Abstract: We propose a two-stage method called Spline-Assisted Partial Differential Equations-based Model Identification that can be used to identify models based on partial differential equations (PDEs) from noisy data. In the first stage, we employ cubic splines to estimate unobservable derivatives. The underlying PDE is based on a subset of these derivatives. This stage is computationally efficient. Its computational complexity is the product of a constant and the sample size, which is the lowest possible order of computational complexity. In the second stage, we apply the least absolute shrinkage and selection operator to identify the underlying PDE-based model. Statistical properties are developed, including the model identification accuracy. We validate our theory using numerical examples and a real-data case study based on an National Aeronautics and Space Administration data set.

Key words and phrases: Cubic splines, Lasso, model identification, partial differential equations.