SEARCH · Engineering Papers

Results for “Bayesian approach”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,621 records · Page 90

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Adaptive Sample Preparation and Target Fabrication for High-Throughput Materials Science

High-repetition-rate brilliant and coherent light sources are significantly increasing the rate at which scientific experiments can be performed. An investment in transformative technologies to make samples of condensed matter could enable a paradigm shift for that field or open new exciting frontiers in high-energy density science (HEDS). This will especially be true for dynamic materials in extremes research or HEDS, where the repetition rate for placing samples into extreme environments is increasing and the samples or targets are irreversibly destroyed in each experiment. Research teams that are able to implement solutions to all aspects of the experimental process and enable a paradigm of high-throughput science will have the greatest success and impact. There are two different directions for adaptive samples. One is research when the number of experiments can be greatly increased with increased volume, such as in high energy density science. The other is when flexibility and agility can aid Bayesian optimization computational methods and speed up the discovery process, as with materials science. Conducting a similar equation-of-state (EOS) experiment took three years on the OMEGA laser facility, compared to five days of shifts at the LCLS XFEL. New materials with improved properties have been found by guided optimization of experimental science. Adaptive sample preparation and target fabrication can create a tremendous return on scientific investment. High-throughput enabling precision science is also a desirable goal. To address these issues, we sought a diverse set of innovative participants who had ideas of how to achieve this paradigm shift. We invited 42 researchers from a variety of disciplines and fields to attend a workshop in College Station, Texas, May 14–16, 2019. Many of the participants had never been in the same room before, and most found it very exciting to hear about new and different research. The goal was twofold: to define the challenges, i.e., “what would we like to be able to do and why it is difficult to do so,” and to describe the progress, approaches and capabilities, as well as the vision, “what we could do if we had more support.”

36 MATERIALS SCIENCE↗

DOE OSTI2020

Dependence of the impurity transport on the dominant turbulent regime in ELM-y H-mode discharges on the DIII-D tokamak

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft X-ray measurements, and VUV spectroscopy provides a detailed uncertainty quantification of transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal 3-fold drop in the impurity confinement time and order of magnitude increase in midradius impurity diffusion, when additional electron heating is applied. Further, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend as electron and carbon density. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO, significantly underpredicts the magnitude of the variation in Al transport. Diffusion increases 3-times steeper with additional electron heat flux and 10-times lower diffusion is observed in ion heated case than predicted by the modeling. Here, the CGYRO model quantitatively matches the increase of the Al diffusion when approaching the linear threshold for the transition from the ion temperature gradient (ITG) to trapped electron mode (TEM).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗

DOE OSTI2015

A Simple Demonstration of Concrete Structural Health Monitoring Framework

Assessment and management of aging concrete structures in nuclear power plants require a more systematic approach than simple reliance on existing code margins of safety. Structural health monitoring of concrete structures aims to understand the current health condition of a structure based on heterogeneous measurements to produce high confidence actionable information regarding structural integrity that supports operational and maintenance decisions. This ongoing research project is seeking to develop a probabilistic framework for health diagnosis and prognosis of aging concrete structures in a nuclear power plant subjected to physical, chemical, environment, and mechanical degradation. The proposed framework consists of four elements—damage modeling, monitoring, data analytics, and uncertainty quantification. This report describes a proof-of-concept example on a small concrete slab subjected to a freeze-thaw experiment that explores techniques in each of the four elements of the framework and their integration. An experimental set-up at Vanderbilt University’s Laboratory for Systems Integrity and Reliability is used to research effective combination of full-field techniques that include infrared thermography, digital image correlation, and ultrasonic measurement. The measured data are linked to the probabilistic framework: the thermography, digital image correlation data, and ultrasonic measurement data are used for Bayesian calibration of model parameters, for diagnosis of damage, and for prognosis of future damage. The proof-of-concept demonstration presented in this report highlights the significance of each element of the framework and their integration.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Factors Affecting Route Selection and Survival of Steelhead Kelts at Snake River Dams in 2012 and 2013

