In the event of a nuclear accident or the detonation of a radiological dispersal device, quickly locating the source of the accident or blast is important for emergency response and environmental decontamination. At a specified time after a simulated instantaneous release of an aerosolized radioactive contaminant, measurements are recorded downwind from an array of radiation sensors. Neural networks are employed to infer the source release parameters in an accurate and rapid manner using sensor and mean wind speed data. We consider two neural network constructions that quantify the uncertainty of the predicted values: a categorical classification neural network and a Bayesian neural network. With the categorical classification neural network, we partition the spatial domain and treat each partition as a separate class for which we estimate the probability that it contains the true source location. In a Bayesian neural network, the weights and biases have a distribution rather than a single optimal value. With each evaluation, these distributions are sampled, yielding a different prediction with each evaluation. The trained Bayesian neural network is thus evaluated to construct posterior densities for the release parameters. Results are compared to Markov chain Monte Carlo (MCMC) results computed using the Delayed Rejection Adaptive Metropolis Algorithm. The Bayesian neural network approach is generally much cheaper computationally than the MCMC approach as it relies on the computational cost of the neural network evaluation to generate posterior densities as opposed to the MCMC approach which depends on the computational expense of the transport and radiation detection models.

The rapid localization of radioactive material in an urban environment is of critical importance to secure radiological sources and prevent radiological attacks. We consider the inverse problem of inferring the three-dimensional location of stationary and moving radiation sources given a set of measurements from an array of radiation sensors. A feedforward neural network is employed to quickly infer the location of the radioactive source. We optimize the weights of the neural network using Nadam gradient-based optimization. This method of source localization lacks the prediction intervals given by other techniques, such as Bayesian inference, but it is extremely fast, so it enables real-time predictions. We utilize this advantage to track the position of a moving radioactive source within a simulated urban environment.

Physiologically based pharmacokinetic (PBPK) models use a mechanistic approach to delineate the processes of the absorption, distribution, metabolism and excretion of biological substances in various species. These models generally comprise coupled systems of ordinary differential equations involving multiple states and a moderate to a large number of parameters. Such models contain compartments corresponding to various organs or tissues in the body. Before employing the models for treatment, the quantification of uncertainties for the parameters, based on a priori information or data for a specific response, is necessary. This requires the determination of identifiable parameters, which are uniquely determined by data, and uncertainty analysis based on frequentist or Bayesian inference. We introduce a strategy to integrate parameter subset selection, based on identifiability analysis, with Bayesian inference. This approach further refines the subset of identifiable parameters, quantifies parameter and response uncertainties, enhances model prediction and reduces computational cost.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 1)'.

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as "fluidization" of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D'Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D'Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D'Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

In this paper, we employ a Bayesian approach to assess the reliability of a critical component in the Mars Sample Return program, focusing on the Earth Entry System's risk of containment not assured upon reentry. Our study uses Gaussian Process modeling under a Bayesian regime to analyze the Earth Entry System's resilience against operational stress. This Bayesian framework allows for a detailed probabilistic evaluation of the risk of containment not assured, indicating the feasibility of meeting the mission's stringent safety goal of 0.999999 probability of success. The findings underscore the effectiveness of Bayesian methods for complex uncertainty quantification analyses of computer simulations, providing valuable insights for computational reliability analysis in a risk-averse setting.

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models.

In this paper, we employ a Bayesian approach to uncertainty quantification of computer simulations used to assess the probability of rare events. As a case study, we assess the reliability of an Earth reentry capsule for sample return missions that must be able to withstand the reentry loads in order to land intact. Our study uses Gaussian Process modeling under a Bayesian regime to analyze the reentry vehicle's resilience against operational stress. This Bayesian framework allows for a detailed probabilistic evaluation of the system's reliability, indicating our ability to verify stringent safety goals of rare events with a 0.999999 of probability of success. The findings underscore the effectiveness of Bayesian methods for complex uncertainty quantification analyses of computer simulations, providing valuable insights for computational reliability analysis in a risk-averse setting.

