
Bayesian equation selection on sparse data for discovery of stochastic dynamical systems
Often the underlying system of differential equations driving a stochast...
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Field dynamics inference for local and causal interactions
Complex systems with many constituents are often approximated in terms o...
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A nonautonomous equation discovery method for time signal classification
Certain neural network architectures, in the infinitelayer limit, lead ...
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Dynamical analysis in a selfregulated system undergoing multiple excitations: first order differential equation approach
In this paper, we discuss a novel approach for studying longitudinal dat...
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Inferring temporal dynamics from crosssectional data using Langevin dynamics
Crosssectional studies are widely prevalent since they are more feasibl...
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Extracting structured dynamical systems using sparse optimization with very few samples
Learning governing equations allows for deeper understanding of the stru...
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HJB and FokkerPlanck equations for river environmental management based on stochastic impulse control with discrete and random observation
We formulate a new twovariable river environmental restoration problem ...
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Inference of Stochastic Dynamical Systems from CrossSectional Population Data
Inferring the driving equations of a dynamical system from population or timecourse 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 FokkerPlanck equation which describes the evolution of the population's probability density, based on stochastic differential equations. Then, following the USDL approach, we project the FokkerPlanck 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 nonlinear, multimodal stochastic differential equations, biochemical reaction networks as well as mass cytometry biological measurements.
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