlinear cases, emphasizing the need for improved efficiency and effectiveness. Traditional methods have typically relied on established knowledge integration to improve problem-solving efficiency. In contrast, this study takes a different approach by introducing a new neural network …

advances algorithms backpropagation cases challenges cs.lg cs.na differential excel functional functions gradient math.na networks neural networks ordinary polynomial solutions spaces