Deep learning models often produce accurate classifiers but do not always produce outputs that are easily interpretable by decision-makers or appropriate estimates of uncertainty or confidence for the classification decision. Furthermore, for some larger architectures, existing uncertainty quantification (UQ) approaches can be computationally expensive. In this paper, we propose two new variational inference loss functions for fitting deep learning classification models and obtaining approximate Bayesian uncertainty quantification. Using text and image datasets, we demonstrate that the proposed framework is more computationally tractable than standard UQ approaches like dropout, and, compared with the competing approaches we consider, yields outputs that better reflect our prior conception of class similarity making the outputs more interpretable and easier to explain to decision-makers. We also demonstrate that the proposed framework balances producing well-calibrated class probabilities with producing posterior credible sets for the class labels that have appropriate coverage.

Fluid reduced-order models (ROMs) that qualify the flow physics within the problem’s physical domain are usually constrained in accuracy to only the parameter points; e.g., Reynolds and Mach numbers, at which reference data were provided. Interpolation-focused quantity-of- interest ROMs are often structured differently and fail to provide flow volume data with the same quality – if at all. In this paper, techniques that reside at the intersection of these two ROM schools – flow physics ROMs that can be interpolated within a parameter space of interest – are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points that are not provided in the ROM training data.

This book provides a self-contained introduction to control and estimator design for distributed parameter systems. Although there exist previous texts on this topic, there are several features that make this text very timely and unique. The text provides a mathematically rigorous framework for control and estimator design for distributed parameter systems. To make the material accessible to a wide range of readers, the author rigorously states results without proof and employs a suite of examples to illustrate the theory and demonstrate differences from finite-dimensional theory. To provide the framework required for stability analysis, linear-quadratic control design, disturbance rejection, state estimation, and input–output control design, the text summarizes the required infinite-dimensional systems theory and functional analysis in a chapter and an appendix. To highlight the central role of examples, several of the functional analysis results are illustrated using an example from sampling theory, which should be familiar to many readers. Through its combination of theory, approximation techniques, and examples, the text provides a valuable resource for both instructors and readers seeking a self-contained introduction to control and estimation for distributed parameter systems.

Presents reviews for the following list of books, (An Applied Mathematician’s Apology, Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives, Mathematical Foundations of Finite Elements and Iterative Solvers, Foundations of Computational Imaging: A Model-Based Approach, How To Be Creative: A Practical Guide for the Mathematical Sciences, A Toolbox For Digital Twins: From Model-Based to Data-Driven, and A Variational Approach to Optimal Control of ODEs).

Sensitivity analysis for computational fluid dynamics (CFD) simulations is a complicated procedure, which still relies, in many cases, on engineering judgment and factors of safety. This is in part because the computational cost of quantifying the simulation’s sensitivity to all meaningful parameters (e.g., body surface roughness) and hyperparameters (e.g., subiteration convergence criterion) is intractable for even a single simulation. Reduced-order modeling dramatically lowers this computational cost of simulating fluid flows, but usually only where similar data are already available. In this work, fluid reduced-order models are utilized to quantify flow sensitivity to certain physical parameters for the purposes of improved sensitivity analysis. Characteristic observability and sensitivity are both explored. The sensitivity results enable more informed CFD frameworks and more rigorous uncertainty bounds on the resulting data.

We advocate a numerically reliable and accurate approach for practical parameter identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead of computing an eigenvalue decomposition of the Fischer information matrix. Identifiability analysis via CSS has three advantages: (i) It quantifies reliability of the subsets of parameters selected as identifiable and unidentifiable. (ii) It establishes criteria for comparing the accuracy of different algorithms. (iii) The implementations are numerically more accurate and reliable than eigenvalue methods applied to the Fischer matrix, yet without an increase in computational cost. The effectiveness of the CSS methods is illustrated with extensive numerical experiments on sensitivity matrices from six physical models, as well as on adversarial synthetic matrices. Among the CSS methods, we recommend an implementation based on the strong rank-revealing QR algorithm because of its rigorous accuracy guarantees for both identifiable and non-identifiable parameters.

