Kalman / covariance propogation solver

[BradyPlanden]

This issue is to decide the implementation language for the solver required for #3.

Options discussed:
Pure Python
JAX
PyBaMM's IDAKLU (C++)

Currently, JAX is the method being considered as it provides compiled performance as well as code modularity between CPU/TPU/GPU.

[davidhowey]

Just to drop in, as an aside, that I do quite like the idea of the "halfway house" observer we discussed a few days ago, i.e., fixed feedback gain parameter K that is learnt as part of the optimisation. Any observer is better than none, and this might mean we can use existing solvers.

[martinjrobins]

is this still in scope for pybop? I notice that the BaseModel class currently handles the timestepping, i.e. timestepping, or the way time is discretised, is considered part of the model, and data only comes into the problem. But the output of a KF is (for parameter estimation anyway) the likelihood, which is a cost function, and the timestepping is also handled by the KF (or any observer), and data comes into the KF. So its unclear where a KF would fit into the current design.

It would be great if this would be included still!

[BradyPlanden]

Hi Martin,

Yes, I think everyone is still keen for this to be included; but I agree that it's not clear how it fits into the current design. I believe the fixed-gain observer could be completed by inserting a fixed gain optimisation parameter into the RHS (although for which state variable is the question) with requiring a change to the design.

For a true KF implementation (and without thinking too much about it), we might be able to formulate the KF as a cost function with methods to change the time step by changing the problem variables/methods. Is this something that you are interested in looking at?

[martinjrobins]

sure, I can look at this. I'm not exactly sure how to implement a KF for a general pybamm model, but I'll look into it....