arXiv subjects

Mickaël Binois

Publications and source records attributed to Mickaël Binois.

11 recordsLinked to original sources

arXiv2026

Trajectory-Oriented Optimization Via Adaptive Thompson Sampling And Grid Refinement: A Tutorial With The ADAPTIVE\_TS Package

Stochastic simulators are increasingly used to expand the frontier of scientific knowledge and inform decision-making across real-world contexts. Simulator calibration, a process by which internal model inputs are tuned to match some external criteria, usually in the form of observed data, is a key step in model design and validation. Epidemiological simulators present an especially compelling use case, as evidenced by the recent COVID-19 pandemic. Among several calibration paradigms, trajectory-oriented optimization is an emerging approach that does not require assumptions on the stochastic behavior of the simulator replicates and is particularly effective at identifying trajectories through the lens of errors between the simulator and observed data, especially when combined with Bayesian optimization. We present a tutorial on trajectory-oriented optimization with \texttt{adaptive\_ts}, an open-source Python package. We also provide a series of worked examples on an accompanying webpage.

stat.CO↗

arXiv2026

Optimal Control of Microswimmers for Trajectory Tracking Using Bayesian Optimization

Trajectory tracking for microswimmers remains a key challenge in microrobotics, where low-Reynolds-number dynamics make control design particularly complex. In this work, we formulate the trajectory tracking problem as an optimal control problem and solve it using a combination of B-spline parametrization with Bayesian optimization, allowing the treatment of high computational costs without requiring complex gradient computations. Applied to a flagellated magnetic swimmer, the proposed method reproduces a variety of target trajectories, including biologically inspired paths observed in experimental studies. We further evaluate the approach on a three-sphere swimmer model, demonstrating that it can adapt to and partially compensate for wall-induced hydrodynamic effects. The proposed optimization strategy can be applied consistently across models of different fidelity, from low-dimensional ODE-based models to high-fidelity PDE-based simulations, showing its robustness and generality. These results highlight the potential of Bayesian optimization as a versatile tool for optimal control strategies in microscale locomotion under complex fluid-structure interactions.

cs.RO↗

arXiv2025

Modular Jump Gaussian Processes

Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or "jumps" in the output variable. The "jump GP" (JGP) was developed for modeling data from such processes, combining local GPs and latent "level" variables under a joint inferential framework. But joint modeling can be fraught with difficulty. We aim to simplify by suggesting a more modular setup, eschewing joint inference but retaining the main JGP themes: (a) learning optimal neighborhood sizes that locally respect manifolds of discontinuity; and (b) a new cluster-based (latent) feature to capture regions of distinct output levels on both sides of the manifold. We show that each of (a) and (b) separately leads to dramatic improvements when modeling processes with jumps. In tandem (but without requiring joint inference) that benefit is compounded, as illustrated on real and synthetic benchmark examples from the recent literature.

stat.ME↗

arXiv2025

Non-Locally Controllable but Trackable Magnetic Head Flagellated Swimmer

Unlike macroscopic swimmers, microswimmers operate in a low-Reynolds-number regime dominated by viscous forces. This paper investigates the controllability of a magnetic microswimmer composed of a spherical magnetic head and an elastic, non-magnetic flagellum. The swimmer evolves in a Stokes flow and is modeled using the resistive force theory. We prove that, under planar motion, the system is not small-time locally controllable and numerically identify regions that remain inaccessible. Nevertheless, simulations show that trajectory tracking can still be achieved via Bayesian optimization, though it requires large-amplitude transverse deformations.

math.OC↗

arXiv2024

Improving Policy-Oriented Agent-Based Modeling with History Matching: A Case Study

Advances in computing power and data availability have led to growing sophistication in mechanistic mathematical models of social dynamics. Increasingly these models are used to inform real-world policy decision-making, often with significant time sensitivity. One such modeling approach is agent-based modeling, which offers particular strengths for capturing spatial and behavioral realism, and for in-silico experiments (varying input parameters and assumptions to explore their downstream impact on key outcomes). To be useful in the real world, these models must be able to qualitatively or quantitatively capture observed empirical phenomena, forming the starting point for subsequent experimentation. Computational constraints often form a significant hurdle to timely calibration and policy analysis in high resolution agent-based models. In this paper, we present a technical solution to address this bottleneck, substantially increasing efficiency and thus widening the range of utility for policy models. We illustrate our approach with a case study using a previously published and widely used epidemiological model.

