相关论文: Learning Heat-based Equations in Self-similar vari…

The analysis of physiological processes over time are often given by spectrometric or gene expression profiles over time with only few time points but a large number of measured variables. The analysis of such temporal sequences is…

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…

This paper considers a demand response agent that must find a near-optimal sequence of decisions based on sparse observations of its environment. Extracting a relevant set of features from these observations is a challenging task and may…

We consider the incompressible Navier-stokes equations (NS) in $\mathbb{R}^{n}$ for $n\geq2$. Global well-posedness is proved in critical Besov-weak-Herz spaces (BWH-spaces) that consist in Besov spaces based on weak-Herz spaces. These…

We propose a self-supervised approach for learning physics-based subspaces for real-time simulation. Existing learning-based methods construct subspaces by approximating pre-defined simulation data in a purely geometric way. However, this…

Supervised learning (SL) methods are indispensable for neural network (NN) training used to perform classification tasks. While resulting in very high accuracy, SL training often requires making NN parameter number dependent on the number…

Neural support vector machines (NSVMs) allow for the incorporation of domain knowledge in the design of the model architecture. In this article we introduce a set of training algorithms for NSVMs that leverage the Pegasos algorithm and…

We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…

Local behaviors near boundary are analyzed for solutions of the Stokes and Navier-Stoke equations in the half space with localized non-smooth boundary data. We construct solutions of Stokes equations whose velocity field is not bounded near…

We construct splitting methods suitable for the solution of the equations of magnetohydrodynamics (MHD). Due to the physical significance of the involved operators, splittings into three or even four operators with positive coefficients are…

We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…

Visual localization is the task of estimating camera pose in a known scene, which is an essential problem in robotics and computer vision. However, long-term visual localization is still a challenge due to the environmental appearance…

Steering vectors (SVs) offer a lightweight way to control large language models (LLMs) at inference time by shifting hidden activations, providing a practical middle ground between prompting and fine-tuning. Yet SVs can be unreliable in…

We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singularity do to cavitation at the origin.

In this paper we promote the use of Support Vector Machines (SVM) as a machine learning tool for searches in high-energy physics. As an example for a new- physics search we discuss the popular case of Supersymmetry at the Large Hadron…

We introduce a machine-learning approach to predict the complex non-Markovian dynamics of supercooled liquids from static averaged quantities. Compared to techniques based on particle propensity, our method is built upon a theoretical…

Unsupervised representation learning methods like SwAV are proved to be effective in learning visual semantics of a target dataset. The main idea behind these methods is that different views of a same image represent the same semantics. In…

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.

Accurate long-horizon prediction of spatiotemporal fields on complex geometries is a fundamental challenge in scientific machine learning, with applications such as additive manufacturing where temperature histories govern defect formation…