Metamodelling of the Hodgkin-Huxley model and the Pinsky-Rinzel model using local multivariate regression and deep learning
Lars Erik Ødegaard · NORA - Norwegian Open Research Archives · 2019
Biological processes, such as the electrical activity in neurons, are often modelled using complex, non-linear and high dimensional differential systems. Such models are usually associated with a high computational cost. Statistical tools are often needed in order to get a comprehensive overview of the behaviour of such systems. Using statistical emulators (metamodels) have been shown useful for providing insight into model behaviour, as well as reducing the computational demand. In this thesis, the two metamodelling techniques, Hierarchical Cluster-based Partial Least Squares Regression (HCPLSR) and deep learning were explored and compared. This was done by metamodelling the simpler Hodgkin-Huxley model and the more complex Pinsky-Rinzel model. The input parameters were varied in a Latin Hypercube Sampling (LHS) design, and the somatic membrane potentials were generated using the single neuron activity models. Further, the metamodelling techniques were used to find input-output and output-input relationships in the two models. The results indicate that deep learning metamodelling is a more efficient emulator of complex non-linear models, while the HCPLSR metamodelling allows for a more detailed interpretation of the model behaviour. These findings emphasize the need for using subspace analysis in order to accurately describe complex models with a wide range of behaviours, suggesting that subspace analysis in combination with deep learning emulation can further improve the understanding of model behaviour.