We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) autoencoders (iii) transfer learning. The method provides an adaptive, hierarchical capitalizes on progressive training approach for multiscale spatio-temporal data. This framework allows inputs across multiple...

Triangles meshes are the most popular standard model used to represent polygonal surfaces in Computer Graphics. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphic engine. The use of primitives such as triangle fans and strips, which make use of the connectivity information between the triangles in the mesh, dramatically reduces th...

Multiresolution histograms have been used for indexing and retrieval of images. Multiresolution histograms used traditionally are 2d-histograms which encode pixel intensities. Earlier we proposed a method for decomposing images by connectivity. In this paper, we propose to encode centroidal distances of an image in multiresolution histograms; the image is decomposed a priori, by connectivity. M...

The Hamilton-Jacobi (HJ) equations arise in optimal control and many other applications. Oftentimes, such are posed high dimensions, this presents great numerical challenges. In paper, we propose an adaptive sparse grid (also called multiresolution) local discontinuous Galerkin (DG) method for solving dimensions. By using the techniques, can treat moderately dimensional cases. Adaptivity is inc...