Neural differential equation

In machine learning, a neural differential equation is a differential equation whose right-hand side is parametrized by the weights θ of a neural network.^[1] In particular, a neural ordinary differential equation (neural ODE) is an ordinary differential equation of the form

$${\displaystyle {\frac {\mathrm {d} \mathbf {h} (t)}{\mathrm {d} t}}=f_{\theta }(\mathbf {h} (t),t).}$$

Neural ODEs can be understood as continuous-time control systems, where their ability to interpolate data can be interpreted in terms of controllability.^[2]