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Enhanced generative model evaluation with Clipped Density and Coverage
No full textAlthough generative models have made remarkable progress in recent years, their use in critical applications has been hindered by their incapacity to reliably evaluate sample quality. Quality refers to at least two complementary concepts: fidelity and coverage. Current quality metrics often lack reliable, interpretable values due to an absence of calibration or insufficient robustness to outliers. To address these shortcomings, we introduce two novel metrics, Clipped Density and Clipped Coverage. By clipping individual sample contributions and, for fidelity, the radii of nearest neighbor balls, our metrics prevent out-of-distribution samples from biasing the aggregated values. Through analytical and empirical calibration, these metrics exhibit linear score degradation as the proportion of poor samples increases. Thus, they can be straightforwardly interpreted as equivalent proportions of good samples. Extensive experiments on synthetic and real-world datasets demonstrate that Clipped Density and Clipped Coverage outperform existing methods in terms of robustness, sensitivity, and interpretability for evaluating generative models
A Hybrid Modelling Approach for Hierarchical Control of Structured CPSs
No full textInternational audienceCyber-physical systems (CPSs) include engineered interacting networks of physical and computational components. As they are widely used in many application domains, guaranteeing their correct and proper behaviour is an essential and a challenging issue. This paper aims to contribute to a flexible design and development of structured CPSs, composed of similar elements, and capable of (self-)adaptation to satisfy evolving internal and external constraints, e.g. using control theory. To this end, we make use of their structure and of their behavioural characteristics for modelling by hierarchical motifs both systems' elements and controllers. The motivations and contributions are illustrated on a smart building example
Improving Urban Cycling Safety and Comfort through Optimized Infrastructure Upgrades
No full textInternational audienceThis paper proposes a bi-level optimization framework to improve urban cycling infrastructure by upgrading bike lanes' degree of separation (DoS) from motorized traffic. The six-level DoS classification reflects increasing safety and comfort as cyclists' exposure to annual average daily traffic decreases. The lower level estimates cyclist flows using an all-or-nothing assignment method that accounts for factors like slope, angular changes, and traffic, ensuring realistic flow distribution. The upper level minimizes traffic exposure by upgrading segments to higher DoS levels within a fixed budget. A case study on Grenoble's cycling network applies this framework using a modified genetic algorithm to optimize safety, comfort, and budget efficiency. Results are compared to a specialized algorithm designed to improve overall perceived safety and comfort. Findings highlight that targeted infrastructure upgrades enhance both local and network-wide safety, better balancing cyclist flows. This framework provides urban planners with a data-driven tool for prioritizing cycling infrastructure investments
Efficient treatment of the model error in the calibration of computer codes: the Complete Maximum a Posteriori method
No full textInternational audienceComputer models are widely used for the prediction of complex physical phenomena. Based on observations of these physical phenomena, it is possible to calibrate the model parameters. In most cases, such computer models are mis-specified, and the calibration process must be improved by including a model error term. The model error hyperparameters are, however, rarely learned jointly with the model parameters to reduce the dimensionality of the problem. Sequential and non-sequential approaches have been introduced to estimate the hyperparameters. The former, such as the Kennedy and O'Hagan (KOH) framework, estimates the model error hyperparameters before calibrating the model parameters. The latter, such as the Full Maximum a Posteriori (FMP), introduces a functional dependence between the model parameters and the model error hyperparameters. Despite being more reliable in some cases (bimodality e.g.), the FMP method still fails to estimate correctly the posterior distribution shape. This work proposes a new methodology for treating the model error term in computer code calibration. It builds upon the KOH and FMP framework. Called the Complete Maximum a Posteriori (CMP) method, it provides a closed-form expression for the marginalization integral over the model error hyperparameters, significantly reducing the dimensionality of the calibration problem. Such expression re-lies on a set of assumptions that are more general and less stringent than the ones usually employed. The CMP method is applied to four examples of increasing complexity, from elementary to real fluid dynamics problems, including or not bimodality. Compared to the true reference solution and unlike the KOH and FMP, the CMP method correctly captures the shape of the posterior distribution, including all modes and their weights. Moreover, it provides an accurate estimate of the distribution tails</div
Good Lie Brackets for classical and quantum harmonic oscillators
No full textInternational audienceWe study the small-time controllability problem on the Lie groups and with Lie bracket methods (here denotes the -dimensional real Heisenberg group). Then, using unitary representations of on and , we recover small-time approximate reachability properties of the Schrödinger PDE for the quantum harmonic oscillator, and find new small-time approximate reachability properties of the Liouville PDE for the classical harmonic oscillator
Riemannian L-systems: Modeling growing forms in curved spaces
