arXiv subjects

Frédéric Barbaresco

Publications and source records attributed to Frédéric Barbaresco.

18 recordsLinked to original sources

arXiv2026

Geometric Dissipation Structures and the Koszul Form

This paper investigates the canonical Koszul one-form at the interface of Jean Marie Souriau's Lie group thermodynamics and Paulette Libermann's symplectically complete foliations to describe geometric dissipation. On the Poincaré half-plane $\mathbb{H}$ under $SL(2, \mathbb{R})$, the equivariant momentum map level sets form a regular Libermann foliation framing the conservative boundaries. The Koszul-derived dissipative vector field acts strictly transverse to these leaves, driving a metriplectic flow that breaks Noether conservation laws and generates entropy. Quantum wise, we develop Berezin quantization on para-Kähler symmetric spaces, where the Koszul potential acts as a weight determining state density via the Fisher Souriau metric, and formalize Kostant's geometric quantization using the real dual polarizations of a bi-Lagrangian web.

math.DG↗

arXiv2026

A Hamiltonian driven Geometric Construction of Neural Networks via the Lognormal family, Application to Financial Fraud Detection and to Network Security

We presents a method for constructing neural networks intrinsically on statistical manifolds via the lognormal distribution. We demonstrate this approach by formulating a neural network architecture directly on statistical manifold. The construction is driven by the Hamiltonian system that is equivalent to the gradient flow on this manifold. We define the network's input values using the coordinate system of this Hamiltonian dynamics, naturally embedded in the Poincar$\acute{e}$ disk. The core of our contribution lies in the derivation of the network's components from geometric principles: the rotation component of the synaptic weight matrix is determined by the Lie group action of $SU(1,1)$ on the disk, while the activation function emerges from the symplectic structure of the system. We subsequently obtain the complete weight matrix, including its translation vector, and the resulting output values.

cs.LG↗

arXiv2026

A Quantum Spectral Framework for Solving PDEs

Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of dimensionality. Attempts to solve this problem typically rely on either classical sparsity and low-rank decompositions, or neural network surrogate models. On the other hand, Quantum Computing offers a promising alternative, as it allows us to operate in significantly larger spaces while demanding far fewer resources. In this work, we present a quantum subroutine to solve second-order linear PDEs by exploiting the structural properties of the filter in Fourier space using Quantum Block Encoding (QBE) with quantum reversible arithmetic. This approach serves as a specialized alternative to standard quantum matrix inversion, which typically relies solely on Quantum Singular Value Transformation (QSVT) without exploiting the inherent structural properties of the matrix. We validate the proposed methodology against its classical counterpart to prove its correctness. This framework provides a foundation for extending these methods toward quantum group Fourier transforms, wavelet-based analysis, and equivariant quantum neural networks (EQNNs), offering a promising path toward solving broader classes of problems, including nonlinear PDEs.

quant-ph↗

arXiv2025

Optimization of Radar Search Patterns for Multiple Scanning Missions in Localized Clutter

Electronic Phased-Array Radars offer new possibilities for Optimization of Radar Search Pattern by using bi-dimensional beam forming and beam steering, along both elevation and azimuth axes. The minimization of the Time-Budget required for multiple Radar scanning missions in localized clutter, under constraints of range and detection probability, can be approximated as a Set Cover Problem. We present a Set Cover Problem approximation for Time-Budget minimization of the Radar Search Pattern, and solved this optimization problem using Integer Programming methods based on Branch\&Bound and linear relaxation.

math.OC↗

arXiv2025

Hybrid Quantum-Classical Multi-Agent Pathfinding

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-andcut-and-price. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulationsand state-of-the-art MAPF solvers.

cs.AI↗

arXiv2025

Systematic benchmarking of quantum computers: status and recommendations

Architectures for quantum computing can only be scaled up when they are accompanied by suitable benchmarking techniques. The document provides a comprehensive overview of the state and recommendations for systematic benchmarking of quantum computers. Benchmarking is crucial for assessing the performance of quantum computers, including the hardware, software, as well as algorithms and applications. The document highlights key aspects such as component-level, system-level, software-level, HPC-level, and application-level benchmarks. Component-level benchmarks focus on the performance of individual qubits and gates, while system-level benchmarks evaluate the entire quantum processor. Software-level benchmarks consider the compiler's efficiency and error mitigation techniques. HPC-level and cloud benchmarks address integration with classical systems and cloud platforms, respectively. Application-level benchmarks measure performance in real-world use cases. The document also discusses the importance of standardization to ensure reproducibility and comparability of benchmarks, and highlights ongoing efforts in the quantum computing community towards establishing these benchmarks. Recommendations for future steps emphasize the need for developing standardized evaluation routines and integrating benchmarks with broader quantum technology activities.

