Related papers: Multiresolution analysis of electronic structure: …
Compared to scalar framelets, multiframelets have certain advantages, such as relatively smaller supports on generators, high vanishing moments, etc. The balancing property of multiframelets is very desired, as it reflects how efficient…
Model quantization can reduce the model size and computational latency, it has become an essential technique for the deployment of deep neural networks on resourceconstrained hardware (e.g., mobile phones and embedded devices). The existing…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
In the rapidly advancing field of multi-modal machine learning (MMML), the convergence of multiple data modalities has the potential to reshape various applications. This paper presents a comprehensive overview of the current state,…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
The Coherent Multiplex is formalized and validated as a scalable, real-time system for identifying, analyzing, and visualizing coherence among multiple time series. Its architecture comprises a fast spectral similarity layer based on cosine…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Deep Learning has implemented a wide range of applications and has become increasingly popular in recent years. The goal of multimodal deep learning is to create models that can process and link information using various modalities. Despite…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effect are strongest in the nuclear region, where the…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
Quantum Monte Carlo approaches based on the stochastic sampling of the determinant space have evolved to be powerful methods to compute the electronic states of molecules. These methods not only calculate the correlation energy at an…