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Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits…
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…
Low-rank training methods reduce the number of trainable parameters by re-parameterizing the weights with matrix decompositions (e.g., singular value decomposition). However, enforcing a fixed low-rank structure caps the rank of the weight…
We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov--Poisson equations based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time…
We study policy evaluation problems in multi-task reinforcement learning (RL) under a low-rank representation setting. In this setting, we are given $N$ learning tasks where the corresponding value function of these tasks lie in an…
The tensor low-rank prior has attracted considerable attention in dynamic MR reconstruction. Tensor low-rank methods preserve the inherent high-dimensional structure of data, allowing for improved extraction and utilization of intrinsic…
In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
Dynamic Rank Reinforcement Learning (DR-RL) approximations rely on static rank assumptions, limiting their flexibility across diverse linguistic contexts. Our method dynamically modulates ranks based on real-time sequence dynamics,…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
We present a data-driven dimensionality reduction method that is well-suited for physics-based data representing hyperbolic wave propagation. The method utilizes a specialized neural network architecture called low rank neural…
Background: In cognitive neuroscience the potential of Deep Neural Networks (DNNs) for solving complex classification tasks is yet to be fully exploited. The most limiting factor is that DNNs as notorious 'black boxes' do not provide…
Radiative transfer calculations in weather and climate models are notoriously complex and computationally intensive, which poses significant challenges. Traditional methods, while accurate, can be prohibitively slow, necessitating the…
In neural network surrogate solvers for electromagnetic simulations, accurately modeling resonant phenomena remains a central challenge. High-amplitude resonances generate strongly localized field patterns that deviate significantly from…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…
High Power Laser (HPL) systems operate in the attoseconds regime -- the shortest timescale ever created by humanity. HPL systems are instrumental in high-energy physics, leveraging ultra-short impulse durations to yield extremely high…
Partial diffusion-based recursive least squares (PDRLS) is an effective method for reducing computational load and power consumption in adaptive network implementation. In this method, each node shares a part of its intermediate estimate…
A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor)…
Quantized tensor trains (QTTs) are a low-rank and multiscale framework that allows for efficient approximation and manipulation of multi-dimensional, high resolution data. One area of active research is their use in numerical simulation of…