publications

2024

1. TMA

   Parallel MCMC algorithms: theoretical foundations, algorithm design, case studies

   Glatt-Holtz, Nathan E, Holbrook, Andrew J, Krometis, Justin A, and Mondaini, Cecilia F

   Transactions of Mathematics and Its Applications 2024

   Abs arXiv HTML

   Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution {}mu \. We build a rigorous foundational framework for pMCMC algorithms that situates these methods within a unified ‘extended phase space’ measure-theoretic formalism. Drawing on our recent work that provides a comprehensive theory for reversible single-proposal methods, we herein derive general criteria for multiproposal acceptance mechanisms that yield ergodic chains on general state spaces. Our formulation encompasses a variety of methodologies, including proposal cloud resampling and Hamiltonian methods, while providing a basis for the derivation of novel algorithms. In particular, we obtain a top-down picture for a class of methods arising from ‘conditionally independent’ proposal structures. As an immediate application of this formalism, we identify several new algorithms including a multiproposal version of the popular preconditioned Crank–Nicolson (pCN) sampler suitable for high- and infinite-dimensional target measures that are absolutely continuous with respect to a Gaussian base measure. To supplement the aforementioned theoretical results, we carry out a selection of numerical case studies that evaluate the efficacy of these novel algorithms. First, noting that the true potential of pMCMC algorithms arises from their natural parallelizability and the ease with which they map to modern high-performance computing architectures, we provide a limited parallelization study using TensorFlow and a graphics processing unit to scale pMCMC algorithms that leverage as many as 100k proposals at each step. Second, we use our multiproposal pCN algorithm (mpCN) to resolve a selection of problems in Bayesian statistical inversion for partial differential equations motivated by fluid measurement. These examples provide preliminary evidence of the efficacy of mpCN for high-dimensional target distributions featuring complex geometries and multimodal structures.

2. NEJ

   Maximizing the Use of Data to Make Winning Decisions in the Face of Finite Resources

   Risher, Kyle, Wolodkin, Daniel, Krometis, Justin, Sieck, Victoria, Freeman, Laura, Werner, Jeremy, and Hobson, Sandra

   Naval Engineers Journal 2024

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   Data collected across the acquisition life cycle, under different conditions, are not always used to maximize the knowledge about the operational performance of Department of Defense (DoD) systems. In the case of an acquisition process intended to deliver warfighting capabilities to address critical operational gaps, all data can and should improve knowledge about the system and must be leveraged to help authorities make the most informed decisions. Care must be given to how such data are used though to avoid their misuse potentially leading to incorrect conclusions and misinformed decisions. This article describes such challenges and introduces key analytical concepts based on math, science, statistics, and software engineering intended to maximize the information extracted from all data collected throughout the acquisition process. This article demonstrates the utility of those concepts on an example focused on the test and evaluation of the operational availability of a notional torpedo.

3. GJI

   A tale of two faults: Statistical reconstruction of the 1820 Flores Sea earthquake using tsunami observations alone

   Paskett, T, Whitehead, J P, Harris, R A, Ashcraft, C, Krometis, J A, Sorensen, I, and Wonnacott, R

   Geophysical Journal International 2024

   Abs arXiv HTML

   Using a Bayesian approach we compare anecdotal tsunami runup observations from the 29 December 1820 Flores Sea earthquake with close to 200,000 tsunami simulations to determine the most probable earthquake parameters causing the tsunami. Using a dual hypothesis of the source earthquake either originating from the Flores Thrust or the Walanae/Selayar Fault, we found that neither source perfectly matches the observational data, particularly while satisfying seismic constraints of the region. Instead both posteriors have shifted to the edge of the prior indicating that the actual earthquake may have run along both faults.

