Journal ArticleDOI
Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertainty
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TLDR
In this paper, the evolution of the dominant dimensionality of dynamical systems with uncertainty governed by stochastic partial differential equations, within the context of dynamically orthogonal (DO) field equations, is studied.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2012-01-01. It has received 97 citations till now. The article focuses on the topics: Stochastic partial differential equation & Dynamical systems theory.read more
Citations
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Journal ArticleDOI
Closed-Loop Turbulence Control: Progress and Challenges
Steven L. Brunton,Bernd R. Noack +1 more
Journal ArticleDOI
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
TL;DR: Two new Physics-Informed Neural Networks (PINNs) are proposed for solving time-dependent SPDEs, namely the NN-DO/BO methods, which incorporate the DO/BO constraints into the loss function with an implicit form instead of generating explicit expressions for the temporal derivatives of the Do/BO modes.
Journal ArticleDOI
Energy-optimal path planning by stochastic dynamically orthogonal level-set optimization
TL;DR: In this article, a stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimally paths of autonomous vehicles navigating in a dynamic flow field.
Journal ArticleDOI
Lessons in uncertainty quantification for turbulent dynamical systems
Andrew J. Majda,Michal Branicki +1 more
TL;DR: A large number of new theoretical and computational phenomena which arise in the emerging statistical-stochastic framework for quantifying and mitigating model error in imperfect predictions, such as the existence of information barriers to model improvement, are developed and reviewed here with the intention to introduce mathematician, applied mathematicians, and scientists to these remarkable emerging topics with increasing practical importance.
Journal ArticleDOI
Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme
TL;DR: In this article, the stochastic Dynamically Orthogonal (DO) field equations and their adaptive subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker-Planck equation.
References
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Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Book
Computational methods for fluid dynamics
Joel H. Ferziger,Milovan Perić +1 more
TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.
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What is dynamic programming
TL;DR: Sequence alignment methods often use something called a 'dynamic programming' algorithm, which can be a good idea or a bad idea, depending on the method used.
Journal ArticleDOI
Measuring the Strangeness of Strange Attractors
TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.
Book
Data Assimilation: The Ensemble Kalman Filter
TL;DR: In this paper, the authors define a statistical analysis scheme for estimating an oil reservoir simulator and an ocean prediction system based on the En-KF model, and propose a sampling strategy for the EnKF and square root analysis schemes.