Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling

• URL: http://arxiv.org/abs/2211.06972v1
• Date: Sun, 13 Nov 2022 17:48:04 GMT
• Title: Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling
• Authors: Alexandre Allauzen and Thiago Petrilli Maffei Dardis and Hannah Plath
• Abstract summary: Some ODE solvers called adaptive can adapt their evaluation strategy depending on the complexity of the problem at hand. 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.
• Score: 72.84259710412293
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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

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