Neural Differential Equations

Computational models have become a powerful tool in the quantita- tive sciences to understand the behaviour of complex systems that evolve in time. However, they often contain a plethora of parameters that cannot be estimated theoretically and need to be inferred from data. This is especially the case for models in the social sciences, economics, or computational epidemiology. Parameters must there- fore be extracted from datasets. Together with my coworkers I am currently developing and researching a fast, scalable method to retrieve probability densities for model parameters using neural differential equations. We have developed a pipeline comprising agent-based models acting as forward solvers for systems of or- dinary or stochastic differential equations, and a deep neural net to then extract parameters from the data generated by the model. The two combined create a powerful tool that can quickly estimate sets of model parameters, often in a matter of seconds, even for very large systems.

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