Search

Epidemiological models must be calibrated to ground truth for downstream tasks such as producing forward projections or running what-if scenarios. The meaning of calibration changes in case of a stochastic model since output from such a model is generally described via an ensemble or a distribution. Each member of the ensemble is usually mapped to a random number seed (explicitly or implicitly). With the goal of finding not only the input parameter settings but also the random seeds that are consistent with the ground truth, we propose a class of Gaussian process (GP) surrogates along with an optimization strategy based on Thompson sampling. This Trajectory Oriented Optimization (TOO) approach produces actual trajectories close to the empirical observations instead of a set of parameter settings where only the mean simulation behavior matches with the ground truth.

This paper focuses on multi-label learning from small number of labelled data. We demonstrate that the straightforward binary-relevance extension of the interpolated label propagation algorithm, the harmonic function, is a competitive learning method with respect to many widely-used evaluation measures. This is achieved mainly by a new transition matrix that better captures the underlying manifold structure. Furthermore, we show that when there exists label dependence, we can use the outputs of a competitive learning method as part of the input to the harmonic function to provide improved results over those of the original model. Finally, since we are using multiple metrics to thoroughly evaluate the performance of the algorithm, we propose to use the game-theory based method of Kalai and Smorodinsky to output a single compromise solution. This method can be applied to any learning model irrespective of the number of evaluation measures used.

International audience; This work aims at proposing an aerodynamic design optimization methodology entirely based on Computer-Aided Design (CAD) representations, yielding a fully integrated geometry-simulation-optimization framework. Specifically, the geometry to optimize is defined thanks to CAD standards, like Non-Uniform Rational B-Splines (NURBS); the resolution of compressible Euler / Navier-Stokes equation is achieved using a Discontinuous Galerkin (DG) method based on rational Bézier elements with adaptive mesh refinement, which is geometrically exact with respect to CAD boundaries; The global optimization of CAD control points is carried out using a Bayesian Optimization method. The whole design chain is therefore consistent with respect to the CAD geometry. The proposed approach is demonstrated for the optimization of an airfoil in transonic regime.

International audience; We propose a Bayesian approach for parameter uncertainty quantification in macroscopic traffic flow models from cross-sectional data. A bias term is introduced and modeled as a Gaussian process to account for the traffic flow models limitations. We validate the results comparing the error metrics of both first and second order models, showing that second order models globally perform better in reconstructing traffic quantities of interest.

International audience; A major difficulty in aerodynamic design is related to the multiplicity of geometrical representations handled during the optimization process. From high-order Computer-Aided Design (CAD) objects to discrete mesh-based descriptions, several geometrical transformations have to be performed, that considerably impact the accuracy, the robustness and the complexity of the design loop. This is even more critical when Multiphysics applications are targeted, including moving bodies.To overcome this limitation, we present here a fully integrated methodology that combines ideas from Iso-Geometric Analysis (IGA) and high-order Discontinuous Galerkin methods, within an Arbitrary Lagrangian-Eulerian (ALE) formulation for compressible Navier-Stokes equations. The resulting approach relies on a single geometrical representation, based on Non-Uniform Rational B- Splines (NURBS), that allows to achieve geometrically exact simulations with adaptive local refinements and moving interfaces.We consider as demonstration the optimization of a morphing airfoil. The profile is defined by two cubic NURBS curves, whose deformations are controlled in terms of frequency, amplitude and length, while a C1 regularity is maintained during the whole process. A multi-objective Bayesian optimization is carried out to select the most promising control parameters with respect to the time-averaged lift, the instantaneous minimum lift and the time-averaged actuation power.

One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by building a surrogate model of the black-box to simultaneously select multiple designs via an infill criterion. Still, despite the increased availability of computing resources that enable large-scale parallelism, the strategies that work for selecting a few tens of parallel designs for evaluations become limiting due to the complexity of selecting more designs. It is even more crucial when the black-box is noisy, necessitating more evaluations as well as repeating experiments. Here we propose a scalable strategy that can keep up with massive batching natively, focused on the exploration/exploitation trade-off and a portfolio allocation. We compare the approach with related methods on noisy functions, for mono and multi-objective optimization tasks. These experiments show orders of magnitude speed improvements over existing methods with similar or better performance.

