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Optimal Controller and Actuator Design for Nonlinear Parabolic Systems
[article]
2019
arXiv
pre-print
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The results are shown to apply to optimal controller/actuator design for the Kuramoto-Sivashinsky equation and also nonlinear diffusion. ...
In this paper, the existence of a concurrent optimal controller and actuator design is established for semilinear parabolic systems. Optimality equations are provided. ...
Optimal control of KS equation using maximum principle was studied in [47] . Optimal control of KS equation with pointwise state and mixed control-state constraints was studied in [48] . ...
arXiv:1910.03124v1
fatcat:bnznwgazfbdcpkfjsqmy742uyi
A computational framework for the regularization of adjoint analysis in multiscale PDE systems
2004
Journal of Computational Physics
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Regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis. ...
The regularization strategies proposed are exemplified using a 1D Kuramoto-Sivashinsky forecasting problem, and computational examples are provided which exhibit their utility. ...
Acknowledgments The authors thank Prof. Scott Collis for his inspiring and thoughtful feedback, and gratefully acknowledge the generous funding of the AFOSR programs directed by Dr. ...
doi:10.1016/j.jcp.2003.08.031
fatcat:mthk2c5zwbggvhru4qhhreie2u
Weak SINDy For Partial Differential Equations
[article]
2020
arXiv
pre-print
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The elimination of pointwise derivative approximations via the weak form enables effective machine-precision recovery of model coefficients from noise-free data (i.e. below the tolerance of the simulation ...
Here we extend our Weak SINDy (WSINDy) framework introduced in (arXiv:2005.04339) to the setting of partial differential equations (PDEs). ...
Figure 5 . 5 Plots of the average loss function L(λ) and resulting optimal threshold λ for the Kuramoto Sivashinsky, Sine-Gordon, Reaction diffusion and Navier-Stokes equations. ...
arXiv:2007.02848v3
fatcat:x6h4lnl2ivb3dojh6zarilu2kq
author index 10 volumes
2005
Journal of Computational and Applied Mathematics
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Tran, Reducedorder-based feedback control of the Kuramoto-Sivashinsky equation 173 (2004) 1-19 Leopold, E., see Gilewicz, J. 178 (2005) 235-245 Li, W., Comparison results for solving preconditioned linear ...
quadratic optimal control problems 173 (2004) 169-198 Helal, M.M. and M.B. ...
doi:10.1016/s0377-0427(05)00273-6
fatcat:4hnauo7pn5b2hksb3pel3ew244
Application of Continuous Data Assimilation in High-Resolution Ocean Modeling
[article]
2024
arXiv
pre-print
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We demonstrate a formulation of the Azouani-Olson-Titi (AOT) algorithm in the MPAS-Ocean implementation of the primitive equations of the ocean, presenting global ocean simulations with realistic coastlines ...
We observe an exponentially fast decay in the error before reaching a certain error level, which depends on the terms involved and whether the AOT feedback control term was handled implicitly or explicitly ...
Acknowledgments This material is based upon work supported by the U.S. Department ...
arXiv:2308.02705v2
fatcat:xyzbm3mjojg6bbmwl66qejmmuy
Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data
[article]
2023
arXiv
pre-print
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We demonstrate the utility of NIF for parametric surrogate modeling, enabling the interpretable representation and compression of complex spatio-temporal dynamics, efficient many-spatial-query tasks, and ...
Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to make solutions computationally tractable in real-time. ...
Acknowledgments and Disclosure of Funding The authors thank Kevin Carlberg, Karthik Duraisamy, Zongyi Li, and Lu Lu for valuable discussions. ...
arXiv:2204.03216v5
fatcat:5527flnnsjcohoexrk4b37dhim
Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds
[article]
2024
arXiv
pre-print
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probability distributions, of the chaotic attractor. ...
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). ...
Kuramoto-Sivashinsky equation To test SSM-based model reduction in higher-dimensional chaotic systems, we consider the Kuramoto-Sivashinsky (KS) equation 68, 69 . ...
arXiv:2310.06067v2
fatcat:odgj2tjmhvdrnj6xp4ketzczhu
Page 2692 of Mathematical Reviews Vol. , Issue Subject Index
[page]
Mathematical Reviews
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(with Armaou, Antonios) Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control. ...
