Softwares
This page lists all of the softwares used or developped during the project. A particular emphasis is given to free and open-source softwares following the FAIR principles: Free, Accessible, Inclusive and Reproducible. To foster scientific collaborations, all codes are developped in dedicated public GitHub repositories. For long-term preservation, every major release is also hosted on Zenodo and recherche.data.gouv.fr with a citable DOI for proper referencing.
nekStab
nekStab is an open-source library written in F77/F90 aiming at extending the capabilities of Nek5000, a well established spectral element solver in the academic hydrodynamic and aerodynamic community. Leveraging Krylov-based techniques and Nek5000’s high-performance time-stepping capabilities, nekStab provides a set of algorithms to compute stable and unstable fixed points or periodic orbits of the Navier-Stokes equations as well as quantifying their stability properties through eigenvalue or singular value analysis of the linearized Navier-Stokes operator. nekStab has initially been developped by J.-Ch. Loiseau and R. S. Frantz.
Over the duration of the current project, the capabilities of nekStab will be extended to include : batch and streaming algorithms for Proper Orthogonal Decomposition and Dynamic Mode Decomposition of high-dimensional velocity fields, Balanced Proper Orthogonal Decomposition and Optimal Time Depedent modes for projection-based reduced-order modeling of the linearized Navier-Stokes equations, as well as gradient-based algorithms for \(H_2\) optimal sensors and actuators placement.
Related publications
- R. S. Frantz, J.-Ch. Loiseau, and J.-Ch. Robinet. Krylov methods for large-scale dynamical systems: applications in fluid dynamics. Applied Mechanics Review, vol. 75 (3), May 2023. [AMR] [arXiv]
| repository | nekstab.github.io |
| License | BSD |
| Programming Language | Fortran 77 / Fortran 90 |
| Core developpers | J.-Ch. Loiseau and R. S. Frantz |
SubmodularOpt.jl
Following a D-optimal design strategy, sensors and/or actuators placement for linear dynamical systems can be formulated as a determinant maximization problem of a suitably defined Fisher information matrix
\[ \mathbf{F} = \mathbf{C}^T \mathbf{S}^T \mathbf{Q}^{-1} \mathbf{S} \mathbf{C} + \boldsymbol{\Sigma}^{-1} \]
where \(\mathbf{C}\) describes for instance all of the sensors available, \(\mathbf{S}\) is a selection operator to be optimized, \(\mathbf{Q}\) is the sensor noise covariance matrix, and \(\boldsymbol{\Sigma}\) the state covariance matrix. Given \(m\) possible sensor locations and a budget for only \(p\) sensors, there are
\[ \binom{m}{p} = \dfrac{m!}{\left(m - p\right)! \times p!} \]
possible combinations, making it an intractable combinatorial problem even for a moderately large search space. Yet, under certains conditions, this objective function is a submodular monotone function whose greedy maximization benefits from a \(1 - \frac{1}{e}\) approximation guarantee.
SubmodularOpt.jl is a Julia package currently under active development by members of the CONMAN project. It provides efficient implementations of standard submodular function maximization algorithms, including the Lazy Greedy (Minoux, 1978) or the Lazier than Lazy Greedy (Mirzasoleiman et al., 2015) algorithms for maximizing a monotone submodular set function with cardinality constraint. Inspired from the concave-convex procedure for minimizing a difference of convex functions, SubmodularOpt.jl also provides an implementation of the SubSup procedure (Iyer & Bilmes, 2013) for the minimization/maximization of the difference of two submodular functions.
Related Publications
- TBA
| repository | SubmodularOpt.jl |
| License | MIT |
| Programming Language | Julia |
| Core developpers | J.-Ch. Loiseau |