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We introduce a novel masked pre-training technique for graph neural networks (GNNs) applied to computational fluid dynamics (CFD) problems. By randomly masking up to 40\% of input mesh nodes during pre-training, we force the model to learn robust representations of complex fluid dynamics. We pair this masking strategy with an asymmetric encoder-decoder architecture and gated multi-layer perceptrons to further enhance performance. The proposed method achieves state-of-the-art results on seven CFD datasets, including a new challenging dataset of 3D intracranial aneurysm simulations with over 250,000 nodes per mesh. Moreover, it significantly improves model performance and training efficiency across such diverse range of fluid simulation tasks. We demonstrate improvements of up to 60\% in long-term prediction accuracy compared to previous best models, while maintaining similar computational costs. Notably, our approach enables effective pre-training on multiple datasets simultaneously, significantly reducing the time and data required to achieve high performance on new tasks. Through extensive ablation studies, we provide insights into the optimal masking ratio, architectural choices, and training strategies.

A fundamental alcove $\mathcal{A}$ is a tile in a paving of a vector space $V$ by an affine reflection group $W_{\mathrm{aff}}$. Its geometry encodes essential features of $W_{\mathrm{aff}}$, such as its affine Dynkin diagram $\widetilde{D}$ and fundamental group $\Omega$. In this article we investigate its full isometry group $\mathrm{Aut}(\mathcal{A})$. It is well known that the isometry group of a regular polyhedron is generated by hyperplane reflections on its faces. Being a simplex, an alcove $\mathcal{A}$ is the simplest of polyhedra, nevertheless it is seldom a regular one. In our first main result we show that $\mathrm{Aut}(\mathcal{A})$ is isomorphic to $\mathrm{Aut}(\widetilde{D})$. Building on this connection, we establish that $\mathrm{Aut}(\mathcal{A})$ is an abstract Coxeter group, with generators given by affine isometric involutions of the ambient space. Although these involutions are seldom reflections, our second main result leverages them to construct, by slicing the Komrakov--Premet fundamental polytope $\mathcal{K}$ for the action of $\Omega$, a family of fundamental polytopes for the action of $\mathrm{Aut}(\mathcal{A})$ on $\mathcal{A}$, whose vertices are contained in the vertices of $\mathcal{K}$ and whose faces are parametrized by the so-called balanced minuscule roots, which we introduce here. In an appendix, we discuss some related negative results on stratified centralizers and equivariant triangulations., Comment: 6 Figures, 3 Tables

In socioeconomic systems, nonequilibrium dynamics naturally stem from the generically non-reciprocal interactions between self-interested agents, whereas equilibrium descriptions often only apply to scenarios where individuals act with the common good in mind. We bridge these two contrasting paradigms by studying a Sakoda-Schelling occupation model with both individualistic and altruistic agents, who, in isolation, follow nonequilibrium and equilibrium dynamics respectively. We investigate how the relative fraction of these two populations impacts the behavior of the system. In particular, we find that when fluctuations in the agents' decision-making process are small (high rationality), a very moderate amount of altruistic agents mitigates the sub-optimal concentration of individualists in dense clusters. In the regime where fluctuations carry more weight (low rationality), on the other hand, altruism progressively allows the agents to coordinate in a way that is significantly more robust, which we understand by reducing the model to a single effective population studied through the lens of active matter physics. We highlight that localizing the altruistic intervention at the right point in space may be paramount for its effectiveness.

We investigated the emerging traffic patterns of Argentine ants (Linepithema humile) as they navigated a narrow bridge between their nest and a food source. By tracking ant movements in experiments with varying bridge widths and colony sizes and analyzing the resulting trajectories, we discovered that a small subset of ants stopped for long periods of time, acting as obstacles and affecting traffic flow. Interestingly, the fraction of these stopped ants increased with wider bridges, suggesting a mechanism to reduce traffic flow to a narrower section of the bridge. To quantify transport efficiency, we measured the average speed of the ants on the bridge as a function of the pressure of ants arriving at the bridge, finding this relationship to be an increasing but saturating function of the pressure. We developed an agent-based model for ant movement and interactions to better understand these dynamics. Including stopped agents in the model was crucial to explaining the experimental observations. We further validated our hypothesis by introducing artificial obstacles on the bridges and found that our simulations accurately mirrored the experimental data when these obstacles were included. These findings provide new insights into how Argentine ants self-organize to manage traffic, highlighting a unique form of dynamic obstruction that enhances traffic flow in high-density conditions. This study advances our understanding of self-regulation in biological traffic systems and suggests potential applications for managing human traffic in congested environments.

