By combining multiresolution analysis (MRA) and adaptive spectral graph wavelets, you might efficiently address you issue. Follow:
Goyal et al., " Fast diffusion wavelet method for partial differential equations ", 2016 - http://web.iitd.ac.in/~mmehra/publication/AMM16.pdf
Goyal et al., " A fast adaptive diffusion wavelet method for Burger’s equation ", 2014 - http://web.iitd.ac.in/~mmehra/publication/CMA14.pdf
[Link with machine learning via RBF-typed ANNs] Goyal et al., " An adaptive meshfree spectral graph wavelet method for partial differential equations ", 2017 - http://web.iitd.ac.in/~mmehra/publication/ANM17.pdf
Mehra et al., " An adaptive wavelet collocation method for the solution of partial differential equations on the sphere ", 2008 - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.414.6086&rep=rep1&type=pdf
O. Vasilyev , " Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets ", 2003 -
Article Solving Multi-dimensional Evolution Problems with Localized ...
Vasilyev et al., " Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations ", 2000 - https://pdfs.semanticscholar.org/0352/e172b5154aa1ba9e549dc6f407836183af7e.pdf