Mapping model validation metrics to subject matter expert scores for model adequacy assessment. - Kirubel Teferra; Michael D. Shields; Adam Hapij; Raymond P. Daddazio (Reliab. Eng. Syst. Saf., 2014)

Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification. - Michael D. Shields; Kirubel Teferra; Adam Hapij; Raymond P. Daddazio (Reliab. Eng. Syst. Saf., 2015)

The generalization of Latin hypercube sampling. - Michael D. Shields; Jiaxin Zhang 005 (Reliab. Eng. Syst. Saf., 2016)

Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis. - Anindya Bhaduri; Yanyan He; Michael D. Shields; Lori Graham-Brady; Robert M. Kirby (J. Comput. Phys., 2018)

Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations. - Dimitris G. Giovanis; Michael D. Shields (J. Comput. Phys., 2018)

Adaptive Monte Carlo analysis for strongly nonlinear stochastic systems. - Michael D. Shields (Reliab. Eng. Syst. Saf., 2018)

Uncertainty quantification (UQ) as an archetype for research: Integrating UQ into undergraduate research education. - B. S. Aakash; D. Perez-Roldan; A. Ibrahim; Michael D. Shields (FIE, 2019)

Budgeting, Psychological Contracts, and Budgetary Misreporting. - Susanna Gallani; Ranjani Krishnan; Eric J. Marinich; Michael D. Shields (Manag. Sci., 2019)

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold. - Dimitris G. Giovanis; Michael D. Shields (CoRR, 2020)

On the quantification and efficient propagation of imprecise probabilities with copula dependence. - Jiaxin Zhang 005; Michael D. Shields (Int. J. Approx. Reason., 2020)

UQpy: A general purpose Python package and development environment for uncertainty quantification. - Audrey Olivier; Dimitris G. Giovanis; B. S. Aakash; Mohit Singh Chauhan; Lohit Vandanapu; Michael D. Shields (J. Comput. Sci., 2020)

Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models. - Katiana Kontolati; Dimitrios Loukrezis; Ketson R. M. dos Santos; Dimitrios G. Giovanis; Michael D. Shields (CoRR, 2021)

Deep transfer learning for partial differential equations under conditional shift with DeepONet. - Somdatta Goswami; Katiana Kontolati; Michael D. Shields; George Em Karniadakis (CoRR, 2022)

Bayesian Inference with Latent Hamiltonian Neural Networks. - Somayajulu L. N. Dhulipala; Yifeng Che; Michael D. Shields (CoRR, 2022)

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference. - Somayajulu L. N. Dhulipala; Yifeng Che; Michael D. Shields (CoRR, 2022)

General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation. - Promit Chakroborty; Somayajulu L. N. Dhulipala; Yifeng Che; Wen Jiang 003; Benjamin W. Spencer; Jason D. Hales; Michael D. Shields (CoRR, 2022)

Active learning with multifidelity modeling for efficient rare event simulation. - Somayajulu L. N. Dhulipala; Michael D. Shields; Benjamin W. Spencer; Chandrakanth Bolisetti; Andrew E. Slaughter; Vincent M. Laboure; Promit Chakroborty (J. Comput. Phys., 2022)

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems. - Katiana Kontolati; Dimitrios Loukrezis; Dimitrios G. Giovanis; Lohit Vandanapu; Michael D. Shields (J. Comput. Phys., 2022)

Reliability estimation of an advanced nuclear fuel using coupled active learning, multifidelity modeling, and subset simulation. - Somayajulu L. N. Dhulipala; Michael D. Shields; Promit Chakroborty; Wen Jiang 003; Benjamin W. Spencer; Jason D. Hales; Vincent M. Laboure; Zachary M. Prince; Chandrakanth Bolisetti; Yifeng Che (Reliab. Eng. Syst. Saf., 2022)

Grassmannian Diffusion Maps-Based Dimension Reduction and Classification for High-Dimensional Data. - Ketson R. M. dos Santos; Dimitrios G. Giovanis; Michael D. Shields (SIAM J. Sci. Comput., 2022)

