Generalized function learning machine

Abstract

The system and methods of the present invention involve estimating model parameters for non-linear systems of Differential Equations (DEs). This includes receiving data from these systems and applying Weak-form Estimation of Nonlinear Dynamics methods to the data. These methods are robust to instances of large measurement noise. The system and methods also involve converting strong form representations of a model to weak forms, solving regression problems to perform parameter inference, and using Errors-In-Variables frameworks and iteratively reweighted least squares algorithms. The system and methods of the present invention can be applied to various models from different fields such as population biology, neuroscience, and biochemistry. The system and methods are highly robust and exhibit computational efficiency when used to estimate parameters in some common models including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, a Protein Transduction Benchmark model and Kuramoto-Sivashinsky.

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