HAL-Ecole des Ponts ParisTech
Not a member yet
42743 research outputs found
Sort by
Quantile Activation: Correcting a failure mode of traditional ML models
No full textInternational audienceStandard ML models fail to infer the context distribution and suitably adapt. For instance, the learning fails when the underlying distribution is actually a mixture of distributions with contradictory labels. Learning also fails if there is a shift between train and test distributions. Standard neural network architectures like MLPs or CNNs are not equipped to handle this.In this article, we propose a simple activation function, quantile activation (QAct), that addresses this problem without significantly increasing computational costs. The core idea is to "adapt" the outputs of each neuron to its context distribution. The proposed quantile activation (QAct) outputs the relative quantile position of neuron activations within their context distribution, diverging from the direct numerical outputs common in traditional networks.A specific case of the above failure mode is when there is an inherent distribution shift, i.e, the test distribution differs slightly from the train distribution. We validate the proposed activation function under covariate shifts, using datasets designed to test robustness against distortions. Our results demonstrate significantly better generalization across distortions compared to conventional classifiers and other adaptive methods, across various architectures. Although this paper presents a proof of concept, we find that this approach unexpectedly outperforms DINOv2 (small), despite DINOv2 being trained with a much larger network and dataset
Modeling the Black and Brown Carbon Absorption and Their Radiative Impact: The June 2023 Intense Canadian Boreal Wildfires Case Study
No full textInternational audienceBlack carbon (BC) and brown carbon (BrC) are light-absorbing aerosols with significant climate impacts, but their absorption properties and direct radiative effect (DRE) remain uncertain. We simulated BC and BrC absorption during the intense Canadian boreal wildfires in June 2023 using an enhanced version of CHIMERE chemical and transport model. The study focused on a domain extending from North America to Eastern Europe, including the Arctic up to 85°N. The enhanced model includes an update treatment for BC absorption enhancement and a BrC aging scheme accounting for browning and blanching through oxidation. Validation against Aerosol Robotic Network and satellite data showed the model accurately reproduced aerosol optical depth (AOD) at multiple wavelengths, both near wildfire sources and during transoceanic transport to Europe. Improvements were observed in simulations of absorbing AOD (absorbing aerosol optical) compared with the baseline model. Significant enhancements were achieved in capturing the spatial distribution of aerosol absorption in areas affected by wildfire emissions. For June 2023, the regional all-sky DRE attributed to Canadian wildfires was reduced from 2.1 W/m 2 in the control model to 1.9 W/m 2 in the enhanced model. This corresponded to an additional warming effect of +0.2 W/m 2 (+10%) due to the advanced treatment of BC and BrC absorption. These results indicate the importance of accurate aerosol absorption modeling in regional climate predictions, during large-scale biomass burning events. They also highlight potential overestimations of cooling effects in traditional models, emphasizing the need of improved aerosol parameterization to better simulate the DRE and for evaluating the impacts of mitigation strategies
MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
No full textInternational audienceWe study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite element type method that performs a Galerkin approximation on a problem-dependent basis set, itself pre-computed in an offline stage. The approach is implemented here using basis functions that locally resolve both the diffusion and the advection terms. Variants with additional bubble functions and possibly weak inter-element continuity are proposed. Some theoretical arguments and a comprehensive set of numerical experiments allow to investigate and compare the stability and the accuracy of the approaches. The best approach constructed is shown to be adequate for both the diffusion- and advection-dominated regimes, and does not rely on an auxiliary stabilization parameter that would have to be properly adjusted
Influence of sampling on the convergence rates of greedy algorithms for parameter-dependent random variables
No full textInternational audienceThe main focus of this article is to provide a mathematical study of the algorithm proposed in [6] where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations using a reduced basis paradigm. We study the effect of Monte-Carlo sampling on the theoretical properties of greedy algorithms. In particular, using concentration inequalities for the empirical measure in Wasserstein distance proved in [14], we provide sufficient conditions on the number of samples used for the computation of empirical variances at each iteration of the greedy procedure to guarantee that the resulting method algorithm is a weak greedy algorithm with high probability. These theoretical results are not fully practical and we therefore propose a heuristic procedure to choose the number of Monte-Carlo samples at each iteration, inspired from this theoretical study, which provides satisfactory results on several numerical test cases
The usefulness of viscosity for the robustness of boundary feedback control of an unstable fluid flow system
No full textInternational audienceThe potential lack of robustness to delays and characteristic velocities is a well known feature of boundary feedback control of hyperbolic systems. We consider the case of a one-dimensional fluid system with the flow rate as control input located at one boundary and the density as measured output located at the other boundary. Using a simple model where friction and viscosity are neglected, the system is open-loop unstable but it can be stabilized by a dynamic controller that involves a delayed output feedback. However this control is not robust with respect to delay uncertainties. Our main contribution is to show that this lack of robustness is actually an artefact which stems from the assumption that the fluid viscosity is negligible when modelling the fluid motion. In the presence of a small unknown viscosity in the model, it appears that the non-robust feedback for the inviscid case is actually a perfectly robust stabilizer for the viscous system and that there is an intrinsic uniform margin of stability which is independent of the viscosity value even if it is asymptotically small
