arXiv subjects

Maxime Gariel

Publications and source records attributed to Maxime Gariel.

8 recordsLinked to original sources

arXiv2026

Lipschitz Optimization for Formal Verification of Homographies

The adoption of vision neural networks in regulated industries requires formal robustness guarantees, especially in safety-critical domains such as healthcare, autonomous vehicles, and aerospace. However, current approaches are confined to incomplete statistical verification or robustness to $\ell_p$-norm and affine transforms, which cover only a narrow subset of perturbations to the image formation process. In particular, robustness to camera motion remains an open problem despite being key to deploy many vision applications. We present a formal verification approach that targets robustness against 3D motion perturbations of the capturing camera. We first establish a closed-form mapping from camera pose to pixel values. By analyzing the continuity properties of the resulting homographies, we show that recent work on Lipschitz optimization and piecewise continuity can be extended to derive tight linear bounds on perturbed pixel values. Our approach applies to scenes with predominantly planar structure, such as ground planes in augmented reality, road markings and traffic signs in autonomous driving, or planar workspaces in robotic manipulation. This enables the first formal verification of projective geometry transforms, without complex simulation, surrogate networks, or explicit image-formation models. We validate our implementation and show up to 89% speedup and 7% tighter bounds over prior work. We then evaluate our method on the VNN-COMP benchmark and reveal systematic weaknesses to projective perturbations. Finally, we demonstrate a real-world case study on a safety-critical runway classifier, highlighting practical vulnerabilities to camera motion, and addressing a key challenge in the certification of learned models. Data and code are publicly available at https://github.com/jeangud/homography-verification .

cs.CV↗

arXiv2023

Bayesian Safety Validation for Failure Probability Estimation of Black-Box Systems

Estimating the probability of failure is an important step in the certification of safety-critical systems. Efficient estimation methods are often needed due to the challenges posed by high-dimensional input spaces, risky test scenarios, and computationally expensive simulators. This work frames the problem of black-box safety validation as a Bayesian optimization problem and introduces a method that iteratively fits a probabilistic surrogate model to efficiently predict failures. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain using importance sampling. We introduce three acquisition functions that aim to reduce uncertainty by covering the design space, optimize the analytically derived failure boundaries, and sample the predicted failure regions. Results show this Bayesian safety validation approach provides a more accurate estimate of failure probability with orders of magnitude fewer samples and performs well across various safety validation metrics. We demonstrate this approach on three test problems, a stochastic decision making system, and a neural network-based runway detection system. This work is open sourced (https://github.com/sisl/BayesianSafetyValidation.jl) and currently being used to supplement the FAA certification process of the machine learning components for an autonomous cargo aircraft.

cs.LG↗

arXiv2023

Framework for Certification of AI-Based Systems

The current certification process for aerospace software is not adapted to "AI-based" algorithms such as deep neural networks. Unlike traditional aerospace software, the precise parameters optimized during neural network training are as important as (or more than) the code processing the network and they are not directly mathematically understandable. Despite their lack of explainability such algorithms are appealing because for some applications they can exhibit high performance unattainable with any traditional explicit line-by-line software methods. This paper proposes a framework and principles that could be used to establish certification methods for neural network models for which the current certification processes such as DO-178 cannot be applied. While it is not a magic recipe, it is a set of common sense steps that will allow the applicant and the regulator increase their confidence in the developed software, by demonstrating the capabilities to bring together, trace, and track the requirements, data, software, training process, and test results.

cs.LG↗

arXiv2011

On the Statistics and Predictability of Go-Arounds

This paper takes an empirical approach to identify operational factors at busy airports that may predate go-around maneuvers. Using four years of data from San Francisco International Airport, we begin our investigation with a statistical approach to investigate which features of airborne, ground operations (e.g., number of inbound aircraft, number of aircraft taxiing from gate, etc.) or weather are most likely to fluctuate, relative to nominal operations, in the minutes immediately preceding a missed approach. We analyze these findings both in terms of their implication on current airport operations and discuss how the antecedent factors may affect NextGen. Finally, as a means to assist air traffic controllers, we draw upon techniques from the machine learning community to develop a preliminary alert system for go-around prediction.

