Robert Koprinkov (10:15 -> 10:45)
Toward Physics-Constrained Gaussian Process regression
Abstract: Gaussian Process regression has often been used for the modeling of physical problems. Solutions of these problems are known to satisfy certain PDE and boundary conditions, and methods for integrating such constraints into the Gaussian Process model have been a popular line of inquiry. We are interested in the extension of such methods to the multiphysics case, which can lead to improvements in accuracy, as well as to improvements in stability in the coupled fixed-point iteration. During this talk, he will present approaches for integrating such constraints, with applications to the heat equation and the linear elasticity equations.
Adama Barry (11:00 -> 11:40)
Bayesian Optimization with Gaussian Processes.
Abstract: This presentation explores Bayesian optimization techniques for costly-to-evaluate functions. Such methods are particularly valuable in fields like industry and engineering, where complex simulators are often costly to run.
We begin by introducing Gaussian process (GP) modeling, which serves as a surrogate for the target function. Building on this, we present the framework of sequential design of experiments, where evaluation points are selected iteratively based on the knowledge from previous observations. Several acquisition functions will be discussed, including the Expected Improvement (EI) and approaches based on the Stepwise Uncertainty Reduction (SUR) paradigm. We will examine how these strategies balance the trade-off between exploration (sampling in regions of high uncertainty) and exploitation (focusing on areas likely to yield optimal results), enabling more efficient optimization.
Finally, we will highlight the application of Bayesian optimization to calibrate expensive computer code. The objective is to approximate the conditional distribution of input parameters so that the code outputs closely match physical observations.
Florian Gossard (11:40 -> 12:20)
Kriging-based prediction of probability measures. Application in numerical simulation for nuclear safety studies.
Abstract: The prediction of complex data is a key topic in several applications related to nuclear safety, particularly in thermohydraulics for the analysis of accidental scenarios by numerical simulation. In practice, the amount of simulated data may be insufficient to perform a detailed analysis of a phenomenon of interest due to the high computational cost of a simulation. To circumvent this difficulty, fast-to-evaluate models or metamodels can be used. In this work, we present the construction of a Kriging-based metamodel for complex data that are probability measures. We exploit the Wasserstein distance derived from optimal transport theory and propose to construct the Kriging estimator as a Wasserstein barycenter.
This approach is then applied to the prediction of measures associated with the temperatures simulated in the core of a nuclear reactor during a loss of primary coolant accident.