A pure dual approach for hedging Bermudan options
No full textInternational audienceThis paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency
Elliptic Approximate Message Passing and an application to theoretical ecology
No full textInternational audienceApproximate Message Passing (AMP) algorithmshave recently gathered significant attention across disciplines such as statistical physics, machine learning, and communication systems. This study aims to extend AMP algorithms to non-symmetric (elliptic) matrices, motivated by analyzing equilibrium properties in ecological systems featuring elliptic interaction matrices.In this article, we provide the general form of an AMP algorithm associated to a random elliptic matrix, the main change lying in a modification of the corrective (Onsager) term. In order to establish the statistical properties of this algorithm, we use and prove a generalized form of Bolthausen conditioning argument, pivotal to proceed by a Gaussian-based induction.We finally address the initial motivating question from theoretical ecology. Large foodwebs are often described by Lotka-Volterra systems of coupled differential equations, where the interaction matrix is elliptic random. In this context, we design an AMP algorithm to analyze the statistical properties of the equilibrium point in a high-dimensional regime. We rigorously recover the results established by [Bunin, 2017] and [Galla,2018] who used techniques from theoretical physics, and extend them with the help of propagation of chaos type arguments
Improving sampling by modifying the effective diffusion
No full text33 pages, 7 figuresInternational audienceMarkov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can introduce a non-constant diffusion matrix to precondition these dynamics, and recent works have optimized it in order to improve the rate of convergence to stationarity by overcoming entropic and energy barriers. However, the introduced methodologies to compute these optimal diffusions are generally not suited to high-dimensional settings, as they rely on costly optimization procedures. In this work, we propose to optimize over a class of diffusion matrices, based on one-dimensional collective variables (CVs), to help the dynamics explore the latent space defined by the CV. The form of the diffusion matrix is chosen in order to obtain an efficient effective diffusion in the latent space. We describe how this class of diffusion matrices can be constructed and learned during the simulation. We provide implementations of the Metropolis–Adjusted Langevin Algorithm and Riemann Manifold (Generalized) Hamiltonian Monte Carlo algorithms, and discuss numerical optimizations in the case when the CV depends only on a few degrees of freedom of the system. We illustrate the efficiency gains by computing mean transition durations between two metastable states of a dimer in a solvent
Neighbourhood Effects Across Generations and the Reproduction of Inequality
No full textInternational audienceThis paper analyses the enduring impact of neighbourhood deprivation on youth development, exploring multigenerational aspects often overlooked in existing research. I investigate how neighbourhood environments experienced across two generations impact youth outcomes, focussing on cognitive skills and socio‐emotional behaviour. Using data from the 1958 National Child Development Study in the UK, this study employs a Regression with Residuals (RWR) design to comprehensively assess any long‐lasting effects. The results point to an enduring impact of neighbourhood deprivation on both outcomes, revealing that sustained exposure to disadvantage drives persistently different developmental trajectories. I find evidence for a transmission mechanism, indicating that exposure to neighbourhood deprivation during parental own formative years affects their offspring's outcomes, directly and indirectly. While parental formative neighbourhood environments significantly shape cognitive development through mechanisms related to education and income, socio‐emotional outcomes are also influenced by the legacy of neighbourhood context across generations. While conventional approaches focus on a single point in time, this study contributes to neighbourhood effects literature by taking a lengthier perspective and acknowledging the protracted and influential role that neighbourhoods as social institutions may play in shaping individual opportunities and inequality dynamics over time
Arctic soil carbon insulation averts large spring cooling from surface–atmosphere feedbacks
No full textInternational audienceThe insulative properties of soil organic carbon (SOC) and surface organic layers (moss, lichens, litter) regulate surface–atmosphere energy exchanges in the Arctic through a coupling with soil temperatures. However, a physical description of this process is lacking in many climate models, potentially biasing their high-latitude climate predictions. Using a coupled surface–atmosphere model, we identified a strong feedback loop between soil insulation, surface air temperature, and snowfall. Without insulation, the latent heat needed for soil ice thawing leads to a late spring and summer cold bias in surface air temperature (above 2 °C) over Arctic regions. The integration of soil insulation eliminates this bias and significantly improves the simulation of permafrost dynamics. Our findings, including the potential consequences of large perturbations (e.g., fires), highlight the importance of combining soil water freezing with a physical representation of SOC and surface organic layer insulation in Earth system models, to improve Arctic climate predictions