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Researcher profile

Chiwoo Park

Chiwoo Park contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer VisionMethodologyEmerging Technologiesmath.OC

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Published work

7 published item(s)

preprint2026arXiv

Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions

We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of a piecewise continuous function on a high-dimensional domain. DJGP addresses the limitations of conventional Jump Gaussian Processes (JGP) in high-dimensional input spaces by integrating region-specific, locally linear projections with JGP modeling. These projections employ region-dependent matrices to capture local low-dimensional subspace structures, making them well suited to the inherently localized modeling behavior of JGPs, a variant of local Gaussian processes. To control model complexity, we place a Gaussian Process prior on the projection matrices, allowing them to evolve smoothly across the input space. The projected inputs are then modeled with a JGP to capture piecewise continuous relationships with the response. This yields a distinctive two-layer deep learning of GP/JGP. We further develop a scalable variational inference algorithm to jointly learn the projection matrices and JGP hyperparameters. Rigorous theoretical analysis and extensive empirical studies are provided to justify the proposed approach. In particular, we derive an oracle error bound for DJGP and decompose it into four distinct sources of error, which are then linked to practical implications. Experiments on synthetic and benchmark datasets demonstrate that DJGP achieves superior predictive accuracy and more reliable uncertainty quantification compared with existing methods.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Online Bayesian Calibration under Gradual and Abrupt System Changes

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Sequential Adaptive Design for Jump Regression Estimation

Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. The first example we undertook was for the purpose of accelerating imaging speed in a high resolution material imaging; the second was use of sequential design for the purpose of mapping a chemical phase diagram. In both examples, the underlying regression functions have discontinuities, so many of the existing design optimization approaches cannot be applied because they mostly assume a continuous regression function. Although some existing adaptive design strategies developed from treed regression models can handle the discontinuities, the Bayesian approaches come with computationally expensive Markov Chain Monte Carlo techniques for posterior inferences and subsequent design point selections, which is not appropriate for the first motivating example that requires computation at least faster than the original imaging speed. In addition, the treed models are based on the domain partitioning that are inefficient when the discontinuities occurs over complex sub-domain boundaries. We propose a simple and effective adaptive design strategy for a regression analysis with discontinuities: some statistical properties with a fixed design will be presented first, and then these properties will be used to propose a new criterion of selecting the design points for the regression analysis. Sequential design with the new criterion will be presented with comprehensive simulated examples, and its application to the two motivating examples will be presented.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Data Science for Motion and Time Analysis with Modern Motion Sensor Data

The motion-and-time analysis has been a popular research topic in operations research, especially for analyzing work performances in manufacturing and service operations. It is regaining attention as continuous improvement tools for lean manufacturing and smart factory. This paper develops a framework for data-driven analysis of work motions and studies their correlations to work speeds or execution rates, using data collected from modern motion sensors. The past analyses largely relied on manual steps involving time-consuming stop-watching and video-taping, followed by manual data analysis. While modern sensing devices have automated the collection of motion data, the motion analytics that transform the new data into knowledge are largely underdeveloped. Unsolved technical questions include: How the motion and time information can be extracted from the motion sensor data, how work motions and execution rates are statistically modeled and compared, and what are the statistical correlations of motions to the rates? In this paper, we develop a novel mathematical framework for motion and time analysis with motion sensor data, by defining new mathematical representation spaces of human motions and execution rates and by developing statistical tools on these new spaces. This methodological research is demonstrated using five use cases applied to manufacturing motion data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Gaussian process surrogate modeling with manipulating factors for carbon nanotube growth experiments

This paper presents a new Gaussian process (GP) surrogate modeling for predicting the outcome of a physical experiment where some experimental inputs are controlled by other manipulating factors. Particularly, we are interested in the case where the control precision is not very high, so the input factor values vary significantly even under the same setting of the corresponding manipulating factors. The case is observed in our main application to carbon nanotube growth experiments, where one experimental input among many is manipulated by another manipulating factors, and the relation between the input and the manipulating factors significantly varies in the dates and times of operations. Due to this variation, the standard GP surrogate that directly relates the manipulating factors to the experimental outcome does not provide a great predictive power on the outcome. At the same time, the GP model relating the main factors to the outcome directly is not appropriate for the prediction purpose because the main factors cannot be accurately set as planned for a future experiment. Motivated by the carbon nanotube example, we propose a two-tiered GP model, where the bottom tier relates the manipulating factors to the corresponding main factors with potential biases and variation independent of the manipulating factors, and the top tier relates the main factors to the experimental outcome. Our two-tier model explicitly models the propagation of the control uncertainty to the experimental outcome through the two GP modeling tiers. We present the inference and hyper-parameter estimation of the proposed model. The proposed approach is illustrated with the motivating example of a closed-loop autonomous research system for carbon nanotube growth experiments, and the test results are reported with the comparison to a benchmark method, i.e. a standard GP model.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Robust Gaussian Process Regression with a Bias Model

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the Laplace distribution and Student-t distribution. However, the use of a non-Gaussian likelihood would incur the need for a computationally expensive Bayesian approximate computation in the posterior inferences. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function, and accordingly, the likelihood contains bias terms to explain the degree of deviations from the regression function. We entail how the biases can be estimated accurately with other hyperparameters by a regularized maximum likelihood estimation. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem with analytical forms of the predictive mean and variance estimates. Therefore, the proposed approach is simple and very computationally attractive. It also gives a very robust and accurate GP estimate for many tested scenarios. For the numerical evaluation, we perform a comprehensive simulation study to evaluate the proposed approach with the comparison to the existing robust GP approaches under various simulated scenarios of different outlier proportions and different noise levels. The approach is applied to data from two measurement systems, where the predictors are based on robust environmental parameter measurements and the response variables utilize more complex chemical sensing methods that contain a certain percentage of outliers. The utility of the measurement systems and value of the environmental data are improved through the computationally efficient GP regression and bias model.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Variable selection for Gaussian process regression through a sparse projection

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance between the projected features. The sparse projection matrix is considered as an unknown parameter. We propose a forward stagewise approach with embedded gradient descent steps to co-optimize the parameter with other covariance parameters based on the maximization of a non-convex marginal likelihood function with a concave sparsity penalty, and some convergence properties of the algorithm are provided. The proposed model covers a broader class of stationary covariance functions than the existing automatic relevance determination approaches, and the solution approach is more computationally feasible than the existing MCMC sampling procedures for the automatic relevance parameter estimation with a sparsity prior. The approach is evaluated for a large number of simulated scenarios. The choice of tuning parameters and the accuracy of the parameter estimation are evaluated with the simulation study. In the comparison to some chosen benchmark approaches, the proposed approach has provided a better accuracy in the variable selection. It is applied to an important problem of identifying environmental factors that affect an atmospheric corrosion of metal alloys.

0 citations0 reviewsNo code linkedOpen access