The rheology of coextruded layered films of polystyrene/poly(methyl methacrylate) (PS/PMMA) has been studied with small and large amplitude oscillations at a temperature above their glass transition. While the complex viscosity remains constant over the experimental time window for the micron-sized layered films, a decrease has been observed for the nanolayered films. The rheological behavior has then been correlated to the morphological evolution of the multilayer films: while the nanolayers dewet. Layer breakup followed by retraction and coalescence leading to a lamellar-like blend morphology succeeded by a nodular-like morphology has been evidenced in the nanolayer films, for all compositions and conditions tested. The analysis of the microscopic images of the film cross-sections also provided the droplet size distribution. The nodular morphology is achieved more rapidly when the initial layers are the thinnest at low strains, while at high strains the formation of these droplets is prevented., Comment: 16 pages, 10 figure + supplementary information

In the context of particle therapy monitoring, we are developing a gamma-ray detector to determine the ion range in vivo from the measurement of particle time-of-flight. For this application, a beam monitor capable to tag in time the incident ion with a time resolution below 235 ps FWHM (100 ps rms) is required to provide a start signal for the acquisition. We have therefore developed a dedicated detector based on a fast organic scintillator (EJ-204) of 25x25x1 mm3 coupled to four SiPM strips that allow measuring the particle incident position by scintillation light sharing. The prototype was characterised with single protons of energies between 63 and 225 MeV at the MEDICYC and ProteusONE facilities of the Antoine Lacassagne proton therapy centre in Nice. We obtained a time resolution of 120 ps FWHM at 63 MeV, and a spatial resolution of ~2 mm rms for single particles. Two identical detectors also allowed to measure the MEDICYC proton energy with 0.3% accuracy.

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural question is the extension of general scalar output regression models to such complex outputs. Changes between input geometries in terms of both size and adjacency structure in particular make this transition non-trivial. In this work, we propose an innovative strategy for Gaussian process regression where inputs are large and sparse graphs with continuous node attributes and outputs are signals defined on the nodes of the associated inputs. The methodology relies on the combination of regularized optimal transport, dimension reduction techniques, and the use of Gaussian processes indexed by graphs. In addition to enabling signal prediction, the main point of our proposal is to come with confidence intervals on node values, which is crucial for uncertainty quantification and active learning. Numerical experiments highlight the efficiency of the method to solve real problems in fluid dynamics and solid mechanics.

Hexagonal boron nitride (hBN) presents valuable intrinsic properties and attracts considerable attention for the development of novel two-dimensional (2D) materials-based technologies. Even though huge efforts have been made to improve the bottom-up synthesis of integrated and high quality hBN, the devices presenting the best performances are still made using hBN exfoliated from bulk crystals. In this context, we explore the Polymer-Derived Ceramics (PDC) route coupled to a high temperature process that produces millimetric and high quality hBN crystals. By investigating the (micro)structure of several samples, we demonstrate that the crystal growth occurs by segregation from a Li3BN2-BN solution upon cooling and from hBN seeds. In particular, we show that crystallization can occur at a temperature as low as 1400{\textdegree}C. Overall, these results show that hBN crystal growth in the Li3BN2-BN system is compatible with conventional flux methods that may be the most promising platform for continuous seeded hBN crystal growth.

