Is the choice of integrator significant for NeuralODE solving?

[srikumarks]

For directly solving known ODEs, of course the choice of integrator is significant.

However, when learning a network that’s part of an ODE, it isn’t clear to me whether the integrator matters, or should matter. Does it make a significant difference? Would the trained NN embody behaviours of the integrator too or would it turn out to be somewhat independent of it? … like if trained with Tsit5 or say KahanLi8, do we already know whether we’d get NNs that can/cannot be used with the other integrator?

[ChrisRackauckas]

@srikumarks

However, when learning a network that’s part of an ODE, it isn’t clear to me whether the integrator matters, or should matter. Does it make a significant difference?

It can. Depends on the accuracy needed and the properties needed.

@srikumarks

like if trained with Tsit5 or say KahanLi8, do we already know whether we’d get NNs that can/cannot be used with the other integrator?

If the tolerance is low enough then you can swap them out. That said, if you try and train a symplectic system with a non-symplectic integrator then you will have numerical error in the training which can effect the results.