Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

Efficient calibration for imperfect epidemic models with applications to the analysis of COVID-19

The estimation of unknown parameters in simulations, also known as calibration, is crucial for practical management of epidemics and prediction of pandemic risk. A simple yet widely used approach is to estimate the parameters by minimizing the sum of the squared distances between actual observations and simulation outputs. It is shown in this paper that this method is inefficient, particularly when the epidemic models are developed based on certain simplifications of reality, also known as imperfect models which are commonly used in practice. To address this issue, a new estimator is introduced that is asymptotically consistent, has a smaller estimation variance than the least squares estimator, and achieves the semiparametric efficiency. Numerical studies are performed to examine the finite sample performance. The proposed method is applied to the analysis of the COVID-19 pandemic for 20 countries based on the SEIR (Susceptible-Exposed-Infectious-Recovered) model with both deterministic and stochastic simulations. The estimation of the parameters, including the basic reproduction number and the average incubation period, reveal the risk of disease outbreaks in each country and provide insights to the design of public health interventions

A generalized Gaussian process model for computer experiments with binary time series

Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which shares some common features with standard GP models. In addition, the proposed model incorporates a flexible mean function that can capture different types of time series structures. Asymptotic properties of the estimators are derived, and an optimal predictor as well as its predictive distribution are constructed. Their performance is examined via two simulation studies. The methodology is applied to study computer simulations for cell adhesion experiments. The fitted model reveals important biological information in repeated cell bindings, which is not directly observable in lab experiments.Comment: 49 pages, 4 figure

Advancing inverse scattering with surrogate modeling and Bayesian inference for functional inputs

Inverse scattering aims to infer information about a hidden object by using the received scattered waves and training data collected from forward mathematical models. Recent advances in computing have led to increasing attention towards functional inverse inference, which can reveal more detailed properties of a hidden object. However, rigorous studies on functional inverse, including the reconstruction of the functional input and quantification of uncertainty, remain scarce. Motivated by an inverse scattering problem where the objective is to infer the functional input representing the refractive index of a bounded scatterer, a new Bayesian framework is proposed. It contains a surrogate model that takes into account the functional inputs directly through kernel functions, and a Bayesian procedure that infers functional inputs through the posterior distribution. Furthermore, the proposed Bayesian framework is extended to reconstruct functional inverse by integrating multi-fidelity simulations, including a high-fidelity simulator solved by finite element methods and a low-fidelity simulator called the Born approximation. When compared with existing alternatives developed by finite basis expansion, the proposed method provides more accurate functional recoveries with smaller prediction variations

Contributions to binary-output computer experiments and large-scale computer experiments

Computer experiments have played an increasingly important role in science and technology and received enormous attention from industries and research institutes. One prominent example is the redesign of a new rocket engine by the U.S. Air Force (Mak et al., 2018). This dissertation makes contributions in two important aspects of computer experiments: (i) binary-output computer experiments and (ii) large-scale computer experiments. For (i), the dissertation contains two chapters: a new emulation method in Chapter 1 and a novel calibration method in Chapter 2, respectively. For (ii), the dissertation contains two chapters, in which new computationally efficient search limiting techniques for local Gaussian process approximation are developed in Chapter 3, and a new model, which is called multi-resolution function ANOVA, is proposed in Chapter 4.Ph.D

Stacking designs: designing multi-fidelity experiments with target predictive accuracy

In an era where scientific experiments can be very costly, multi-fidelity emulators provide a useful tool for cost-efficient predictive scientific computing. For scientific applications, the experimenter is often limited by a tight computational budget, and thus wishes to (i) maximize predictive power of the multi-fidelity emulator via a careful design of experiments, and (ii) ensure this model achieves a desired error tolerance with some notion of confidence. Existing design methods, however, do not jointly tackle objectives (i) and (ii). We propose a novel stacking design approach that addresses both goals. Using a recently proposed multi-level Gaussian process emulator model, our stacking design provides a sequential approach for designing multi-fidelity runs such that a desired prediction error of $\epsilon > 0$ is met under regularity assumptions. We then prove a novel cost complexity theorem that, under this multi-level Gaussian process emulator, establishes a bound on the computation cost (for training data simulation) needed to achieve a prediction bound of $\epsilon$. This result provides novel insights on conditions under which the proposed multi-fidelity approach improves upon a standard Gaussian process emulator which relies on a single fidelity level. Finally, we demonstrate the effectiveness of stacking designs in a suite of simulation experiments and an application to finite element analysis

Assessing Postural Stability Via the Correlation Patterns of Vertical Ground Reaction Force Components

Background Many methods have been proposed to assess the stability of human postural balance by using a force plate. While most of these approaches characterize postural stability by extracting features from the trajectory of the center of pressure (COP), this work develops stability measures derived from components of the ground reaction force (GRF). Methods In comparison with previous GRF-based approaches that extract stability features from the GRF resultant force, this study proposes three feature sets derived from the correlation patterns among the vertical GRF (VGRF) components. The first and second feature sets quantitatively assess the strength and changing speed of the correlation patterns, respectively. The third feature set is used to quantify the stabilizing effect of the GRF coordination patterns on the COP. Results In addition to experimentally demonstrating the reliability of the proposed features, the efficacy of the proposed features has also been tested by using them to classify two age groups (18–24 and 65–73 years) in quiet standing. The experimental results show that the proposed features are considerably more sensitive to aging than one of the most effective conventional COP features and two recently proposed COM features. Conclusions By extracting information from the correlation patterns of the VGRF components, this study proposes three sets of features to assess human postural stability during quiet standing. As demonstrated by the experimental results, the proposed features are not only robust to inter-trial variability but also more accurate than the tested COP and COM features in classifying the older and younger age groups. An additional advantage of the proposed approach is that it reduces the force sensing requirement from 3D to 1D, substantially reducing the cost of the force plate measurement system