eess.SY↗

arXiv2011

Aircraft Proximity Maps Based on Data-Driven Flow Modeling

With the forecast increase in air traffic demand over the next decades, it is imperative to develop tools to provide traffic flow managers with the information required to support decision making. In particular, decision-support tools for traffic flow management should aid in limiting controller workload and complexity, while supporting increases in air traffic throughput. While many decision-support tools exist for short-term traffic planning, few have addressed the strategic needs for medium- and long-term planning for time horizons greater than 30 minutes. This paper seeks to address this gap through the introduction of 3D aircraft proximity maps that evaluate the future probability of presence of at least one or two aircraft at any given point of the airspace. Three types of proximity maps are presented: presence maps that indicate the local density of traffic; conflict maps that determine locations and probabilities of potential conflicts; and outliers maps that evaluate the probability of conflict due to aircraft not belonging to dominant traffic patterns. These maps provide traffic flow managers with information relating to the complexity and difficulty of managing an airspace. The intended purpose of the maps is to anticipate how aircraft flows will interact, and how outliers impact the dominant traffic flow for a given time period. This formulation is able to predict which "critical" regions may be subject to conflicts between aircraft, thereby requiring careful monitoring. These probabilities are computed using a generative aircraft flow model. Time-varying flow characteristics, such as geometrical configuration, speed, and probability density function of aircraft spatial distribution within the flow, are determined from archived Enhanced Traffic Management System data, using a tailored clustering algorithm. Aircraft not belonging to flows are identified as outliers.

eess.SY↗

arXiv2010

Trajectory Clustering and an Application to Airspace Monitoring

This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Nominal trajectories are determined and learned using data driven methods. Standard procedures are used by air traffic controllers (ATC) to guide aircraft, ensure the safety of the airspace, and to maximize the runway occupancy. Even though standard procedures are used by ATC, the control of the aircraft remains with the pilots, leading to a large variability in the flight patterns observed. Two methods to identify typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as standard. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is "healthy" when all aircraft are flying according to the nominal procedures. A measure of complexity is introduced, measuring the conformance of current flight to nominal flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure a safe separation between aircraft.

cs.LG↗

arXiv2008

Graceful Degradation of Air Traffic Operations

The introduction of new technologies and concepts of operation in the air transportation system is not possible, unless they can be proven not to adversely affect the system operation under not only nominal, but also degraded conditions. In extreme scenarios, degraded operations due to partial or complete technological failures should never endanger system safety. Many past system evolutions, whether ground-based or airborne, have been based on trial-and-error, and system safety was addressed only after a specific event yielded dramatic or near- dramatic consequences. Future system evolutions, however, must leverage available computation, prior knowledge and abstract reasoning to anticipate all possible system degradations and prove that such degradations are graceful and safe. This paper is concerned with the graceful degradation of high-density, structured arrival traffic against partial or complete surveillance failures. It is shown that for equal performance requirements, some traffic configurations might be easier to handle than others, thereby offering a quantitative perspective on these traffic configurations. ability to "gracefully degrade". To support our work, we also introduce a new conflict resolution algorithm, aimed at solving conflicts involving many aircraft when aircraft position information is in the process of degrading.

cs.OH↗

arXiv2007

A Dynamic I/O Model for TRACON Traffic Management

This work investigates the TRACON flow management around a major airport. Aircraft flows are analyzed through a study of TRACON trajectories records. Rerouting and queuing processes are highlighted and airport characteristics are shown as function of the number of planes in the TRACON. Then, a simple input-output TRACON queuing and landing model is proposed. This model is calibrated and validated using available TRACON data. It reproduces the same phenomenon as the real system. This model is used to show the impact of limiting the number of aircrafts in the TRACON. A limited number of aircraft does not increase delays but reduces the controller's workload and increases safety.

cs.OH↗