No full textSoftware availability: The L-Py software is freely available through the conda environment at: https://anaconda.org/fredboudon/openalea.lpy. The L-Py Riemannian L-system software plugin and the notebooks describing the examples displayed in this paper are freely available at: https://github.com/fredboudon/RiemannianLsystems.International audienceIn the past 50 years, the formalism of L-systems has been successfully used and developed to model the growth of filamentous and branching biological forms. These simulations take place in classical 2-D or 3-D Euclidean spaces. However, various biological forms actually grow in curved, non-Euclidean, spaces. This is for example the case of vein networks growing within curved leaf blades, of unicellular filaments, such as pollen tubes, growing on curved surfaces to fertilize distant ovules, of teeth patterns growing on folded epithelia of animals, of diffusion of chemical or mechanical signals at the surface of plant or animal tissues, etc. To model these forms growing in curved spaces, we thus extended the formalism of L-systems to non-Euclidean spaces. In a first step we show that this extension can be carried out by integrating concepts of differential geometry in the notion of turtle geometry. We then illustrate how this extension can be applied to model and program the development of both mathematical and biological forms on curved surfaces embedded in our Euclidean space. We provide various examples applied to plant development. We finally show that this approach can be extended to more abstract spaces, called abstract Riemannian spaces, that are not embedded into any higher dimensional space, while being intrinsically curved. We suggest that this abstract extension can be used to provide a new approach for effective modeling of tropism phenomena and illustrate this idea on a few conceptual examples
Third-order sectorially A-stable alternating implicit Runge-Kutta schemes
No full textInternational audienceWe design pairs of six-stage, third-order, alternating implicit Runge--Kutta (RK) schemes that can be used to integrate in time two stiff operators by an operator-splitting technique. We also design for each pair a companion explicit RK scheme to be used for a third, nonstiff operator in an implicit-explicit (IMEX) fashion. The main application we have in mind is (non)linear parabolic problems, where the two stiff operators represent diffusion processes (for instance, in two spatial directions) and the nonstiff operator represents (non)linear transport. We identify necessary conditions for linear sectorial A(\alpha)-stability by considering a scalar ODE with two (complex) eigenvalues lying in some fixed cone of the half-complex plane with nonpositive real part. We show numerically that it is possible to achieve A(0)-stability when combining two operators with negative eigenvalues, irrespective of their relative magnitude. Finally, we show by numerical examples including two-dimensional nonlinear transport problems discretized in space using finite elements that the proposed schemes behave well
From fault likelihood to fault networks: stochastic seismic interpretation through a marked point process with interactions
No full textInternational audienceFaults are crucial subsurface features that significantly influence the mechanical behavior and hydraulic properties of rock masses. Interpreting them from seismic data may lead to various scenarios due to uncertainties arising from limited seismic bandwidth and possible imaging errors. Although methods addressing fault uncertainty exist, only a few of them can produce curved and sub-seismic faults at once while quantitatively honoring seismic images and avoiding anchoring in a reference interpretation. In this work, we use a mathematical framework of marked point processes to approximate fault networks in two dimensions with a set of line segments. The proposed stochastic model, namely Candy Model, incorporates simple pairwise and nearby connections to capture the interactions between fault segments. The novelty of this approach lies in conditioning the stochastic model using input image of fault probabilities generated by a Convolutional Neural Network (CNN). The Metropolis-Hastings algorithm is used to generate various scenarios of fault network configurations, thereby exploring the model space associated with the Candy Model and reflecting the uncertainty. Probability level sets constructed from these fault segment configurations provide insights on the obtained realizations and on the model parameters. The empty space function produces a ranking of the generated fault networks against an existing interpretation by testing and quantifying their spatial variability. The approach is applied on two-dimensional sections of seismic data, acquired in the Central North Sea
Models and algorithms for configuring and testing prototype cars
No full textInternational audienceIn this paper, we consider a new scheduling problem, which occurs in the context of the automobile industry. Given a set of machines, and a set of jobs, we seek a fixed configuration for each machine (i.e. a set of values for different parameters), and an assignment of jobs to machines along the time horizon that respects compatibility constraints between jobs and machine configurations. Two objectives are optimized lexicographically: the number of late jobs, and the number of machines used. First we prove that even finding a feasible solution for the problem is NP-hard, and characterize the cases where compatibility constraints amount to ensuring that only pairwise compatible jobs are assigned to each machine. Then we propose a mathematical model for this problem, and a reformulation into a path-flow formulation. We use a refined labelling algorithm embedded in a column-and-row generation algorithm to produce primal and dual bounds from this formulation. We conducted computational experiments with industrial data from Renault, and compared our results with those obtained by solving a constraint programming model provided by the company. Our approach finds better solutions than those obtained by the company, and proves the optimality for all instances of our benchmark for the first objective function. We also obtain small optimality gaps for the second objective function
Asymptotically constant-free and polynomial-degree-robust a posteriori error estimates for time-harmonic Maxwell's equations
No full textInternational audienceWe propose a novel a posteriori error estimator for the Nédélec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to reconstruct approximations to the electric displacement and the magnetic field, with such approximations respectively fulfilling suitable divergence and curl constraints. These reconstructed fields are in turn used to construct an a posteriori error estimator which is shown to be reliable and efficient. Specifically, the estimator controls the error from above up to a constant that tends to one as the mesh is refined and/or the polynomial degree is increased, and from below up to constant independent of p. Both bounds are also fully-robust in the low-frequency regime. The properties of the proposed estimator are illustrated on a set of numerical examples