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The neural ODE technique, to my knowledge, presents a neural network based way of solving ODEs efficiently, which implies it needs an ODE and an initial value in order to construct the evolution over time.

Does the technique still apply if I wish to flip the problem - given a small number of measurements, predict the evolution in the future by attempting to model it as an ODE?

Firebug
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HighVoltage
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  • Yes, more or less. The method is used to model continuous time measurements by solving $x'(t) = F(x(t))$. Here, $F$ is actually a neural network. The method is not omnipotent, obviously. In their paper, Chen et. al provide some very good examples. – Demetri Pananos Mar 10 '20 at 04:10
  • In one simple example they provide of the Lotka-Volterra model, the forward pass evaluates dx/dt for an arbitrary x, thus assuming knowledge of the ODE and solving it to obtain the evolution of x. Instead, in my case, I don't know the underlying dynamics, but have some data about x vs. t. – HighVoltage Mar 10 '20 at 06:26
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    If you knew the dynamics, you wouldn’t need a neural ode. The method is for when you don’t know the dynamics but have data on the system. – Demetri Pananos Mar 10 '20 at 12:21

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