Related papers: Convolution Quadrature for Wave Simulations
This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.
Quaternion-valued signal processing has received increasing attention recently. One key operation involved in derivation of all kinds of adaptive algorithms is the gradient operator. Although there have been some derivations of this…
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when…
Quantitative evaluations of differences and/or similarities between data samples define and shape optimisation problems associated with learning data distributions. Current methods to compare data often suffer from limitations in capturing…
We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which…