quant-ph↗

arXiv2024

BACQ -- Application-oriented Benchmarks for Quantum Computing

With the support of the national program on measurements, standards, and evaluation of quantum technologies MetriQs-France, a part of the French national quantum strategy, the BACQ project is dedicated to application-oriented benchmarks for quantum computing. The consortium gathering THALES, EVIDEN, an Atos business, CEA, CNRS, TERATEC, and LNE aims at establishing performance evaluation criteria of reference, meaningful for industry users.

quant-ph↗

arXiv2024

Optimal matching between curves in a manifold

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the ''shape space''. We introduce a simple algorithm allowing to compute geodesics of the quotient shape space using a canonical decomposition of a path in the associated principal bundle. We consider the particular case of elastic metrics and show simulations for open curves in the plane, the hyperbolic plane and the sphere.

math.DG↗

arXiv2023

Tracking mulitple targets with multiple radars using Distributed Auctions

Coordination of radars can be performed in various ways. To be more resilient radar networks can be coordinated in a decentralized way. In this paper, we introduce a highly resilient algorithm for radar coordination based on decentralized and collaborative bundle auctions. We first formalize our problem as a constrained optimization problem and apply a market-based algorithm to provide an approximate solution. Our approach allows to track simultaneously multiple targets, and to use up to two radars tracking the same target to improve accuracy. We show that our approach performs sensibly as well as a centralized approach relying on a MIP solver, and depending on the situations, may outperform it or be outperformed.

cs.AI↗

arXiv2022

Collaborative Multi-Radars Tracking by Distributed Auctions

In this paper, we present an algorithm which lies in the domain of task allocation for a set of static autonomous radars with rotating antennas. It allows a set of radars to allocate in a fully decentralized way a set of active tracking tasks according to their location, considering that a target can be tracked by several radars, in order to improve accuracy with which the target is tracked. The allocation algorithm proceeds through a collaborative and fully decentralized auction protocol, using a collaborative auction protocol (Consensus Based Bundle Auction algorithm). Our algorithm is based on a double use of our allocation protocol among the radars. The latter begin by allocating targets, then launch a second round of allocation if theyhave resources left, in order to improve accuracy on targets already tracked. Our algorithm is also able to adapt to dynamism, i.e. to take into account the fact that the targets are moving and that the radar(s) most suitable for Tracking them changes as the mission progresses. To do this, the algorithm is restarted on a regular basis, to ensure that a bid made by a radar can decrease when the target moves away from it. Since our algorithm is based on collaborative auctions, it does not plan the following rounds, assuming that the targets are not predictable enough for this. Our algorithm is however based on radars capable of anticipating the positions of short-term targets, thanks to a Kalman filter. The algorithm will be illustrated based on a multi-radar tracking scenario where the radars, autonomous, must follow a set of targets in order to reduce the position uncertainty of the targets. Standby aspects will not be considered in this scenario. It is assumed that the radars can pick up targets in active pursuit, with an area ofuncertainty corresponding to their distance.

cs.MA↗

arXiv2020

Multi-Radar Tracking Optimization for Collaborative Combat

Smart Grids of collaborative netted radars accelerate kill chains through more efficient cross-cueing over centralized command and control. In this paper, we propose two novel reward-based learning approaches to decentralized netted radar coordination based on black-box optimization and Reinforcement Learning (RL). To make the RL approach tractable, we use a simplification of the problem that we proved to be equivalent to the initial formulation. We apply these techniques on a simulation where radars can follow multiple targets at the same time and show they can learn implicit cooperation by comparing them to a greedy baseline.

cs.AI↗

arXiv2020

The Basic Geometric Structures of Electromagnetic Digital Information: Statistical characterization of the digital measurement of spatio-Doppler and polarimetric fluctuations of the radar electromagnetic wave

The aim is to describe new geometric approaches to define the statistics of spatio-temporal and polarimetric measurements of the states of an electromagnetic wave, using the works of Maurice Fr{é}chet, Jean-Louis Koszul and Jean-Marie Souriau, with in particular the notion of 'average' state of this digital measurement as a Fr{é}chet barycentre in a metric space and a model derived from statistical mechanics to define and calculate a maximum density of entropy (extension of the notion of Gaussian) to describe the fluctuations of the electromagnetic wave. The article will illustrate these new tools with examples of radar application for Doppler, spatio-temporal and polarimetric measurement of the electromagnetic wave by introducing a distance on the covariance matrices of the electromagnetic digital signal, based on Fisher's metric from Information Geometry.

