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Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…
Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
We formulate the problem of learning to imitate multiple, non-deterministic teachers with minimal interaction cost. Rather than learning a specific policy as in standard imitation learning, the goal in this problem is to learn a…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…
Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…
To address the challenges of reliability analysis in high-dimensional probability spaces, this paper proposes a new metamodeling method that couples active subspace, heteroscedastic Gaussian process, and active learning. The active subspace…
This paper introduces an active learning approach to the fitting of machine learning interatomic potentials. Our approach is based on the D-optimality criterion for selecting atomic configurations on which the potential is fitted. It is…
Reliable plasma transport modeling for magnetic confinement fusion depends on accurately resolving the ion charge state distribution and radiative power losses of the plasma. These quantities can be obtained from solutions of a…
Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation. With the ever-increasing incorporation of these data-driven models into the estimation domain, model…
Due to the high cost and reliability of sensors, the designers of a pump reduce the needed number of sensors for the estimation of the feasible operating point as much as possible. The major challenge to obtain a good estimation is the low…
Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…
This paper presents a robust adaptive learning Model Predictive Control (MPC) framework for linear systems with parametric uncertainties and additive disturbances performing iterative tasks. The approach refines the parameter estimates…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
In this work, we consider the general problem of constructing a neural network surrogate model using multi-fidelity information. Motivated by error-complexity estimates for ReLU neural networks, we formulate the correlation between an…
Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Systematic exploration of Agent-Based Models (ABMs) is challenged by the curse of dimensionality and their inherent stochasticity. We present a multi-stage pipeline integrating the systematic design of experiments with machine learning…
We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…