In 2012 and 2013, Pacific Northwest National Laboratory conducted a study that summarized the passage proportions and route-specific survival rates of steelhead kelts that passed through Federal Columbia River Power System (FCRPS) dams. To accomplish this, a total of 811 steelhead kelts were tagged with Juvenile Salmon Acoustic Telemetry System (JSATS) transmitters. Acoustic receivers, both autonomous and cabled, were deployed throughout the FCRPS to monitor the downstream movements of tagged-kelts. Kelts were also tagged with Passive Integrated Transponder tags to monitor passage through juvenile bypass systems and detect returning fish. The current study evaluated data collected in 2012 and 2013 to identify individual, behavioral, environmental and dam operation variables that were related to passage and survival of steelhead kelts that passed through FCRPS dams. Bayesian model averaging of multivariable logistic regression models was used to identify the environmental, temporal, operational, individual, and behavioral variables that had the highest probability of influencing the route of passage and the route-specific survival probabilities for kelts that passed Lower Granite (LGR), Little Goose (LGS), and Lower Monumental (LMN) dams in 2012 and 2013. The posterior probabilities of the best models for predicting route of passage ranged from 0.106 for traditional spill at LMN to 0.720 for turbine passage at LGS. Generally, the behavior (depth and near-dam searching activity) of kelts in the forebay appeared to have the greatest influence on their route of passage. Shallower-migrating kelts had a higher probability of passing via the weir and deeper-migrating kelts had a higher probability of passing via the JBS and turbines than other routes. Kelts that displayed a higher level of near-dam searching activity had a higher probability of passing via the spillway weir and those that did less near-dam searching had a higher probability of passing via the JBS and turbines. The side of the river in which kelts approached the dam and dam operations also affected route of passage. Dam operations and the size and condition of kelts were found to have the greatest effect on route-specific survival probabilities for fish that passed via the spillway at LGS. That is, longer kelts and those in fair condition had a lower probability of survival for fish that passed via the spillway weir. The survival of spillway weir- and deep-spill passed kelts was positively correlated with the percent of the total discharge that passed through turbine unit 4. Too few kelts passed through the traditional spill, JBS, and turbine units to evaluate survival through these routes. The information gathered in this study describes Snake River steelhead kelt passage behavior, rates, and distributions through the FCRPS as well as provide information to biologists and engineers about the dam operations and abiotic conditions that are related to passage and survival of steelhead kelts.

13 HYDRO ENERGY↗

DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization

Bayesian analyses of the full-shape clustering of Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) exhibit prior-volume projection effects, whereby weakly constrained nuisance parameters of the Effective Field Theory of Large Scale Structure (EFTofLSS) shift marginalized cosmological posteriors away from the posterior maximum. We reanalyze DESI DR1 power spectrum multipoles using two complementary mitigation strategies: (i) nonlinear orthogonalization to decorrelate nuisance and cosmological parameter priors, and (ii) a fully reparameterization-invariant Jeffreys prior over all EFTofLSS coefficients, evaluated on-the-fly via closed-form Jacobians. Including data from DESI, Big-Bang Nuclesynthesis and a constraint on $n_{\mathrm{s}}$, baseline priors lead to multi-$σ$ projection in the Hubble parameter $H_{0}$ and dark energy equation of state parameters $w_{0}$ and $w_{a}$; the Jeffreys prior successfully recenters these posteriors to enclose the maximum a posteriori estimate within the 68% credible regions, demonstrating clear mitigation of projection effects for these late-time expansion parameters. A hybrid Jeffreys+baseline-Gaussian configuration controls residual over-broad tails in the physical cold dark matter density $ω_{\mathrm{c}}$ while preserving the volume correction, and is our favoured approach. We compare the credible intervals derived using our methodology to those obtained using Halo Occupation Distribution (HOD)-informed priors and to confidence intervals derived using frequentist profile likelihood analyses, finding agreement in both central values and degeneracy directions in the $w_{0}$--$w_{a}$ plane. This demonstrates that, once projection effects are properly controlled, we can make robust inferences about the late-time cosmological expansion independent of the statistical framework adopted.