2023

1. AAP

   On the accept–reject mechanism for Metropolis–Hastings algorithms

   Glatt-Holtz, Nathan, Krometis, Justin, and Mondaini, Cecilia

   The Annals of Applied Probability 2023

   Abs arXiv HTML

   This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis–Hastings-type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling methods with more complicated “extended phase space” algorithms based around ideas from Hamiltonian dynamics. Our starting point is an abstract result developed in the generality of measurable state spaces that addresses proposal kernels that possess a certain involution structure. Note that, while this underlying proposal structure suggests a scope which includes Hamiltonian-type kernels, we demonstrate that our abstract result is, in an appropriate sense, equivalent to an earlier general state space setting developed in (Ann. Appl. Probab. 8 (1998) 1–9) where the connection to Hamiltonian methods was more obscure. On the basis of our abstract results we develop several new classes of extended phase space, HMC-like algorithms. First we tackle the classical finite-dimensional setting of a continuously distributed target measure. We then consider an infinite-dimensional framework for targets which are absolutely continuous with respect to a Gaussian measure with a trace-class covariance. Each of these algorithm classes can be viewed as “surrogate-trajectory” methods, providing a versatile methodology to bypass expensive gradient computations through skillful reduced order modeling and/or data driven approaches as we begin to explore in a forthcoming companion work (Glatt-Holtz et al. (2023)). On the other hand, along with the connection of our main abstract result to the framework in (Ann. Appl. Probab. 8 (1998) 1–9), these algorithm classes provide a unifying picture connecting together a number of popular existing algorithms which arise as special cases of our general frameworks under suitable parameter choices. In particular we show that, in the finite-dimensional setting, we can produce an algorithm class which includes the Metropolis adjusted Langevin algorithm (MALA) and random walk Metropolis method (RWMC) alongside a number of variants of the HMC algorithm including the geometric approach introduced in (J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 (2011) 123–214). In the infinite-dimensional situation, we show that the algorithm class we derive includes the preconditioned Crank–Nicolson (pCN), ∞MALA and ∞HMC methods considered in (Stoch. Dyn. 8 (2008) 319–350; Stochastic Process. Appl. 121 (2011) 2201–2230; Statist. Sci. 28 (2013) 424–446) as special cases.

2. IP

   A statistical framework for domain shape estimation in Stokes flows

   Borggaard, Jeff, Glatt-Holtz, Nathan E., and Krometis, Justin

   Inverse Problems 2023

   Abs arXiv HTML

   We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this ‘uncertainty’ can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov chain Monte Carlo algorithms designed to resolve infinite-dimensional statistical quantities.

3. CAMWA

   A numerical comparison of simplified Galerkin and machine learning reduced order models for vaginal deformations

   Snyder, William, Anaya, Alex Santiago, Krometis, Justin, Iliescu, Traian, and De Vita, Raffaella

   Computers & Mathematics with Applications 2023

   Abs HTML

   High-fidelity computer simulations of childbirth remain prohibitively expensive and time consuming, making them impractical for guiding decision-making during obstetric emergencies. Cheap computer simulations that preserve the accuracy of high-fidelity models can be developed using surrogate modeling. Two common approaches to surrogate modeling are physics-based reduced order modeling (ROM) and machine learning (ML), with the latter gaining popularity as the scientific computing community seeks to leverage advances from other, mostly non-physics-based, computational strategies. Although ROM and ML have been compared for various problems, to our knowledge, such a comparison for simulations of vaginal deformations is currently missing. This study provides a baseline numerical comparison between methods from these two fundamentally different approaches. Since there are many methods falling into each modeling approach, to provide a fair and natural comparison, we select a basic model from each category, with each allowing (i) a straightforward implementation in commercial software packages, and (ii) use by practitioners with limited experience in the field. As a benchmark for the numerical comparison of the ROM and ML approaches, we use the finite element (FE) modeling of the ex vivo deformations of rat vaginal tissue subjected to inflation testing to study the effect of a pre-imposed tear. From the ROM strategies, we consider a simplified Galerkin ROM (G-ROM) that is based on the linearization of the underlying nonlinear equations. From the ML strategies, we select a feed-forward neural network to create mappings from constitutive model parameters and luminal pressure values to either the FE displacement history (in which case we denote the resulting model ML) or the proper orthogonal decomposition (POD) coefficients of the displacement history (in which case we denote the resulting model POD-ML). The numerical investigation of G-ROM, ML, and POD-ML takes place in the reconstructive regime. The numerical results show that the G-ROM outperforms the ML model in terms of offline central processing unit (CPU) time for model training, online CPU time required to generate approximations, and relative error with respect to the FE models. The G-ROM achieves superior error performance to the best ML model with 11 POD basis functions. With higher-dimensional POD bases, the G-ROM achieves a relative error 3 orders of magnitude lower than that of the best ML model with an online CPU time still on the same order of magnitude as the best ML model. The POD-ML model improves on the speed performance of the ML, having online CPU times comparable to those of the G-ROM given the same size of POD bases. However, the POD-ML model does not improve on the error performance of the ML and is still outperformed by the G-ROM for POD bases of size greater than 11. This baseline numerical investigation serves as a starting point for future computer simulations that consider state-of-the-art G-ROM and ML strategies, and the in vivo geometry, boundary conditions, and material properties of the human vagina, as well as their changes during labor.