(English summary) 2002c:93011
Arada, Nadir (with Raymond, Jean-Pierre) Optimal control problems with mixed control- state constraints. ...
Page 552 of Mathematical Reviews Vol. 25, Issue Index
[page]
Mathematical Reviews
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elliptic equations with pointwise constraints on the gradient of the state. ...
(English summary) (see 93h:49003)
Casas Renteria, Eduardo Optimal control in coefficients of elliptic equations with state constraints. 93b:49004
— (with Fernandez, Luis Alberto) Optimal control of semilinear ...
Asymptotic consistency of the WSINDy algorithm in the limit of continuum data
[article]
2022
arXiv
pre-print
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We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models which includes the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. ...
We demonstrate our results numerically using the Lorenz system, the cubic oscillator, a viscous Burgers growth model, and a Kuramoto-Sivashinsky-type higher-order PDE. ...
We now test the theoretical results in the previous sections using four example problems: (1) the Lorenz system, (2) a hyper-diffusive Kuramoto-Sivashinsky (KS)-type equation, (3) a cubic oscillator, and ...
arXiv:2211.16000v1
fatcat:tkk4f2fm2nbvra4dzjmgyefwoe
Modern Koopman Theory for Dynamical Systems
[article]
2021
arXiv
pre-print
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This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems ...
In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. ...
We also thank Shervin Bagheri, Bing Brunton, Bethany Lusch, Ryan Mohr, Frank Noe, Josh Proctor, Clancy Rowley, and Peter Schmid for many fruitful discussions on DMD, Koopman theory, and control. ...
arXiv:2102.12086v2
fatcat:2oylyx25dbctvkjfnirfcgjuqu
User guide on Hopf bifurcation and time periodic orbits with pde2path
[article]
2020
arXiv
pre-print
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Additionally we explain the treatment of Hopf bifurcations in systems with continuous symmetries, including the continuation of traveling waves and rotating waves in O(2) equivariant systems as relative ...
We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. ...
Also for n H > 0, the computation of Floquet multipliers is based on (A.13), i.e., ignores the Hopf-constraints Q H . ...
arXiv:1908.00905v2
fatcat:r2hpmlz5gzgwrjuvx4qosadnbq
Wavelet Methods in Computational Fluid Dynamics
2010
Annual Review of Fluid Mechanics
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This article reviews state-of-the-art adaptive, multiresolution wavelet methodologies for modeling and simulation of turbulent flows with various examples. ...
The most intriguing part of WDNS is its ability to take advantage of spatial and temporal intermittency and perform simulations of high-Reynolds number flows with computational complexity lower than commonly ...
& Schneider 1994 , Stokes' equation (e.g., Dahmen et al. 1996 Dahmen et al. , 2002 , poro-viscoelastic and viscoelastic equations (e.g., Vasilyev et al. 1998 Vasilyev et al. , 2001 , the Kuramoto-Sivashinsky ...
doi:10.1146/annurev-fluid-121108-145637
fatcat:cqqlm55ggjgitdtnvabehxtwye
Control theory for infinite dimensional dynamical systems and applications to falling liquid film flows
2016
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We find that using point actuated controls it is possible to stabilise the full range of solutions to the generalised Kuramoto-Sivashinsky equation, and that distributed controls have a similar effect ...
We first derive the controls for weakly nonlinear models such as the Kuramoto-Sivashinsky equation and some of its generalisations, and then use the insight that the analytical results obtained there provide ...
equation, where both the solution and the (distributed) control have pointwise constraints, while Sun [200] investigates the problem for optimal boundary control, presenting first order necessary conditions ...
doi:10.25560/39041
fatcat:5i4rmpoudfdfbkmu4a4f5s6q6i
Stochastic PDEs and Lack of Regularity
2015
Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner)
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Results in this direction are known already for the 3D-Navier Stokes by Li and Sinai, treating complex valued solutions, and more recently by Tao by constructing an equation of Navier-Stokes type with ...
In the physically relevant dimension d = 2 and with the physically relevant space-time white noise driving the equation, the direct fixed-point argument for mild solutions fails, as there is not sufficient ...
We also like to thank Franco Flandoli for joint work on the inviscid surface growth, Martin Hairer for many interesting discussions, and Michael Winkler for discussions on possible blow up. ...
doi:10.1365/s13291-015-0123-0
fatcat:du343hynxfabzkeful7sorhypm
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