Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks

Traditionally, we provide technical parameters for ODE solvers, such as the order, the stepsize and the local error threshold. However, there is no for performance metrics that users care about, such as the time consumption and the global error. In this paper, we provide such a user-oriented by using neural networks to fit the complex relationship between the technical parameters and performance metrics. The form of the neural network is carefully designed to incorporate the prior knowledge from time complexity analysis of ODE solvers, which has better performance than purely data-driven approaches. We test our strategy on some parametrized ODE problems, and experimental results show that the fitted model can achieve high accuracy, thus providing error for fixed methods and time for adaptive stepsize methods.