Related papers: Surrogate Modeling with Low-Rank Function Represen…

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluid…

We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test…

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desired. In absence of the governing equations describing the…

Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…

Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…

Recent approaches based on transform-based tensor nuclear norm (TNN) have demonstrated notable effectiveness in hyperspectral image (HSI) inpainting by leveraging low-rank structures in latent representations. Recent developments…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Surrogate models have several uses in engineering design, including speeding up design optimization, noise reduction, test measurement interpolation, gradient estimation, portability, and protection of intellectual property. Traditionally,…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some…

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

Surrogates provide a cheap solution evaluation and offer significant leverage for optimizing computationally expensive problems. Usually, surrogates only approximate the original function. Recently, the perfect linear surrogates were…

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…

This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…