stat.AP↗

arXiv2023

Developing Distributed High-performance Computing Capabilities of an Open Science Platform for Robust Epidemic Analysis

COVID-19 had an unprecedented impact on scientific collaboration. The pandemic and its broad response from the scientific community has forged new relationships among domain experts, mathematical modelers, and scientific computing specialists. Computationally, however, it also revealed critical gaps in the ability of researchers to exploit advanced computing systems. These challenging areas include gaining access to scalable computing systems, porting models and workflows to new systems, sharing data of varying sizes, and producing results that can be reproduced and validated by others. Informed by our team's work in supporting public health decision makers during the COVID-19 pandemic and by the identified capability gaps in applying high-performance computing (HPC) to the modeling of complex social systems, we present the goals, requirements, and initial implementation of OSPREY, an open science platform for robust epidemic analysis. The prototype implementation demonstrates an integrated, algorithm-driven HPC workflow architecture, coordinating tasks across federated HPC resources, with robust, secure and automated access to each of the resources. We demonstrate scalable and fault-tolerant task execution, an asynchronous API to support fast time-to-solution algorithms, an inclusive, multi-language approach, and efficient wide-area data management. The example OSPREY code is made available on a public repository.

cs.DC↗

arXiv2021

Sensitivity Prewarping for Local Surrogate Modeling

In the continual effort to improve product quality and decrease operations costs, computational modeling is increasingly being deployed to determine feasibility of product designs or configurations. Surrogate modeling of these computer experiments via local models, which induce sparsity by only considering short range interactions, can tackle huge analyses of complicated input-output relationships. However, narrowing focus to local scale means that global trends must be re-learned over and over again. In this article, we propose a framework for incorporating information from a global sensitivity analysis into the surrogate model as an input rotation and rescaling preprocessing step. We discuss the relationship between several sensitivity analysis methods based on kernel regression before describing how they give rise to a transformation of the input variables. Specifically, we perform an input warping such that the "warped simulator" is equally sensitive to all input directions, freeing local models to focus on local dynamics. Numerical experiments on observational data and benchmark test functions, including a high-dimensional computer simulator from the automotive industry, provide empirical validation.

stat.ML↗

arXiv2021

Shapes enhancing the propulsion of multiflagellated helical microswimmers

In this paper we are interested in optimizing the shape of multi-flagellated helical microswimmers. Mimicking the propagation of helical waves along the flagella, they self-propel by rotating their tails. The swimmer's dynamics is computed using the Boundary Element Method, implemented in the open source Matlab library $Gypsilab$. We exploit a Bayesian optimization algorithm to maximize the swimmer's speeds through their shape optimization. Our results show that the optimal tail shapes are helices with large wavelength, such that the shape periodicity is disregarded. Moreover, the best propulsion speed is achieved for elongated heads when the swimmer has one or two flagella. Surprisingly, a round head is obtained when more flagella are considered. Our results indicate that the position and number of flagella modify the propulsion pattern and play a significant role in the optimal design of the head. It appears that Bayesian optimization is a promising method for performance improvement in microswimming.

cond-mat.soft↗

arXiv2019

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame.

math.OC↗

arXiv2018

On the choice of the low-dimensional domain for global optimization via random embeddings

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. Specifically, in the case of time consuming black-box functions and when the budget of evaluations is severely limited, global optimization with random embeddings appears as a sound alternative to random search. Yet, in the case of box constraints on the native variables, defining suitable bounds on a low dimensional domain appears to be complex. Indeed, a small search domain does not guarantee to find a solution even under restrictive hypotheses about the function, while a larger one may slow down convergence dramatically. Here we tackle the issue of low-dimensional domain selection based on a detailed study of the properties of the random embedding, giving insight on the aforementioned difficulties. In particular, we describe a minimal low-dimensional set in correspondence with the embedded search space. We additionally show that an alternative equivalent embedding procedure yields simultaneously a simpler definition of the low-dimensional minimal set and better properties in practice. Finally, the performance and robustness gains of the proposed enhancements for Bayesian optimization are illustrated on numerical examples.

math.OC↗

arXiv2015

A warped kernel improving robustness in Bayesian optimization via random embeddings

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

math.OC↗