Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2006.14428

On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis

Mahmoud Gadalla·Marta Cianferra·Marco Tezzele·Giovanni Stabile·Andrea Mola·Gianluigi Rozza
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mahmoud Gadalla, Marta Cianferra, Marco Tezzele, Giovanni Stabile, Andrea Mola, Gianluigi Rozza. 2020-12-28. On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis. https://doi.org/10.1016/j.compfluid.2020.104819

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

How many continuous measurements are needed to learn a vector?

One can recover vectors from $\mathbb{R}^m$ with arbitrary precision, using only $\lceil \log_2(m)\rceil +1$ continuous measurements that are chosen adaptively. This surprising result is explained and discussed, and we present applications to infinite-dimensional approximation problems.

math.NA↗
arXiv2026

IterativeCUR: Large Rank-Adaptive Approximation From a Small Recycled Sketch

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed using SVD-based approaches such as truncated SVD or Randomized SVD. Although these SVD approaches---especially Randomized SVD---have proven to be very computationally efficient, other low-rank approximation methods can offer even greater performance. One such approach is the CUR decomposition, which forms a low-rank approximation using direct row and column subsets of a matrix. Because CUR uses direct matrix subsets, it is also often better able to preserve native matrix structures like sparsity or non-negativity than SVD-based approaches and can facilitate data interpretation in many contexts. This paper introduces IterativeCUR, which draws on previous work in randomized numerical linear algebra to build a new algorithm that is highly competitive compared to prior work. IterativeCUR is adaptive in the sense that it takes as an input parameter the desired tolerance $ε$ and outputs (with arbitrarily high probability) an approximation of error bounded by $ε$, rather than requiring an a priori guess of the numerical rank. IterativeCUR typically runs significantly faster than both existing CUR algorithms and techniques such as Randomized SVD. Its asymptotic complexity is $\mathcal{O}(mn + (m+n)r^2)$ for an $m\times n$ matrix of output rank $r$. IterativeCUR relies on a single small sketch from the matrix that is successively downdated as the algorithm proceeds. We demonstrate through extensive experiments that IterativeCUR achieves up to $4\times$ speed-up over state-of-the-art pivoting-on-sketch approaches with no loss of accuracy, and up to $40\times$ speed-up over rank-adaptive randomized SVD approaches.

math.NA↗
arXiv2026

Multigrid with Linear Storage Complexity

As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases. Storing the solution's finite element coefficients explicitly requires $\mathcal O(n \log n)$ bits of storage, where $n$ is the number of degrees of freedom (DoFs). This paper presents a full multigrid method to compute the solution in a compressed format that reduces the storage complexity of the solution and intermediate vectors to $\mathcal O(n)$ bits. This reduction allows a matrix-free implementation to solve elliptic PDEs with an overall linear space complexity. For problems limited by the memory capacity of current supercomputers, we expect a memory footprint reduction of about an order of magnitude compared to state-of-the-art mixed-precision methods. We demonstrate the applicability of our algorithm by solving two model problems. Depending on the PDE and polynomial degree, but irrespective of the problem size, the solution vector on the finest grid requires between 4 and 12 bits per DoF, and the residual and correction require 3 to 6 bits each. Additional data is stored on the coarse grids with modestly increasing bit widths toward coarser grids.

math.NA↗