About

Michael Shields is a professor in the Department of Civil and Systems Engineering at Johns Hopkins University, with a secondary appointment in the Department of Materials Science and Engineering. He is a fellow in the Hopkins Extreme Materials Institute and a member of the Data Science and AI Institute. Shields serves as the director of the Center on High-Throughput Materials Discovery for Extremes and is part of the leadership team for the Center on Artificial Intelligence for Materials in Extreme Environments. His research focuses on uncertainty quantification for problems in computational mechanics and computational materials science, utilizing machine learning and stochastic methods to understand the effects of uncertainties and random variations on the performance of materials and structures. His work aims to improve the reliability of structures and materials during extreme events such as fires, earthquakes, high winds, shocks, blasts, and impacts, especially where computational efficiency is critical and system behavior is highly unpredictable. Shields’ group, known as the Shields Uncertainty Research Group (SURG), develops open-source software like UQPy to model uncertainty in physical and mathematical systems, employing approaches such as polynomial chaos expansions, Gaussian process regression, neural networks, and Monte Carlo methods. His research has been funded by multiple agencies including the NSF, Office of Naval Research, Army Research Laboratory, and others. Shields has received numerous awards, including the 2025 Early Achievement Research Award from the International Association for Structural Safety and Reliability, the Department of Energy Early Career Award, NSF CAREER Award, and ONR Young Investigator Award. He holds dual bachelor’s degrees in physics and civil engineering, earned in 2006, and completed his PhD in civil engineering and engineering mechanics at Columbia University in 2010. Prior to joining Johns Hopkins in 2013, he was a research engineer at Weidlinger Associates, Inc. Shields is actively involved in professional organizations, serving as chair of the Machine Learning in Mechanics Committee for the Engineering Mechanics Institute of the American Society of Civil Engineers and vice chair of the Uncertainty Quantification and Probabilistic Modeling Technical Thrust Area for the U.S. Association for Computational Mechanics.

Research topics

• Computer Science
• Machine Learning
• Artificial Intelligence
• Mathematics
• Algorithm
• Data Mining
• Physics
• Statistics
• Computational science
• Programming language
• Mathematical optimization
• Nuclear engineering
• Applied mathematics
• Theoretical computer science
• Pure mathematics
• Mathematical analysis
• Engineering
• Nuclear physics

Selected publications

• Physics-informed Polynomial Chaos Expansion with Enhanced Constrained Optimization Solver and D-optimal Sampling

  SSRN Electronic Journal · 2026-01-01

  preprintOpen access
  PublisherDOI

• Polynomial chaos expansion for operator learning

  Computer Methods in Applied Mechanics and Engineering · 2026-02-12

  articleSenior authorCorresponding
  PublisherDOI

• Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Models

  arXiv (Cornell University) · 2026-01-06

  preprintOpen accessSenior author

  Understanding and modeling the constitutive behavior of concrete is crucial for civil and defense applications, yet widely used phenomenological models such as Karagozian \& Case concrete (KCC) model depend on empirically calibrated failure surfaces that lack flexibility in model form and associated uncertainty quantification. This work develops a physics-informed framework that retains the modular elastoplastic structure of KCC model while replacing its empirical failure surface with a constrained Gaussian Process Regression (GPR) surrogate that can be learned directly from experimentally accessible observables. Triaxial compression data under varying confinement levels are used for training, and the surrogate is then evaluated at confinement levels not included in the training set to assess its generalization capability. Results show that an unconstrained GPR interpolates well near training conditions but deteriorates and violates essential physical constraints under extrapolation, even when augmented with simulated data. In contrast, a physics-informed GPR that incorporates derivative-based constraints aligned with known material behavior yields markedly better accuracy and reliability, including at higher confinement levels beyond the training range. Probabilistic enforcement of these constraints also reduces predictive variance, producing tighter confidence intervals in data-scarce regimes. Overall, the proposed approach delivers a robust, uncertainty-aware surrogate that improves generalization and streamlines calibration without sacrificing the interpretability and numerical efficiency of the KCC model, offering a practical path toward an improved constitutive models for concrete.

  PublisherDOI

• Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Models

  ArXiv.org · 2026-01-06

  articleOpen accessSenior author

  Understanding and modeling the constitutive behavior of concrete is crucial for civil and defense applications, yet widely used phenomenological models such as Karagozian \& Case concrete (KCC) model depend on empirically calibrated failure surfaces that lack flexibility in model form and associated uncertainty quantification. This work develops a physics-informed framework that retains the modular elastoplastic structure of KCC model while replacing its empirical failure surface with a constrained Gaussian Process Regression (GPR) surrogate that can be learned directly from experimentally accessible observables. Triaxial compression data under varying confinement levels are used for training, and the surrogate is then evaluated at confinement levels not included in the training set to assess its generalization capability. Results show that an unconstrained GPR interpolates well near training conditions but deteriorates and violates essential physical constraints under extrapolation, even when augmented with simulated data. In contrast, a physics-informed GPR that incorporates derivative-based constraints aligned with known material behavior yields markedly better accuracy and reliability, including at higher confinement levels beyond the training range. Probabilistic enforcement of these constraints also reduces predictive variance, producing tighter confidence intervals in data-scarce regimes. Overall, the proposed approach delivers a robust, uncertainty-aware surrogate that improves generalization and streamlines calibration without sacrificing the interpretability and numerical efficiency of the KCC model, offering a practical path toward an improved constitutive models for concrete.

