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Modeling Reaction-Diffusion Systems with Dynamic Boltzmann Distributions


Computational models are an essential tool to understand biological systems. A common challenge in this field is to find reduced models that offer a simpler effective description of a system with increased computational efficiency. Recent revived interest in applications of machine learning has produced algorithms that are naturally suited for this task. This thesis introduces dynamic Boltzmann distributions (DBDs) for model reduction of chemical reaction networks. DBDs are an unsupervised learning method, framed in the language of probabilistic graphical models. This allows a close connection to be made between DBDs and the description of chemical reaction networks by master equations. In this framework, this thesis shows how the physics of the system can be incorporated into otherwise application-agnostic machine learning algorithms. DBDs and their accompanying physics-informed machine learning algorithms provide a new path forward to apply reduced modeling methods to study reaction pathways at scale in synaptic neuroscience and other applications in biology.

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