Abstract
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many
others. Despite the existence of algorithms that learn the dynamics from trajectorial measurements
there are few attempts to infer the dynamical system straight from population data. In this work, we
deduce and then computationally estimate the Fokker-Planck equation which describes the evolution
of the population’s probability density, based on stochastic differential equations. Then, following
the USDL approach 22, we project the Fokker-Planck equation to a proper set of test functions,
transforming it into a linear system of equations. Finally, we apply sparse inference methods to
solve the latter system and thus induce the driving forces of the dynamical system. Our approach
is illustrated in both synthetic and real data including non-linear, multimodal stochastic differential
equations, biochemical reaction networks as well as mass cytometry biological measurements.
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