High-resolution label-free imaging of oocytes and embryos is essential for in vitro fertilization procedures. Yet conventional microscopy fails in this task because of aberrations and multiple scattering induced by refractive index heterogeneities inside the sample. These detrimental phenomena drastically degrade the images of early embryos particularly in depth. To overcome these fundamental problems without sacrificing the frame rate, optical matrix imaging (OMI) is a suitable tool. Relying on an ultra-fast measurement of the reflection matrix associated with the sample, it can compensate for aberration and forward multiple scattering in post-processing, thereby providing three-dimensional and highly contrasted images of embryos at a confocal resolution. As a first proof-of-concept, bovine oocytes and embryos are imaged at a 300 nm resolution almost in real time. Our system enables visualization of intracellular structures such as lipids and mitochondria in the cytoplasm or the zona pellucida surrounding it. Altogether, we demonstrate that OMI is a promising tool for research in developmental biology and for time-lapse monitoring of oocytes and embryos in assisted reproduction., Comment: 18 pages, 6 figures

Neutron noise analysis is a predominant technique for fissile matter identification with passive methods. Quantifying the uncertainties associated with the estimated nuclear parameters is crucial for decision-making. A conservative uncertainty quantification procedure is possible by solving a Bayesian inverse problem with the help of statistical surrogate models but generally leads to large uncertainties due to the surrogate models' errors. In this work, we develop two methods for robust uncertainty quantification in neutron and gamma noise analysis based on the resolution of Bayesian inverse problems. We show that the uncertainties can be reduced by including information on gamma correlations. The investigation of a joint analysis of the neutron and gamma observations is also conducted with the help of active learning strategies to fine-tune surrogate models. We test our methods on a model of the SILENE reactor core, using simulated and real-world measurements.

Bayesian calibration is an effective approach for ensuring that numerical simulations accurately reflect the behavior of physical systems. However, because numerical models are never perfect, a discrepancy known as model error exists between the model outputs and the observed data, and must be quantified. Conventional methods can not be implemented in transposition situations, such as when a model has multiple outputs but only one is experimentally observed. To account for the model error in this context, we propose augmenting the calibration process by introducing additional input numerical parameters through a hierarchical Bayesian model, which includes hyperparameters for the prior distribution of the calibration variables. Importance sampling estimators are used to avoid increasing computational costs. Performance metrics are introduced to assess the proposed probabilistic model and the accuracy of its predictions. The method is applied on a computer code with three outputs that models the Taylor cylinder impact test. The outputs are considered as the observed variables one at a time, to work with three different transposition situations. The proposed method is compared with other approaches that embed model errors to demonstrate the significance of the hierarchical formulation., Comment: Submitted to International Journal for Uncertainty Quantification

We provide a fundamental domain for the action of the finite Weyl group on a maximal torus of a compact Lie group of the corresponding type. The general situation is reduced to the adjoint case and, from the perspective of root data, this problem can be rephrased by asking for a fundamental polytope for the action of the extended affine Weyl group on the (dual) toral subalgebra. We solve the problem in this second form. Using the theory of minuscule weights, we obtain a description of this fundamental polytope as a convex hull of explicit vertices, and as an intersection of closed half-spaces. The latter description was first obtained by Komrakov and Premet in 1984 but, as the present work is independent of that of Komrakov-Premet, we give a new self-contained proof of it. We also derive some consequences on the structure of automorphism groups of extended Dynkin diagrams.

Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural Networks (CNNs) have found success in CFD by mapping meshes into images, recent attention has turned to leveraging Graph Neural Networks (GNNs) for direct mesh processing. This paper introduces a novel model merging Self-Attention with Message Passing in GNNs, achieving a 15\% reduction in RMSE on the well known flow past a cylinder benchmark. Furthermore, a dynamic mesh pruning technique based on Self-Attention is proposed, that leads to a robust GNN-based multigrid approach, also reducing RMSE by 15\%. Additionally, a new self-supervised training method based on BERT is presented, resulting in a 25\% RMSE reduction. The paper includes an ablation study and outperforms state-of-the-art models on several challenging datasets, promising advancements similar to those recently achieved in natural language and image processing. Finally, the paper introduces a dataset with meshes larger than existing ones by at least an order of magnitude. Code and Datasets will be released at https://github.com/DonsetPG/multigrid-gnn.

