Fitting population dynamic models to time-series data by gradient matching

By Stephen P. Ellner, Y. Seifu, Robert H. Smith. 2002

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Parameter estimation of ODE’s via nonparametric estimators (2007, methodology): “ al. [29] with cubic splines (and a well-chosen sequence of knots). In the same spirit, approximation of the solutions of the ODE are provided by smoothing methods such as local polynomial regression [22, 30, 11], or neural networks [42], within the same two-step estimation scheme. Slight modiﬁcatio”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “1) is some unknown function of x, that is, is given by F(x(t)) with F unknown, and proceed to its estimation via nonparametric methods, see, for example, [10].”
MEASUREMENT OF INTERACTION STRENGTH IN NATURE (2005, background): “…is to estimate instantaneous rates of change by fitting some arbitrary function, such as separate linear, polynomial, or exponential functions, to a small subset of points around a focal data point and calculating the average slope of the function at the focal data point (e.g., Ellner et al. 2002).”
Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, background): “…to overcome the computational challenges associated with solving (3), collocation meth-ods have been employed by a number of authors (Varah, 1982; Ellner et al., 2002; Ramsay et al., 2007; Brunel, 2008; Cao and Zhao, 2008; Liang and Wu, 2008; Cao et al., 2011; Lu et al., 2011; Gugushvili and…”