论文标题
动态系统建模的自适应求解器神经ODE训练的实验研究
Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling
论文作者
论文摘要
神经普通微分方程（ODE）最近被引入了一个新的神经网络模型家族，该系列依赖于黑盒ode求解器进行推理和训练。一些称为Adaptive的ODE求解器可以根据手头问题的复杂性来调整其评估策略，从而在机器学习中开辟了很高的观点。但是，本文描述了一组简单的实验，以表明为什么自适应求解器不能无缝作为动态系统建模的黑框。通过将Lorenz'63系统作为展示，我们表明Fehlberg方法的幼稚应用不会产生预期的结果。此外，提出了一个简单的解决方法，该解决方案假设求解器与培训策略之间的相互作用更加紧密。该代码可在github上找到：https：//github.com/allauzen/adaptive-step-size-neural-ode
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