Deep transfer operator learning for partial differential equations under conditional shift. - Somdatta Goswami; Katiana Kontolati; Michael D. Shields; George Em Karniadakis (Nat. Mac. Intell., 2022)

Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion. - Lukás Novák; Michael D. Shields; Václav Sadílek; Miroslav Vorechovský (CoRR, 2023)

Learning in latent spaces improves the predictive accuracy of deep neural operators. - Katiana Kontolati; Somdatta Goswami; George Em Karniadakis; Michael D. Shields (CoRR, 2023)

On the influence of over-parameterization in manifold based surrogates and deep neural operators. - Katiana Kontolati; Somdatta Goswami; Michael D. Shields; George Em Karniadakis (J. Comput. Phys., 2023)

Efficient Bayesian inference with latent Hamiltonian neural networks in No-U-Turn Sampling. - Somayajulu L. N. Dhulipala; Yifeng Che; Michael D. Shields (J. Comput. Phys., 2023)

UQpy v4.1: Uncertainty quantification with Python. - Dimitrios Tsapetis; Michael D. Shields; Dimitris G. Giovanis; Audrey Olivier; Lukás Novák; Promit Chakroborty; Himanshu Sharma; Mohit Singh Chauhan; Katiana Kontolati; Lohit Vandanapu; Dimitrios Loukrezis; Michael Gardner (SoftwareX, 2023)

Reliability Analysis of Complex Systems using Subset Simulations with Hamiltonian Neural Networks. - Denny Thaler; Somayajulu L. N. Dhulipala; Franz Bamer; Bernd Markert; Michael D. Shields (CoRR, 2024)

Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification. - Himanshu Sharma; Lukás Novák; Michael D. Shields (CoRR, 2024)

Bayesian neural networks for predicting uncertainty in full-field material response. - George D. Pasparakis; Lori Graham-Brady; Michael D. Shields (CoRR, 2024)

A Resolution Independent Neural Operator. - Bahador Bahmani; Somdatta Goswami; Ioannis G. Kevrekidis; Michael D. Shields (CoRR, 2024)

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification. - Dimitris G. Giovanis; Dimitrios Loukrezis; Ioannis G. Kevrekidis; Michael D. Shields (J. Comput. Phys., 2024)

Physics-informed polynomial chaos expansions. - Lukás Novák; Himanshu Sharma; Michael D. Shields (J. Comput. Phys., 2024)

On active learning for Gaussian process-based global sensitivity analysis. - Mohit Singh Chauhan; Mariel Ojeda-Tuz; Ryan Catarelli; Kurtis R. Gurley; Dimitrios Tsapetis; Michael D. Shields (Reliab. Eng. Syst. Saf., 2024)

Simulation of non-Gaussian wind field as a 3rd-order stochastic wave. - Lohit Vandanapu; Michael D. Shields (Reliab. Eng. Syst. Saf., 2024)

Neural chaos: A spectral stochastic neural operator. - Bahador Bahmani; Ioannis G. Kevrekidis; Michael D. Shields (J. Comput. Phys., 2025)

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis. - Promit Chakroborty; Somayajulu L. N. Dhulipala; Michael D. Shields (SIAM/ASA J. Uncertain. Quantification, 2025)

Synergistic learning with multi-task DeepONet for efficient PDE problem solving. - Varun Kumar; Somdatta Goswami; Katiana Kontolati; Michael D. Shields; George Em Karniadakis (Neural Networks, 2025)

Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards. - Somdatta Goswami; Dimitris G. Giovanis; Bowei Li; Seymour M. J. Spence; Michael D. Shields (CoRR, 2025)

Joint space-time wind field data extrapolation and uncertainty quantification using nonparametric Bayesian dictionary learning. - George D. Pasparakis; Ioannis A. Kougioumtzoglou; Michael D. Shields (CoRR, 2025)

Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators. - Ponkrshnan Thiagarajan; Tamer A. Zaki; Michael D. Shields (CoRR, 2025)