Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling
This work addresses a practical limitation for researchers and practitioners using Neural ODEs in dynamical systems, but it is incremental as it focuses on a specific issue with a known method.
The paper investigates the challenges of using adaptive ODE solvers as black-box components in Neural ODEs for dynamical systems modeling, showing that naive application fails on the Lorenz'63 system, and proposes a simple workaround requiring tighter solver-training integration.
Neural Ordinary Differential Equations (ODEs) was recently introduced as a new family of neural network models, which relies on black-box ODE solvers for inference and training. Some ODE solvers called adaptive can adapt their evaluation strategy depending on the complexity of the problem at hand, opening great perspectives in machine learning. However, this paper describes a simple set of experiments to show why adaptive solvers cannot be seamlessly leveraged as a black-box for dynamical systems modelling. By taking the Lorenz'63 system as a showcase, we show that a naive application of the Fehlberg's method does not yield the expected results. Moreover, a simple workaround is proposed that assumes a tighter interaction between the solver and the training strategy. The code is available on github: https://github.com/Allauzen/adaptive-step-size-neural-ode