We investigate here effects of adaptations like dimension reduction, omission of parameter correlation, and grid refinement on parameter influence over material temperature response and total recession. The task is accomplished by applying Morris screening and method of Sobol' sensitivity studies applied to a range of 3-D, 1-D, and 1-D TC1-driver cases for the MSL entry through the Martian atmosphere, where the material response of the MSL heat shield is simulated with NASA's PATO toolbox. Results of the investigation show that lower-dimensional approaches can, in some cases, be utilized for initial parameter screening prior to execution of a fully-detailed simulation, but in general, obtained sensitivities differ. Moreover, coarse computational grids do not impose significantly distinct input-output mechanics and can be utilized for accurate screening and quantitative sensitivity analysis exercises even with non-negligible residual values. The investigation also discusses the implications of an unknown correlation structure on parameter sensitivities while finding little evidence of significant correlation effects on parameter classification given input uncertainty bounds defined in this work.

. We advocate a numerically reliable and accurate approach for practical parameter 5 identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead of 6 computing an eigenvalue decomposition of the Fischer information matrix. Identifiability analysis 7 via CSS has three advantages: (i) It quantifies reliability of the subsets of parameters selected as 8 identifiable and unidentifiable. (ii) It establishes criteria for comparing the accuracy of different 9 algorithms. (iii) The implementations are numerically more accurate and reliable than eigenvalue 10 methods applied to the Fischer matrix, yet without an increase in computational cost. The effective- 11 ness of the CSS methods is illustrated with extensive numerical experiments on sensitivity matrices 12 from six physical models, as well as on adversarial synthetic matrices. Among the CSS methods, 13 we recommend an implementation based on the strong rank-revealing QR algorithm because of its 14 rigorous accuracy guarantees for both identifiable and non-identifiable parameters. 15

The quantification of uncertainty in intelligent material systems and structures requires methods to objectively compare complex models to measurements, where the majority of cases include multiple model outputs and quantities of interests given multiphysics coupling. This creates questions about constructing appropriate measures of uncertainty during fusion of data and comparisons between data and models. Novel materials with complex or poorly understood coupling can benefit from advanced statistical analysis to judge models in light of multiphysics data. Here, we apply the Maximum Entropy (ME) method to more complicated ferroelectric single crystals containing domain structures and soft electrostrictive membranes under both mechanical and electrical loading. Multiple quantities of interest are considered, which requires fusing heterogeneous information together when quantifying the uncertainty of lower fidelity models. We find that parameters, which were initially unidentifiable using a single quantity of interest, become identifiable using multiple quantities of interest. We also show that posterior densities may broaden or narrow when multiple data sets are fused together. This is likely due to conflict or agreement, respectively, between the different quantities of interest and the multiple model outputs. Such information is important to advance our predictions of intelligent materials and structures from multi-model inputs and heterogeneous data.

The ability to efficiently and accurately localize potentially threatening nuclear radiation sources in urban environments is of critical importance to national security. Techniques to infer the location and intensity of a source using data from a configuration of radiation detectors, and the effectiveness of the source localization depends critically on how the detectors are configured. In this paper, we introduce a framework that uses surrogate models to efficiently compare and optimize different detector configurations. We compare our technique to others and demonstrate its effectiveness for selecting optimal detector configurations in the context of urban source localization.

Dielectric elastomers are employed for a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many cases a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. Accurate estimation of the elastomer’s viscoelastic behavior to quantify parameter uncertainty motivates the use of Markov Chain Monte Carlo (MCMC) methods. Since MCMC is a sampling based method, requiring many model evaluations, efficient estimation of the fractional derivative operator is crucial. In this paper, we demonstrate the effectiveness of using quadrature techniques to approximate the Riemann–Liouville definition for fractional derivatives in the context of estimating the uncertainty of a nonlinear viscoelastic model. We also demonstrate the use of parameter subset selection techniques to isolate parameters that are identifiable in the sense that they are uniquely determined by measured data. For those identifiable parameters, we employ Bayesian inference to compute posterior distributions for parameters. Finally, we propagate parameter uncertainties through the models to compute prediction intervals for quantities of interest.