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Related papers: Accelerating GMRES with Deep Learning in Real-Time

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We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…

Machine Learning · Statistics 2017-07-19 Wenjing Liao , Mauro Maggioni

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…

Optimization and Control · Mathematics 2018-06-21 Robert M. Gower , Filip Hanzely , Peter Richtárik , Sebastian Stich

In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal…

Computational Finance · Quantitative Finance 2018-11-22 Ali Al-Aradi , Adolfo Correia , Danilo Naiff , Gabriel Jardim , Yuri Saporito

Reinforcement Learning (RL) is increasingly utilized to enhance the reasoning capabilities of Large Language Models (LLMs). However, effectively scaling these RL methods presents significant challenges, primarily due to the difficulty in…

Machine Learning · Computer Science 2025-09-30 Alexandre Piché , Ehsan Kamalloo , Rafael Pardinas , Xiaoyin Chen , Dzmitry Bahdanau

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

Graphics · Computer Science 2018-05-16 Yue Peng , Bailin Deng , Juyong Zhang , Fanyu Geng , Wenjie Qin , Ligang Liu

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

Computation · Statistics 2026-03-18 Aleksei G. Sorokin , Pieterjan Robbe , Fred J. Hickernell

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

Numerical Analysis · Mathematics 2020-07-17 Jiequn Han , Arnulf Jentzen , Weinan E

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently importance to drastically reduce computational time and energy consumed is…

Machine Learning · Computer Science 2020-06-26 Antonio Candelieri , Riccardo Perego , Francesco Archetti

We propose a novel technique for faster deep neural network training which systematically applies sample-based approximation to the constituent tensor operations, i.e., matrix multiplications and convolutions. We introduce new sampling…

Machine Learning · Computer Science 2021-10-27 Menachem Adelman , Kfir Y. Levy , Ido Hakimi , Mark Silberstein

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

Methodology · Statistics 2018-06-08 Aliaksandr Hubin , Geir Storvik , Florian Frommlet

We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…

Numerical Analysis · Mathematics 2022-01-13 Jennifer A. Loe , Ronald B. Morgan

The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…

Machine Learning · Computer Science 2021-12-08 Valentin Mercier , Serge Gratton , Pierre Boudier

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

Numerical Analysis · Mathematics 2019-11-28 Suprosanna Shit , Abinav Ravi Venkatakrishnan , Ivan Ezhov , Jana Lipkova , Marie Piraud , Bjoern Menze

While Vision-Language Models (VLMs) have significantly advanced remote sensing interpretation, enabling them to perform complex, step-by-step reasoning remains highly challenging. Recent efforts to introduce Chain-of-Thought (CoT) reasoning…

Computer Vision and Pattern Recognition · Computer Science 2026-05-27 Lang Sun , Ronghao Fu , Zhuoran Duan , Haoran Liu , Xueyan Liu , Bo Yang

Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…

Machine Learning · Computer Science 2022-03-15 Luca Grementieri , Paolo Galeone

Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…

Machine Learning · Statistics 2025-04-15 Praveen T. W. Hettige , Benjamin W. Ong

In recent years, deep learning methods applying unsupervised learning to train deep layers of neural networks have achieved remarkable results in numerous fields. In the past, many genetic algorithms based methods have been successfully…

Neural and Evolutionary Computing · Computer Science 2017-11-22 Eli David , Iddo Greental

Abstract visual reasoning (AVR) domain encompasses problems solving which requires the ability to reason about relations among entities present in a given scene. While humans, generally, solve AVR tasks in a "natural" way, even without…

Artificial Intelligence · Computer Science 2025-02-24 Mikołaj Małkiński , Jacek Mańdziuk

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

Machine Learning · Computer Science 2024-08-02 Han Gao , Sebastian Kaltenbach , Petros Koumoutsakos