Bonici, M. [Waterloo U.; Perimeter Inst. Theor. Ph↗

NASA NTRSDate not supplied

In-Time Safety Assessment & Risk Prediction for Unmanned Aerial Systems

One of the critical challenges in emerging autonomous systems is timely mitigation of hazards encountered during operation which may not be known or accounted for at the time of design. Efficient execution of unmanned systems therefore demands a paradigm shift from scheduled periodic maintenance to predictive risk analysis that includes condition-based-monitoring, real-time reliability assessment and hazard mitigation. Particularly, the state-of-health parameters needs to be computed at the component level, unit level as well as the integrated system level. While in the former two levels, the physics of health propagation may be based on underlying electro-mechanical properties, system level prognostics often relies on data-driven models. Further, uncertainty from model, measurements and input sources should be accurately quantified to generate meaningful prediction results that can be fed into reliable decision making processes. Finally, the expected risk and time to failure has to be computed based on the current state-of-health of the overall system. This talk presents a conceptual design of such an in-time safety assurance approach for unmanned aerial vehicles (UAV) operating at low altitudes near and over populated areas. Typical in-flight hazard incidents include unplanned detour, proximity to obstacles, mid-flight component faults, limited battery life and poor quality of GPS measurements. Safety assessment therefore comprises trajectory generation and re-plan, battery RUL computation, distributed fault diagnostics and uncertainty management of predicted trajectory based on GPS measurement noise. The entire monitoring framework will be demonstrated on simulated as well as real UAV flight experiments conducted at the NASA Langley Research Center. This tutorial will therefore guide the audience through a step-by-step tracking of an autonomous system with focus on in-time risk prediction in the presence of unforeseen hazards and uncertain environment.

diagnostics↗

DOE OSTI2016

High Accuracy Signal Validation Framework for Sensor Calibration Assessment in NPPs

Effective and efficient health management of sensing channels and instrumentation supports reliable and accurate process monitoring capacities in any industry. Current practice in the nuclear industry relies on periodic calibration assessment and correction activities. This time based maintenance technique consists of three steps: i) removal of sensor to a test environment, ii) testing and recalibration, and iii) reinstallation of sensor into its working environment. This procedure is highly labor intensive, adds to the outage cost and timeline, and contributes to worker radiation exposure and ALARA requirements. Furthermore, the human element contributes to error factors in all stages of the procedure. The effectiveness of this calibration procedure after sensors are returned to working environmental variables also raises concerns, and the practicability of this periodic approach is uncertain for future reactor designs with longer operating cycles between refueling outages. Studies indicate that periodic calibration assessment find only 10% of sensing instrumentations with calibration issues during a single outage (18- 24 months), meaning at least 90% of sensors are undergoing unnecessary maintenance actions. This provides an opportunity to maintain the current levels of safety and functional integrity with fewer, more targeted maintenance actions and lower economic burden. Performance-based maintenance planning shows much promise over current periodic maintenance approaches. Specifically, online monitoring (OLM) utilizes the continually collected process data to non-intrusively monitor the calibration status of process instrumentation and detect the onset of de-calibration, thereby minimizing the number of recalibration procedures required. Ultimately, this can lead to termination of time based recalibration at NPPs. OLM utilizes the process measurements made for process monitoring and control to evaluate the calibration status of the sensors and instrumentation making the measurements. OLM can detect and differentiate sensor faults and process anomalies, thus providing a valuable tool to suit the industry's and regulatory body's requirements. Though supported by more than a decade of research, OLM for sensor calibration assessment is yet to be implemented in the US fleet due to regulatory requirements and constraints. As shown in Figure 1, OLM utilizes process data to train statistical models that predict normal, error-free process behavior. Measured process values are compared with error-corrected predictions to ascertain the presence of faults. The reliability of OLM is dependent on the quality of its predictions, measured in part by the uncertainty in these predictions. This research develops a framework to accurately quantify the prediction uncertainty based on Bayesian inference techniques to provide the required confidence levels for OLM systems. The expected outcomes include signal validation by high-accuracy, high-confidence uncertainty quantification for variable sensor types and operating ranges. Furthermore, the framework will facilitate fault detection capacities and so-called virtual sensors, a capability to replace faulty sensor measurements with error-corrected values when a sensor fault is detected. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Model-independent limits and constraints on extended theories of gravity from cosmic reconstruction techniques

The onset of dark energy domination depends on the particular gravitational theory driving the cosmic evolution. Model independent techniques are crucial to test the both the present ΛCDM cosmological paradigm and alternative theories, making the least possible number of assumptions about the Universe. In this paper we investigate whether cosmography is able to distinguish between different gravitational theories, by determining bounds on model parameters for three different extensions of General Relativity, namely quintessence, F (Τ) and f ( R ) gravitational theories. We expand each class of theories in powers of redshift z around the present time, making no additional assumptions. This procedure is an extension of previous work and can be seen as the most general approach for testing extended theories of gravity through the use of cosmography. In the case of F (Τ) and f ( R ) theories, we show that some assumptions on model parameters often made in previous works are superfluous or even unjustified. We use data from the Union 2.1 supernovae catalogue, baryonic acoustic oscillation data and H ( z ) differential age compilations, which probe cosmology on different scales of the cosmological evolution. We perform a Monte Carlo analysis using a Metropolis-Hastings algorithm with a Gelman-Rubin convergence criterion, reporting 1-σ and 2-σ confidence levels. To do so, we perform two distinct fits, assuming only data within z < 1 first and then without limitations in redshift. We obtain the corresponding numerical intervals in which coefficients span, and find that the data is compatible the ΛCDM limit of all three theories at the 1-σ level, while still compatible with quite a large portion of parameter space. We compare our results to the truncated ΛCDM paradigm, demonstrating that our bounds divert from the expectations of previous works, showing that the permitted regions of coefficients are significantly modified and in general widened with respect to values usually reported in the existing literature. Finally, we test the extended theories through the Bayesian selection criteria AIC and BIC.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

