
Efficiently solve nonlinear PDEs using near-linear complexity algorithm with sparse Cholesky factorization.


coremsg

sparse-cholesky-factorization-for-solving-nonlinear-pdes-with-gaussian-processes


Sparse Cholesky Factorization for Solving Nonlinear PDEs with Gaussian Processes


title_rewrite


Efficient algorithm for solving nonlinear PDEs using sparse Cholesky factorization with Gaussian processes.



The authors present a near-linear complexity algorithm for working with kernel matrices, transforming the solving of general nonlinear PDEs into solving quadratic optimization problems. They rigorously justify the near-sparsity of the Cholesky factor by connecting it to GP regression and exponential decay of basis functions.
