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Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…
Physics-Informed Neural Networks (PINNs) have shown continuous and increasing promise in approximating partial differential equations (PDEs), although they remain constrained by the curse of dimensionality. In this paper, we propose a…
Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly increases…
The growing demands of distributed learning on resource constrained edge devices underscore the importance of efficient on device model compression. Tensor Train Decomposition (TTD) offers high compression ratios with minimal accuracy loss,…
Retrieval augmentation is a powerful but expensive method to make language models more knowledgeable about the world. Memory-based methods like LUMEN pre-compute token representations for retrieved passages to drastically speed up…
The nonequilibrium Green's functions (NEGF) approach is a versatile theoretical tool, which allows to describe the electronic structure, spectroscopy and dynamics of strongly correlated systems. The applicability of this method is, however,…
Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the…
In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…
This paper describes a new method for representing embedding tables of graph neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We consider the scenario where (a) the graph data that lack node features, thereby…
Simulations of quantum matter rely mainly on Kohn-Sham density functional theory (DFT), which often fails for strongly correlated systems. Quantum embedding (QE) theories address this limitation by mapping the system onto an auxiliary…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
Deploying large-scale transformer models on edge devices presents significant challenges due to strict constraints on memory, compute, and latency. In this work, we propose a lightweight yet effective multi-stage optimization pipeline…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
Internet of Things and Deep Learning are synergetically and exponentially growing industrial fields with a massive call for their unification into a common framework called Edge AI. While on-device inference is a well-explored topic in…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…