eess.SP↗

arXiv2020

AI-Augmented Multi Function Radar Engineering with Digital Twin: Towards Proactivity

Thales new generation digital multi-missions radars, fully-digital and software-defined, like the Sea Fire and Ground Fire radars, benefit from a considerable increase of accessible degrees of freedoms to optimally design their operational modes. To effectively leverage these design choices and turn them into operational capabilities, it is necessary to develop new engineering tools, using artificial intelligence. Innovative optimization algorithms in the discrete and continuous domains, coupled with a radar Digital Twins, allowed construction of a generic tool for "search" mode design (beam synthesis, waveform and volume grid) compliant with the available radar time budget. The high computation speeds of these algorithms suggest tool application in a "Proactive Radar" configuration, which would dynamically propose to the operator, operational modes better adapted to environment, threats and the equipment failure conditions.

eess.SP↗

arXiv2020

Multi-criteria Analysis for Evaluation of Adaptive Radar Resource Management algorithms on a Naval setting with and without clutter

Multifunction radars (MFR) are met with complex capability requirements, involving various kinds of targets and saturating scenarios. In order to achieve these goals, radar systems use Active Electronically Scanned Array (AESA) to switch between their functions. This complexity makes it difficult to assess their performance both taking into account their functional requirements and the induces cost. In this paper, we first introduce Figures of Merit for phased array radar operation and performance. We compute these metrics on a set of test scenarios of varying complexity, involving different kinds of targets, and we aggregate them into a global notation of MFR radar performances. To achieve our purpose, we rely on the domain of Multi Criteria Decision Analysis (MCDA), and more precisely 2-additive Choquet integral.

eess.SP↗

arXiv2020

Branch-and-Bound Method for Just-in-Time Optimization of Radar Search Patterns

Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved using integer programming, while accounting for localized clutter and terrain masks in detection constraints. We present a set cover problem approximation for time-budget minimization of radar search patterns, under constraints of range, detection probability and direction-specific scan update rates. Branch\&Bound is a classical optimization procedure for solving combinatorial problems. It is known mainly as an exact algorithm, but features interesting characteristics, making it particularly fit for solving optimization problems in real-time applications and producing just-in-time solutions.

math.OC↗

arXiv2016

Robust Burg Estimation of Radar Scatter Matrix for Autoregressive structured SIRV based on Fréchet medians

We address the estimation of the scatter matrix of a scale mixture of Gaussian stationary autoregressive vectors. This is equivalent to consider the estimation of a structured scatter matrix of a Spherically Invariant Random Vector (SIRV) whose structure comes from an autoregressive modelization. The Toeplitz structure representative of stationary models is a particular case for the class of structures we consider. For Gaussian autoregressive processes, Burg method is often used in case of stationarity for its efficiency when few samples are available. Unfortunately, if we directly apply these methods to estimate the common scatter matrix of N vectors coming from a non-Gaussian distribution, their efficiency will strongly decrease. We propose then to adapt these methods to scale mixtures of autoregressive vectors by changing the energy functional minimized in the Burg algorithm. Moreover, we study several approaches of robust modification of the introduced Burg algorithms, based on Fréchet medians defined for the Euclidean or the Poincaré metric, in presence of outliers or contaminating distributions. The considered structured modelization is motivated by radar applications, the performances of our methods will then be compared to the very popular Fixed Point estimator and OS-CFAR detector through radar simulated scenarios.

math.ST↗

arXiv2015

Reparameterization invariant metric on the space of curves

This paper focuses on the study of open curves in a manifold M, and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [11] to define a reparameterization invariant metric on the space of immersions M' = Imm([0,1], M) by pullback of a metric on the tangent bundle TM' derived from the Sasaki metric. We observe that such a natural choice of Riemannian metric on TM' induces a first-order Sobolev metric on M' with an extra term involving the origins, and leads to a distance which takes into account the distance between the origins and the distance between the SRV representations of the curves. The geodesic equations for this metric are given, as well as an idea of how to compute the exponential map for observed trajectories in applications. This provides a generalized theoretical SRV framework for curves lying in a general manifold M .

math.DG↗

arXiv2011

Medians and means in Riemannian geometry: existence, uniqueness and computation

This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, Fréchet medians are considered. We prove their statistical consistency and give some quantitative estimations of their robustness with the aid of upper curvature bounds. We also show that, in compact Riemannian manifolds, the Fréchet medians of generic data points are always unique. Stochastic and deterministic algorithms are proposed for computing Riemannian p-means. The rate of convergence and error estimates of these algorithms are also obtained. Finally, we apply the medians and the Riemannian geometry of Toeplitz covariance matrices to radar target detection.

math.DG↗