The omnipresence of fluid–structure interaction (FSI) in biological systems is indisputable—
from the vibration of leaves to the locomotion of fish, to the flying of birds, and to the …

We investigate numerous structural connections between numerical algorithms for partial
differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of …

We further develop a new framework, called PDE acceleration, by applying it to calculus of
variation problems defined for general functions on R^ n R n, obtaining efficient numerical …

This paper provides a rigorous convergence rate and complexity analysis for a recently
introduced framework, called PDE acceleration, for solving problems in the calculus of …

Long-term evolutions of parabolic partial differential equations, such as the heat equation,
are the subject of interest in many applications. There are several numerical solvers marking …

Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image
from a small subset of its pixels. This makes it an attractive foundation for PDE based image …

We investigate what can be learned from translating numerical algorithms into neural
networks. On the numerical side, we consider explicit, accelerated explicit, and implicit …

Inpainting-based codecs store sparse selected pixel data and decode by reconstructing the
discarded image parts by inpainting. Successful codecs (coders and decoders) traditionally …

Deep learning has revolutionized the field of computer vision by introducing large scale
neural networks with millions of parameters. Training these networks requires massive …

The main task in three-dimensional non-rigid shape correspondence is to retrieve
similarities between two or more similar three-dimensional objects. An important building …