This study evaluates the performance of analog-based methodologies to predict, in a statistical way, the longitudinal velocity in a turbulent flow. The data used comes from hot wire experimental measurements from the Modane wind tunnel. We compared different methods and explored the impact of varying the number of analogs and their sizes on prediction accuracy. We illustrate that the innovation, defined as the difference between the true velocity value and the prediction value, highlights particularly unpredictable events that we directly link with extreme events of the velocity gradients and so to intermittency. A statistical study of the innovation indicates that while the estimator effectively seizes linear correlations, it fails to fully capture higher-order dependencies. The innovation underscores the presence of intermittency, revealing the limitations of current predictive models and suggesting directions for future improvements in turbulence forecasting.This study evaluates the performance of analog-based methodologies to predict the longitudinal velocity in a turbulent flow. The data used comes from hot wire experimental measurements from the Modane wind tunnel. We compared different methods and explored the impact of varying the number of analogs and their sizes on prediction accuracy. We illustrate that the innovation, defined as the difference between the true velocity value and the prediction value, highlights particularly unpredictable events that we directly link with extreme events of the velocity gradients and so to intermittency. This result indicates that while the estimator effectively seizes linear correlations, it fails to fully capture higher-order dependencies. The innovation underscores the presence of intermittency, revealing the limitations of current predictive models and suggesting directions for future improvements in turbulence forecasting.

We present a benchmarking protocol that combines the characterization of boron nitride (BN) crystals and films with the evaluation of the electronic properties of graphene on these substrates. Our study includes hBN crystals grown under different conditions and scalable BN films deposited by either chemical or physical vapor deposition (CVD or PVD). We explore the complete process from boron nitride growth, over its optical characterization by time-resolved cathodoluminescence (TRCL), to the optical and electronic characterization of graphene by Raman spectroscopy after encapsulation and Hall bar processing. Within our benchmarking protocol we achieve a homogeneous electronic performance within each Hall bar device through a fast and reproducible processing routine. We find that a free exciton lifetime of 1 ns measured on as-grown hBN crystals by TRCL is sufficient to achieve high graphene room temperature charge carrier mobilities of 80,000 cm$^2$/(Vs) at a carrier density of |n| = 10$^{12}$ cm$^{-2}$, while respective exciton lifetimes around 100 ps yield mobilities up to 30,000 cm$^2$/(Vs). For scalable PVD-grown BN films, we measure carrier mobilities exceeding 10,000 cm$^2$/(Vs) which correlates with a graphene Raman 2D peak linewidth of 22 cm$^{-1}$. Our work highlights the importance of the Raman 2D linewidth of graphene as a critical metric that effectively assesses the interface quality (i.e. surface roughness) to the BN substrate, which directly affects the charge carrier mobility of graphene. Graphene 2D linewidth analysis is suitable for all BN substrates and is particularly advantageous when TRCL or BN Raman spectroscopy cannot be applied to specific BN materials such as amorphous or thin films. This underlines the superior role of spatially-resolved spectroscopy in the evaluation of BN crystals and films for the use of high-mobility graphene devices., Comment: 18 pages, 11 figures

Understanding the learning process and the embedded computation in transformers is becoming a central goal for the development of interpretable AI. In the present study, we introduce a hierarchical filtering procedure for generative models of sequences on trees, allowing us to hand-tune the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformers can approximate the exact inference algorithm when trained on root classification and masked language modeling tasks, and study how this computation is discovered and implemented. We find that correlations at larger distances, corresponding to increasing layers of the hierarchy, are sequentially included by the network during training. Moreover, by comparing attention maps from models trained with varying degrees of filtering and by probing the different encoder levels, we find clear evidence of a reconstruction of correlations on successive length scales corresponding to the various levels of the hierarchy, which we relate to a plausible implementation of the exact inference algorithm within the same architecture., Comment: 21 pages, 15 figures

Research infrastructures have been identified as an important source of greenhouse gas emissions of astronomical research. Based on a comprehensive inventory of 1,211 ground-based observatories and space missions, we assessed the evolution of the number of astronomical facilities and their carbon footprint from 1945 to 2022. We found that space missions dominate greenhouse gas emissions in astronomy, showing an important peak at the end of the 1960ies, followed by a decrease that has turned again into a rise over the last decade. Extrapolating past trends, we predict that greenhouse gas emissions from astronomical facilities will experience no strong decline in the future, and may even rise substantially, unless research practices are changed. We demonstrate that a continuing growth in the number of operating astronomical facilities is not environmentally sustainable. These findings should motivate the astronomical community to reflect about the necessary evolutions that would put astronomical research on a sustainable path., Comment: 53 pages, 17 figures, 3 tables

