4 papers
A Bayesian Machine Learning Algorithm for Predicting ENSO Using Short Observational Time Series
Nan Chen, Faheem Gilani, John Harlim
A simple and efficient Bayesian machine learning (BML) training and forecasting algorithm, which exploits only a 20-year short observational time series and an approximate prior mo…
Kernel-based Prediction of Non-Markovian Time Series
Faheem Gilani, Dimitrios Giannakis, John Harlim
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding…
Periodic Orbits on Obtuse Edge Tessellating Polygons
Benjamin R. Baer, Faheem Gilani, Zhigang Han +1
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period…
Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernels
Faheem Gilani, John Harlim
A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approac…