Document Type


Date of Award


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Casey Diekman

Second Advisor

Victor Victorovich Matveev

Third Advisor

David Shirokoff

Fourth Advisor

Usman W. Roshan

Fifth Advisor

James R. Kozloski


Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on the major ideas that are important for this dissertation. It provides an introduction to parameter inference techniques and highlights some of the methodologies available for solving stochastic inverse problems. Chapter 2 starts with a brief overview of the Hodgkin-Huxley model, and then introduces other conductance-based models that are used in the dissertation. The first part of Chapter 3 focuses on methodologies for global sensitivity analysis and global optimization, in particular Sobol sensitivity analysis and Differential Evolution. The second part of this chapter explains how the Markov chain Monte Carlo (MCMC) algorithm can be used for parameter inference and then introduces a novel parameter inference tool based on conditional Generative Adversarial Networks (cGANs). In Chapter 4, the performance of cGAN and MCMC are compared on synthetic targets. Chapter 5 then uses cGAN to infer biophysicalparameters from experimental data recorded at the single-cell and network levels from neurons involved in the regulation of circadian (~24-hour) rhythms and from brain regions associated with neurodegenerative diseases. Finally, conclusions and suggestions for further research are presented in Chapter 6.



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