FixFit

A tool for parameter-compression to solve the inverse problem in models with redundant parameters.

Code can be found at: https://github.com/lcneuro/FixFit

A: A schematic representing the goodness of fit landscape of a model with two interacting parameters. These interactions cause multiple parameter combinations to fit experimental data equally (the redundant maxima in red). B: The same landscape but with the two interacting parameters first combined into a single latent variable. In contrast to the native parameters, numerical fitting over latent variables will converge to a unique solution. C: FixFit generates such unique latent representations using a neural network with an encoder, bottleneck layer, and decoder.

We developed FixFit to address a fundamental problem with using complex nonlinear models: data-driven parameter estimation often fails because interactions between model parameters lead to multiple parameter sets fitting the data equally well. FixFit solves this issue by compressing a given mathematical model’s parameters into a latent representation unique to model outputs. We acquire this representation by training a neural network with a bottleneck layer on data pairs of model parameters and model outputs. The bottleneck layer nodes correspond to the unique latent parameters, and their dimensionality indicates the information content of the model. The trained neural network can be split at the bottleneck layer into an encoder to characterize the redundancies and a decoder to uniquely infer latent parameters from measurements.

For details and examples, see our preprint. Here, we demonstrate FixFit in two use cases drawn from classical physics and neuroscience.