This chapter addresses the question of how to efficiently solve many-objective optimization problems in a computationally demanding black-box simulation context. We shall motivate the question by applications in machine learning and engineering, and discuss specific harsh challenges in using classical Pareto approaches when the number of objectives is four or more. Then, we review solutions combining approaches from Bayesian optimization, e.g., with Gaussian processes, and concepts from game theory like Nash equilibria, Kalai-Smorodinsky solutions and detail extensions like Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding algorithms and provide some illustrating results.

International audience; In this work we present a fully integrated framework for aerodynamic shape optimisation. In order to develop an efficient design chain, a high level of automation is required. To this end, we propose an isogeometric approach, in which the same mathematical representation is adopted for the shape to optimize, the computational domain and the physical solution, without any geometrical approximation. It results in a tight coupling between the Computer Aided Design (CAD) tool, the mesh generation / adaption and the Computational Fluid Dynamics (CFD) solver. As a consequence, all transfers of information between the components of the design loop are significantly facilitated. The compressible Navier-Stokes equations are solved using the Isogeometric Discontinuous Galerkin scheme. The flow solver is then coupled with an Efficient Global Optimisation (EGO) algorithm to complete the design chain. We first demonstrate the capability of the developed methodology by considering a classic drag reduction problem, in which an airfoil shape is optimised for a transonic flow condition. Since the position of the shock on the airfoil surface is a function of the geometry, traditional approaches require highly refined meshes in a large area to properly capture the discontinuity for all the possible designs. However, thanks to the isogeometric formulation, we can exploit an Adaptive Mesh Refinement technique presented to further reduce the computational costs by refining locally the mesh while preserving exactly the geometry. As a second test case, we study an active morphing technique to control the boundary layer separation over an airfoil. The Arbitrary Lagrangian-Eulerian approach proposed is used for solving the flow equations on the time-dependent deforming domain. The isogeometric methodology allows an accurate description and a control of the regularity of the deformation of the airfoil surface. The EGO algorithm is thus used to find the optimal set of parameters for the morphing technique.

International audience; An increasing number of time-consuming simulators exhibit a complex noise structure that depends on the inputs. To conduct studies with limited budgets of evaluations, new surrogate methods are required to model simultaneously the mean and variance fields. To this end, we present recent advances in Gaussian process modeling with input-dependent noise. First, we describe a simple, yet efficient, joint modeling framework that rely on replication for both speed and accuracy. Then we tackle the issue of leveraging replication and exploration in a sequential manner for various goals, such as obtaining a globally accurate model, for optimization, contour finding, and active subspace estimation. We illustrate these on applications coming from epidemiology and inventory management.

Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on-site design and surrogate modeling for a computer simulator acting on a high-dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data-faithful modeling and computational tractability in a calibration framework--tailoring the computer model to a limited field experiment. Situating our on-site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example., 31 pages, 12 figures

Emulation of computer experiments via surrogate models can be difficult when the number of input parameters determining the simulation grows any greater than a few dozen. In this dissertation, we explore dimension reduction in the context of computer experiments. The active subspace method is a linear dimension reduction technique which uses the gradients of a function to determine important input directions. Unfortunately, we cannot expect to always have access to the gradients of our black-box functions. We thus begin by developing an estimator for the active subspace of a function using kernel methods to indirectly estimate the gradient. We then demonstrate how to deploy the learned input directions to improve the predictive performance of local regression models by ``undoing" the active subspace. Finally, we develop notions of sensitivities which are local to certain parts of the input space, which we then use to develop a Bayesian optimization algorithm which can exploit locally important directions. Doctor of Philosophy Increasingly, scientists and engineers developing new understanding or products rely on computers to simulate complex phenomena. Sometimes, these computer programs are so detailed that the amount of time they take to run becomes a serious issue. Surrogate modeling is the problem of trying to predict a computer experiment's result without having to actually run it, on the basis of having observed the behavior of similar simulations. Typically, computer experiments have different settings which induce different behavior. When there are many different settings to tweak, typical surrogate modeling approaches can struggle. In this dissertation, we develop a technique for deciding which input settings, or even which combinations of input settings, we should focus our attention on when trying to predict the output of the computer experiment. We then deploy this technique both to prediction of computer experiment outputs as well as to trying to find which of the input settings yields a particular desired result.