We study the propagation of surface waves across structured surfaces with random, localized inhomogeneities. A discrete analogue of Gurtin-Murdoch model is employed and surface elasticity, in contrast to bulk elasticity, is captured by distinct point masses and elastic constants for nearest-neighbour interactions parallel to the surface. Expressions for the surface wave reflectance and transmittance, as well as the radiative loss, are provided for every localized patch of point mass perturbation on the surface. As the main result in the article, we provide the statistics of surface wave reflectance and transmittance and the radiative loss for an ensemble of random mass perturbations, independent and identically distributed with mean zero, on the surface. In the weakly scattering regime, the mean radiative loss is found to be proportional to the size of the perturbed patch, to the variance of the mass perturbations, and to an effective parameter that depends on the continuous spectrum of the unperturbed system. In the strongly scattering regime, the mean radiative loss is found to depend on another effective parameter that depends on the continuous spectrum, but not on the variance of the mass perturbations. Numerical simulations are found in quantitative agreement with the theoretical predictions for several illustrative values of the surface structure parameters., Comment: 27 pages

Astronomical observatories have been identified as substantial contributors to the carbon footprint of astrophysical research. Being part of the collaboration that currently develops the Medium-Sized Telescope (MST) of the Cherenkov Telescope Array, a ground-based observatory for very-high-energy gamma rays that will comprise 64 telescopes deployed on two sites, we assessed the environmental impacts of one MST on the Northern site by means of a Life Cycle Assessment. We identified resource use and climate change as the most significant impacts, being driven by telescope manufacturing and energy consumption during operations. We estimate life cycle greenhouse gas emissions of 2,660 +/- 274 tCO2 equivalent for the telescope, 44% of which arise from construction, 1% from on-site assembly and commissioning, and 55% from operations over 30 years. Environmental impacts can be reduced by using renewable energies during construction and operations, use of less electronic components and metal casting, and use of recycled materials. We propose complementing project requirements with environmental budgets as an effective measure for impact management and reductions., Comment: 32 pages, 4 main figures, 3 extended data figures

We propose an efficient sensitivity analysis method for a wide class of colored noise-driven interacting particle systems (IPS). Our method is based on unperturbed simulations and significantly extends the Malliavin weight sampling method proposed by Szamel (EPL, 117 (2017) 50010) for evaluating sensitivities such as linear response functions of IPS driven by simple Ornstein-Uhlenbeck processes. We show that the sensitivity index depends not only on two effective parameters that characterize the variance and correlation time of the noise, but also on the noise spectrum. In the case of a single particle in a harmonic potential, we obtain exact analytical formulas for two types of linear response functions. By applying our method to a system of many particles interacting via a repulsive screened Coulomb potential, we compute the mobility and effective temperature of the system. Our results show that the system dynamics depend, in a nontrivial way, on the noise spectrum.

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method leverages the recently defined infinite-dimensional score-based diffusion models as a learning-based prior, while enabling provable posterior sampling through a Langevin-type MCMC algorithm defined on function spaces. A novel convergence analysis is conducted, inspired by the fixed-point methods established for traditional regularization-by-denoising algorithms and compatible with weighted annealing. The obtained convergence bound explicitly depends on the approximation error of the score; a well-approximated score is essential to obtain a well-approximated posterior. Stylized and PDE-based examples are provided, demonstrating the validity of our convergence analysis. We conclude by presenting a discussion of the method's challenges related to learning the score and computational complexity.

In this article, we consider two different statistical models. First, we focus on the estimation of the jump intensity of a compound Poisson process in the presence of unknown noise. This problem combines both the deconvolution problem and the decompounding problem. More specifically, we observe several independent compound Poisson processes but we assume that all these observations are noisy due to measurement noise. We construct an Fourier estimator of the jump density and we study its mean integrated squared error. Then, we propose an adaptive method to correctly select the cutoff of the estimator and we illustrate the efficiency of the method with numerical results. Secondly, we introduce in this paper the multiplicative decompounding problem. We study this problem with Mellin density estimators. We develop an adaptive procedure to select the optimal cutoff parameter.

