BradyPlanden
commented
4 days ago Hi @MarkBlyth,
Thanks for opening this issue! This is an interesting area to consider, I don't fit Thevenin style models that often, so it's interesting to hear your experience. In terms of OLS, we capture this estimator via the GaussianLogLikelihood classes, as OLS can be represented by maximum likelihood estimation (MLE) under a Gaussian distributed likelihood function [1][2]. This example provides usage on the likelihood classes, but it would be great to present this information more formally in a notebook, if you are interested in creating that while comparing Gaussian MLE with OLS :)
More generally, we could implement an OLS class that either constructs the GaussianLogLikelihood class with additional features (?) or perhaps update the docstring and examples to better signpost this.
MarkBlyth
Feature description
Enable parameters to be computed using ordinary least squares, for linear fitting problems.
Motivation
Fitting equivalent circuit models using purely optimisation-based methods turns out to not be particularly easy or robust, and needs careful tuning of optimisation methods, parameter bounds and priors, etc. However, for a given RC timescale, the optimal parameters of a Thevenin-style empirical model can be found directly, using ordinary least-squares. From experience, the fastest and most reliable way to fit these sorts of models is to (a) get a nonlinear optimiser to propose the RC time-constants; (b) for those RC time-constants, fit parameters using least squares; (c) use the resulting least-squares error as the cost for the nonlinear optimiser. Developing least-squares fitting in PyBOP would therefore make it a particularly useful tool for these sorts of parameterisation problems.
Possible implementation
No response
Additional context
No response