2022

1. MAKE

   Improving Deep Learning for Maritime Remote Sensing through Data Augmentation and Latent Space

   Sobien, Daniel, Higgins, Erik, Krometis, Justin, Kauffman, Justin, and Freeman, Laura

   Machine Learning and Knowledge Extraction 2022

   Abs HTML

   Training deep learning models requires having the right data for the problem and understanding both your data and the models’ performance on that data. Training deep learning models is difficult when data are limited, so in this paper, we seek to answer the following question: how can we train a deep learning model to increase its performance on a targeted area with limited data? We do this by applying rotation data augmentations to a simulated synthetic aperture radar (SAR) image dataset. We use the Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction technique to understand the effects of augmentations on the data in latent space. Using this latent space representation, we can understand the data and choose specific training samples aimed at boosting model performance in targeted under-performing regions without the need to increase training set sizes. Results show that using latent space to choose training data significantly improves model performance in some cases; however, there are other cases where no improvements are made. We show that linking patterns in latent space is a possible predictor of model performance, but results require some experimentation and domain knowledge to determine the best options.

2021

1. JGR

   Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis: a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami

   Ringer, Hayden, Whitehead, Jared P, Krometis, Justin, Harris, Ronald A, Glatt-Holtz, Nathan, Giddens, Spencer, Ashcraft, Claire, Carver, Garret, Robertson, Adam, Harward, McKay, and others,

   Journal of Geophysical Research 2021

   arXiv HTML
2. Embracing Uncertainty in “Small Data” Problems: Estimating Earthquakes from Historical Anecdotes

   Krometis, Justin A, Ringer, Hayden J, Whitehead, Jared P, Glatt-Holtz, Nathan E, and Harris, Ronald A

   arXiv preprint arXiv:2106.07797 2021

   arXiv
3. IJERPH

   The demographics of SDWA compliance in Virginia community water systems

   Marcillo, Cristina, Krometis, Leigh-Anne, and Krometis, Justin

   International Journal of Environmental Research and Public Health 2021

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2020

1. AAP

   On Bayesian Consistency for Flows Observed Through a Passive Scalar

   Borggaard, Jeff, Glatt-Holtz, Nathan, and Krometis, Justin

   Annals of Applied Probability 2020

   arXiv HTML
2. JUQ

   A Bayesian Approach to Estimating Background Flows from a Passive Scalar

   Borggaard, Jeff, Glatt-Holtz, Nathan, and Krometis, Justin

   SIAM/ASA Journal on Uncertainty Quantification 2020

   arXiv HTML

2019

1. JCP

   GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for Inverse Problems Constrained by Diffusion PDEs

   Borggaard, Jeff, Glatt-Holtz, Nathan, and Krometis, Justin

   Journal of Computational Physics 2019

   arXiv HTML

2018

1. Thesis

   A Bayesian Approach to Estimating Background Flows from a Passive Scalar

   Krometis, Justin

   2018

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2011

1. TRB

   Site considerations for points of dispensing after biological terrorist attack: integrated role of transportation planning and medical services

   Ma, Yongchang, Willauer, David, Krometis, Justin, Sen, Atri, and Baccam, Sid

   Transportation Research Record: Journal of the Transportation Research Board 2011

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2005

1. EPL

   Will jams get worse when slow cars move over?

   Schmittmann, Beate, Krometis, Justin, and Zia, Royce KP

   Europhysics Letters 2005

   arXiv HTML

2004

1. Thesis

   Lane preference in a simple traffic model

   Krometis, Justin

   2004

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