  PublisherOA PDF

• Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves

  arXiv (Cornell University) · 2026-01-10

  preprintOpen accessSenior author

  A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a probabilistic Taylor series expansion in conjunction with the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. This work is motivated by the need to investigate shock-driven material response for materials discovery and for offering mechanistic insights in regimes where experimental characterizations and simulations are costly. The proposed methodology relies on large-scale molecular dynamics which are an accurate but expensive computational alternative to experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and atomic-level simulations are performed using a reverse ballistic approach together with appropriate interatomic potentials. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior.

  PublisherDOI

• Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves

  ArXiv.org · 2026-01-10

  articleOpen accessSenior author

  A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a probabilistic Taylor series expansion in conjunction with the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. This work is motivated by the need to investigate shock-driven material response for materials discovery and for offering mechanistic insights in regimes where experimental characterizations and simulations are costly. The proposed methodology relies on large-scale molecular dynamics which are an accurate but expensive computational alternative to experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and atomic-level simulations are performed using a reverse ballistic approach together with appropriate interatomic potentials. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior.

  PublisherOA PDF

• Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators

  ArXiv.org · 2025-07-19

  preprintOpen accessSenior author

  Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network's parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. We show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

  PublisherOA PDFDOI

• UQpy Version 4.2: Uncertainty quantification with Python

  SoftwareX · 2025-09-25

  articleOpen accessSenior authorCorresponding

  We introduce a new module for the UQpy software package which extends its capabilities into the field of Scientific Machine Learning. This module builds on PyTorch to create a flexible and robust platform for uncertainty quantification in machine learning. The scientific machine learning module of UQpy introduces custom layers, neural networks, and neural network trainers that are compatible with torch version 2.2.2 and allow for “plug and play” integration into existing torch code.

  PublisherDOI

• Joint space-time wind field data extrapolation and uncertainty quantification using nonparametric Bayesian dictionary learning

  ArXiv.org · 2025-07-15

  preprintOpen accessSenior author

  A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing sparse/incomplete measured data, a time-dependent optimization problem is formulated for determining the expansion coefficients of an associated low-dimensional representation of the stochastic wind field. Compared to an alternative, standard, compressive sampling treatment of the problem, the developed methodology exhibits the following advantages. First, the Bayesian formulation enables also the quantification of the uncertainty in the estimates. Second, the requirement in standard CS-based applications for an a priori selection of the expansion basis is circumvented. Instead, this is done herein in an adaptive manner based on the acquired data. Overall, the methodology exhibits enhanced extrapolation accuracy, even in cases of high-dimensional data of arbitrary form, and of relatively large extrapolation distances. Thus, it can be used, potentially, in a wide range of wind engineering applications where various constraints dictate the use of a limited number of sensors. The efficacy of the methodology is demonstrated by considering two case studies. The first relates to the extrapolation of simulated wind velocity records consistent with a prescribed joint wavenumber-frequency power spectral density in a three-dimensional domain (2D and time). The second pertains to the extrapolation of four-dimensional (3D and time) boundary layer wind tunnel experimental data that exhibit significant spatial variability and non-Gaussian characteristics.

  PublisherOA PDFDOI

• Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards

  arXiv (Cornell University) · 2025-02-16

  preprintOpen accessSenior author

  Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. In this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and wind. Specifically, we propose two architectures, a self-adaptive FNO and a Fast Fourier Transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Wind Tunnel Modeling of Higher-Order Turbulence and its Effects on Structural Loads and Response

  NSF · $319k · 2019–2024

• CAREER: Higher-Order Methods for Nonlinear Stochastic Structural Dynamics

  NSF · $500k · 2017–2023

• GOALI: Improving the Reliability of Aluminum Structures During Fire Through Computational Modeling

  NSF · $359k · 2014–2018

Frequent coauthors

• Joan L. Luft

  Michigan State University

  26 shared

• Dimitris G. Giovanis

  Johns Hopkins University

  23 shared

• Somayajulu L. N. Dhulipala

  20 shared

• Promit Chakroborty

  16 shared

• Katiana Kontolati

  Johns Hopkins University

  16 shared

• Yifeng Che

  13 shared

• George Deodatis

  12 shared

• Lori Graham‐Brady

  11 shared

Awards & honors

• 2025 Early Achievement Research Award from the International…
• Department of Energy Early Career Award
• NSF CAREER Award
• ONR Young Investigator Award
• IASSAR Early Achievement Award