SDE estimation based on a set of features

[mobar]

I would like to get started with non-linear time timeseries learning and extrapolation in Julia by learning the drift parameters in an SDE based on a pre-defined set of latent features (for this particular application it is not so important to estimate the noise term).

So given an SDE for the process X of the form:

dX(t) = f(V,t)X(t)dt+σX(t)dW(t)

where σ is a given constant, V is a vector of latent features and we can only make fairly minimum statements about how changes in a given feature should affect the drift - …what would then be a good way to approach the problem in Julia using SciML?

Thanks

[ChrisRackauckas]

@mobar

where σ is a given constant, V is a vector of latent features and we can only make fairly minimum statements about how changes in a given feature should affect the drift - …what would then be a good way to approach the problem in Julia using SciML?

Here’s some examples:

https://diffeqflux.sciml.ai/dev/examples/optimization_sde/

https://turing.ml/dev/tutorials/10-bayesian-differential-equations/