One of the main interests of 2D materials is their ability to be assembled with many degrees of freedom for tuning and manipulating excitonic properties. There is a need to understand how the structure of the interfaces between atomic layers influences exciton properties. Here we use cathodoluminescence (CL) and time-resolved CL experiments to study how excitons interact with the interface between two twisted hexagonal boron nitride (hBN) crystals with various angles. An efficient capture of free excitons by the interface is demonstrated, which leads to a population of long lived and interface-localized (2D) excitons. Temperature dependent experiments indicate that for high twist angles, these excitons localized at the interface further undergo a self-trapping. It consists in a distortion of the lattice around the exciton on which the exciton traps itself. Our results suggest that this exciton-interface interaction causes a broad optical emission of highly twisted hBN-hBN structures around 300 nm (4 eV). Exciton self-trapping is finally discussed as a common feature of sp2 hybridized boron nitride polytypes and nanostructures due to the ionic nature of the B-N bond and their compact excitons., Comment: 15 pages, 13 figures

We consider the free propagation geometry of a light beam (or fluid of light) in a multimode waveguide. As a result of the effective photon-photon interactions, the photon fluid thermalizes to an equilibrium state during its conservative propagation. In this configuration, Rayleigh-Jeans (RJ) thermalization and condensation of classical light waves have been recently observed experimentally in graded index multimode optical fibers characterized by a 2D parabolic trapping potential. As well-known, the properties of RJ condensation differ substantially from those of Bose-Einstein (BE) condensation: The condensate fraction decreases quadratically with the temperature for BE condensation, while it decreases linearly for RJ condensation. Furthermore, for quantum particles the heat capacity tends to zero at small temperatures, and it takes a constant value in the classical particle limit at high temperatures. This is in contrast with classical RJ waves, where the specific heat takes a constant value at small temperatures, and tends to vanish above the condensation transition in the normal (uncondensed) state. Here, we reconcile the thermodynamic properties of BE and RJ condensation: By introducing a frequency cut-off inherent to light propagation in a waveguide, we derive generalized expressions of the thermodynamic properties that include the RJ and BE limits as particular cases. We extend the approach to encompass negative temperatures. In contrast to positive temperatures, the specific heat does not display a singular behavior at negative temperatures, reflecting the non-critical nature of the transition to a macroscopic population of the highest energy level. Our work contributes to understanding the quantum-to-classical crossover in the equilibrium properties of light, within a versatile experimental platform based on nonlinear optical propagation in multimode waveguides., Comment: 21 pages, 12 figures

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz--Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, Singular Value Decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.

Recently, Marin and Gonz\'alez-Meneses introduced a class of ``parabolic'' subgroups for generalized braid groups associated to arbitrary complex reflection groups. Using notably Garside group structures on these generalized braid groups, they proved general results on parabolic subgroups for all cases but one. This last case is that of the complex braid group B(G31), which has no Garside group structure known so far, but instead a Garside groupoid structure. Using this Garside groupoid structure, we complete the results of Marin and Gonz\'alez-Meneses by proving their main theorems for the parabolic subgroups of the complex braid group B(G31)., Comment: 35 pages. arXiv admin note: text overlap with arXiv:2208.11938 by other authors

Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace complex computer codes. Some sequential design strategies can be understood within the Stepwise Uncertainty Reduction (SUR) framework. In the SUR framework, each new design point is chosen by minimizing the expectation of a metric of uncertainty with respect to the yet unknown new data point. These methods offer an accessible framework for sequential experiment design, including almost sure convergence for common uncertainty functionals. This paper introduces two strategies. The first one, entitled Constraint Set Query (CSQ) is adapted from D-optimal designs where the search space is constrained in a ball for the Mahalanobis distance around the maximum a posteriori. The second, known as the IP-SUR (Inverse Problem SUR) strategy, uses a weighted-integrated mean squared prediction error as the uncertainty metric and is derived from SUR methods. It is tractable for Gaussian process surrogates with continuous sample paths. It comes with a theoretical guarantee for the almost sure convergence of the uncertainty functional. The premises of this work are highlighted in various test cases, in which these two strategies are compared to other sequential designs., Comment: 22 pages, 12 figures, 2 appendices