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Mathematics
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Machine Learning in Fluid Dynamics: Theory and Applications
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Machine Learning in Fluid Dynamics: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (15 June 2020) | Viewed by 9481

Special Issue Editor

Dr. Omer San

E-Mail Website
Guest Editor
Mechanical and Aerospace Engineering, Oklahoma State University, 201 General Academic Building, Stillwater, OK 74078-5016, USA
Interests: fluid mechanics; complex systems; pattern formation; partial differential equations; non-Newtonian fluids; fluid–structure interaction; hydrodynamic stability; non-equilibrium thermodynamics; vortex induced oscillations; rheology; pathological flows; network analysis; philosophy of science; sustainability and science and creativity in mathematics and science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, artificial intelligence plays a vital role in learning and extracting patterns from complex data. Despite their immense success in other disciplines, machine leraning tecniques are just beginning to be applied in the field of fluid dynamics. Such data analytics and statistical tools have been utilized, for example, for the physical model inference, subgrid scale closure modeling, model reduction, and fast emulators for data assimilation, paramater estimation, uncertainlty quantification, control and optimization. However, most of the approaches so far are black boxes and their generalizability, interpretibility, robustness and numerical analysis remain an open challange. Therefore, we invite you to submit your contribution in all aspects of data-driven/scientific/statistical learning to this special issue.

Topics in this call include, but are not limited to: new learning algorithms, parallel computing implementations, numerical analysis, parameterizations and turbulence modeling, reduced order modeling, intrusive and non-intrusive model development, near real time predictions, digital twins, and hybrid frameworks between physics-based and data-driven approaches as well as their implementations to the problems ariasing in canonical or realistic fluid dynamics applications.

Dr. Omer San
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • data mining
  • big data analytics
  • artificial intelligence
  • data-driven modeling
  • physics-based modelling
  • hybrid analytics
  • model order reduction
  • data assimilation
  • flow control and optimization
  • turbulence modeling
  • uncertainty quantification
  • computational learning theory
  • neural networks
  • kernel methods
  • sampling methods
  • exploratory data analysis

Published Papers (2 papers)

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Research

25 pages, 7034 KiB  
Article
An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics
by Suraj Pawar, Shady E. Ahmed, Omer San and Adil Rasheed
Mathematics 2020, 8(4), 570; https://doi.org/10.3390/math8040570 - 11 Apr 2020
Cited by 15 | Viewed by 3341
Abstract
In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize [...] Read more.
In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then present two variants of correction formula based on the assumption that the observed data are a manifestation of all relevant processes. The first method uses a standard least-squares regression with a quadratic approximation and requires solving a rank-deficient linear system, while the second approach employs a recurrent neural network emulator to account for the correction term. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward real-time simulations, where the full process model is not known a priori. Full article
(This article belongs to the Special Issue Machine Learning in Fluid Dynamics: Theory and Applications)
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15 pages, 1456 KiB  
Article
Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network
by Xuping Xie, Guannan Zhang and Clayton G. Webster
Mathematics 2019, 7(8), 757; https://doi.org/10.3390/math7080757 - 19 Aug 2019
Cited by 22 | Viewed by 4008
Abstract
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems [...] Read more.
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches. Full article
(This article belongs to the Special Issue Machine Learning in Fluid Dynamics: Theory and Applications)
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