Information-theoretic formulation of dynamical systems: Causality, modeling, and control

Lozano-Durán, Adrián; Arranz, Gonzalo

doi:10.1103/physrevresearch.4.023195

Cited by 26 publications

(25 citation statements)

References 99 publications

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“…Recently, Lozano-Durán (Lozano-Durán, Bae & Encinar 2020;Lozano-Durán et al 2021) highlighted the importance of causal inference in fluid mechanics and proposed leveraging information-theoretic metrics to explore causality in turbulent flows. Lozano-Durán & Arranz (2022) revisited the definition of information flux and derived a new definition of causality, which is grounded on the conservation of information in the dynamics of a system. The new definition takes into account the intermediate variables, which Schreiber's definition does not.…”

Section: Introductionmentioning

confidence: 99%

Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

et al. 2022

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The interaction between boundary layer turbulence and a porous layer is the cornerstone of interface engineering. In this study, the spatial and spectral-resolved transfer entropy is used to assess the asymmetry of the causal interaction next to the permeable wall. The analysis is based on pore-resolved direct numerical simulation of turbulent channel flow over cylinder arrays. The spatial map of transfer entropy reveals the information flux between the porous medium and arbitrary nearby positions, and paths connecting locations with maximum information transfer are identified. The paths in the ‘top-down’ and ‘bottom-up’ directions, respectively, lean upstream and downstream, demonstrating that the coupling process is directionally dependent. The scale dependence of transfer entropy is inspected with a surrogate data strategy. As wall permeability increases, the active scale range in causal interaction shifts from near-wall vortices to Kelvin–Helmholtz type eddies. In addition, linear stochastic estimation is used to determine the statistical velocity field for a local informative event. In an average sense, the interaction between a convecting sweep or ejection event and the up/down-welling motions at the pore unit is the core mechanism that contributes to the causal coupling. The statistical findings derived from the transfer entropy are then validated using a neural network-based remote sensing model.

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Section: Introductionmentioning

confidence: 99%

Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

et al. 2022

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“…In the case of turbulence research, causality is usually implied from the cross-time correlation between pairs of time signals representing the events of interest. Here, causality is directly inferred using the information-theoretic framework proposed by Lozano-Durán and Arranz [64] (see also Lozano-Durán et al [65]). The approach relies on the quantification of the information flux from the present states of the system to the future states as a proxy for causal inference.…”

Section: Example Analysis: Cause-and-effect Analysis Of Inner-outer F...mentioning

confidence: 99%

“…For the two signals considered, causality from 𝑢 𝑂 (𝑡) to 𝑢 𝐼 (𝑡) (𝑇 𝑂→𝐼 ) is defined as the information flux from the past of 𝑢 𝑂 (𝑡) to the future of 𝑢 𝐼 (𝑡) [64],…”

Section: Example Analysis: Cause-and-effect Analysis Of Inner-outer F...mentioning

confidence: 99%

“…Moreover, the present approach only requires the inner/outer time signals without any further manipulation. The information flux is based on probability distributions and, as such, is invariant under shifting, rescaling and, in general, nonlinear 𝐶 1 -diffeomorphism transformations of the signals [64,67]. Hence, our approach unveils in a simple manner the interactions between inner and outer layer velocity motions while minimizing the number of arbitrary parameters typically used in previous studies such as the type of signal transformation, filter width, reference convection velocity, selection of parameters for the extraction of a universal signal, etc.…”

Section: Example Analysis: Cause-and-effect Analysis Of Inner-outer F...mentioning

confidence: 99%

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A Database for Reduced-Complexity Modeling of Fluid Flows

Towne¹,

Dawson²,

Brès³

et al. 2022

Preprint

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We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all of these aspects of model development for both data-driven and physics-based methods. The database contains time-resolved data for six distinct datasets: a large eddy simulation of a turbulent jet, direct numerical simulations of a zero-pressure-gradient turbulent boundary layer, particle-image-velocimetry measurements for the same boundary layer at several Reynolds numbers, direct numerical simulations of laminar stationary and pitching flat-plate airfoils, particle-image-velocimetry and force measurements of an airfoil encountering a gust, and a large eddy simulation of the separated, turbulent flow over an airfoil. These six cases span several key flow categories: laminar and turbulent, statistically stationary and transient, tonal and broadband spectral content, canonical and application-oriented, wall-bounded and free-shear flow, and simulation and experimental measurements. For each dataset, we describe the flow setup and computational/experimental methods, catalog the data available in the database, and provide examples of how these data can be used for reduced-complexity modeling. All data can be downloaded using a browser interface or Globus. Our vision is that the common testbed provided by this database will aid the fluid mechanics community in clarifying the distinct capabilities of new and existing methods.for reduced-complexity modeling. Finally, in §VIII we conclude the paper with a brief recap of the database and a discussion of our vision for its future applications and extensions. II. Turbulent jet large eddy simulationThe first flow included in the database is a turbulent jet. A jet is a canonical example of a free shear flow, i.e., a flow containing mean velocity gradients but unaffected by walls. Despite the geometrical simplicity of a jet -consisting of a fast inner stream that mixes with a slow outer stream -turbulent jets contain a diverse set of physics. Large-scale coherent structures created by the Kelvin-Helmholtz instability of the annular shear layer, along with their emitted acoustic radiation, have been studied continuously since the 1960s with increasingly sophisticated tools [16,17]. More recently, the important role of other physical mechanisms, including the Orr mechanism [18], streaks generated by the lift-up effect [19,20], and acoustic waves trapped within the core of the jet [21], have been identified and explored. This diverse, coexisting set of physics makes a turbulent jet an excellent testbed for reduced-complexity models. The available dataset contains 10,000 time-resolved snapshots of the jet computed via LES and other quantities derived from these data. A. SetupThis dataset corresponds to an subsonic turbulent jet issued from a contoured convergent-straight nozzle [22]. The jet Mach number is 𝑀 𝑗 = 𝑈 𝑗 /𝑐 𝑗 = 0.9 and the jet is isot...

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“…The fundamental nature of information provides the foundations for the principles of conservation of information and maximum entropy highly regarded within the physics community. Recently, Lozano-Durán and Arranz [9] formulated the problem of control for high-dimensional, chaotic dynamcical systems in information-theoretic terms. They envisioned the tandem sensor-actuator as a device aimed at reducing the unknown information associated with the state of the system to be controlled and formulated the conditions for optimal control.…”

Section: Introductionmentioning

confidence: 99%

Assessment of information-theoretic-based control of turbulent flow separation of an aircraft in stall

Arranz

Lozano-Durán

2022

AIAA SCITECH 2022 Forum

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The problem of control for turbulent flows is investigated within the framework of information theory. The key quantity of interest is the Shannon entropy, which quantifies the amount of information in the states of the turbulent flow. Control theory is then cast in informationtheoretic terms by envisioning the controller as a device aimed at reducing the unknown information associated with the flow state to be controlled. Two cases are considered to assess the effectiveness of the formulation: opposition control in a turbulent channel flow for drag reduction and suppression of the separation bubble in an aircraft in stall using JAXA standard model. In the channel flow, it is found that information-theoretic control enables optimal control for drag reduction consistent with previous results reported in the literatute. In the JAXA standard model, we show that our formulation is able to inform the location of the actuation to suppress the trailing-edge separation bubble.

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Information-theoretic formulation of dynamical systems: Causality, modeling, and control

Cited by 26 publications

References 99 publications

Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

A Database for Reduced-Complexity Modeling of Fluid Flows

Assessment of information-theoretic-based control of turbulent flow separation of an aircraft in stall

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