Related papers: Scalable resolvent analysis for three-dimensional …

The massive scale of modern AI accelerators presents critical challenges to traditional fault assessment methodologies, which face prohibitive computational costs and provide poor coverage of critical failure modes. This paper introduces…

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in aerospace and marine engineering applications. While traditional full-order models based on the Navier-Stokes equations are not…

We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and…

The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…

We combine three-dimensional (3D) large-eddy simulations (LES) and resolvent analysis to design active separation control techniques on a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of…

We explore the unsupervised clustering technique introduced in [25] to identify viscous/turbulent from inviscid regions in incompressible flows. The separation of regions allows solving the Navier-Stokes equations including Large Eddy…

The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

We discuss the application of the resolvent technique to prove stability of plane Couette flow. Using this technique, we derive a threshold amplitude for perturbations that can lead to turbulence in terms of the Reynolds number. Our main…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

Recently, Test-Time Scaling (TTS) has gained increasing attention for improving LLM reasoning performance at test time without retraining the model. A notable TTS technique is Self-Consistency (SC), which generates multiple reasoning chains…

In this paper, we first propose a filter-based continuous Ensemble Eddy Viscosity (EEV) model for stochastic turbulent flow problems. We then propose a generic algorithm for a family of fully discrete, grad-div regularized, efficient…

We discuss how searching for finite amplitude disturbances of a given energy which maximise their subsequent energy growth after a certain later time $T$ can be used to probe phase space around a reference state and ultimately to find other…

Reasoning tasks are crucial in many domains, especially in science and engineering. Although large language models (LLMs) have made progress in reasoning tasks using techniques such as chain-of-thought and least-to-most prompting, these…

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…

We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by adding to the equations for the mean field $(v, p)$ a term like $-\alpha \nabla\cdot(\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the Prandtl mixing…

Monitoring the atmospheric dispersion of pollutants is increasingly critical for environmental impact assessments. High-fidelity computational models are often employed to simulate plume dynamics, guiding decision-making and prioritizing…

We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…

Astrophysical turbulent flows display an intrinsically multi-scale nature, making their numerical simulation and the subsequent analyses of simulated data a complex problem. In particular, two fundamental steps in the study of turbulent…