Noise creates a harmful transformation on the estimation of derivative signal. In this paper, we suggest an easy to implement and adequate approximation method for function signal with noise. It is based polynomial regression constructed least squares differences, but degree depending signal-to-noise ratio. Numerical results similar accuracy compared established methods as Savitzsky-Golay smoot...

This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. relies on introduction random latent vectors having priori independent von Mises-Fisher distributions defined hypersphere. statistical model leads complete data likelihood whose expected value, conditioned observed data, has Von distribution. As result...

Problems in astrophysics, space weather research, and geophysics usually need to analyze big noisy data on the sphere. This paper develops distributed filtered hyperinterpolation for sphere, which assigns fitting task multiple servers find a good approximation of mapping input output data. For each server, is sphere by small proportion quadrature nodes. The strategy allows parallel computing pr...

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying spatio-temporal data set using sparse regression on library of possible functions and their derivatives. A neural network is used as function approximator its output to construct library, allowing perform within network. This construction makes it extremely robus...