An approach to characterizing spatial aspects of image system blur

Quantitative X-ray radiographic imaging systems that utilize a charged couple device (CCD) camera connected to a thick, monolithic scintillator can exhibit blur that varies spatially across the field of view, especially for thick scintillators used in pulse-power radiography of dynamically compressed objects. Here, a three-point approach to estimating and accounting for this effect is demonstrated by (a) using a local estimation technique to measure the effect of blurring a calibration object at key locations across the field of view, (b) combining each of the local estimates into a spatially varying blurring function via partitions of unity interpolation, and (c) resolving the effects of that blur on the image by solving an ill-posed inverse problem using a spatially varying regularization term. The technique is demonstrated on synthetic examples and actual radiographs collected at the Naval Research Laboratory’s (NRL)Mercury pulsed power facility.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Overview of the Tolerance Limit Calculations with Application to TSURFER

To establish confidence in the results of computerized physics models, a key regulatory requirement is to develop a scientifically defendable process. The methods employed for confidence, characterization, and consolidation, or C3, are statistically involved and are often accessible only to avid statisticians. This manuscript serves as a pedagogical presentation of the C3 process to all stakeholders—including researchers, industrial practitioners, and regulators—to impart an intuitive understanding of the key concepts and mathematical methods entailed by C3. The primary focus is on calculation of tolerance limits, which is the overall goal of the C3 process. Tolerance limits encode the confidence in the calculation results as communicated to the regulator. Understanding the C3 process is especially critical today, as the nuclear industry is considering more innovative ways to assess new technologies, including new reactor and fuel concepts, via an integrated approach that optimally combines modeling and simulation and minimal targeted validation experiments. This manuscript employs intuitive, analytical, numerical, and visual representations to explain how tolerance limits may be calculated for a wide range of configurations, and it also describes how their values may be interpreted. Various verification tests have been developed to test the calculated tolerance limits and to help delineate their values. The manuscript demonstrates the calculation of tolerance limits for TSURFER, a computer code developed by the Oak Ridge National Laboratory for criticality safety applications. The goal is to evaluate the tolerance limit for TSURFER-determined criticality biases to support the determination of upper, subcritical limits for regulatory purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

SOCIAL MODELING IN ASSESSEMENT OF A STATE’S PROPENSITY FOR NUCLEAR PROLIFERATION

This paper presents approach for assessing a State’s propensity for nuclear weapons proliferation using social modeling. We supported this modeling by first reviewing primarily literature by social scientists on factors related to the propensity of a State to proliferation and by leveraging existing relevant data compiled by social scientists. We performed a number of validation tests on our model including one that incorporates use of benchmark data defining the proliferation status of countries in the years between 1945 and 2000. We exercise the BN model against a number of country cases representing different perceived levels of proliferation risk. We also describe how the BN model could be further refined to be a proliferation assessment tool for decision making.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2013

Large-Scale Optimization for Bayesian Inference in Complex Systems

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT₋Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas₋Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Inferring the source of evaporated waters using stable H and O isotopes

Stable isotope ratios of H and O are widely used to identify the source of water, e.g., in aquifers, river runoff, soils, plant xylem, and plant-based beverages. In situations where the sampled water is partially evaporated, its isotope values will have evolved along an evaporation line (EL) in δ 2 H/δ 18 O space, and back-correction along the EL to its intersection with a meteoric water line (MWL) has been used to estimate the source water’s isotope ratios. Here, we review the theory underlying isotopic estimation of source water for evaporated samples (iSW E ). We note potential for bias from a commonly used regression-based approach for EL slope estimation and suggest that a model-based approach may be preferable if assumptions of the regression approach are not valid. We then introduce a mathematical framework that eliminates the need to explicitly estimate the EL–MWL intersection, simplifying iSW E analysis and facilitating more rigorous uncertainty estimation. We apply this approach to data from the US EPA's 2007 National Lakes Assessment. We find that data for most lakes are consistent with a water source similar to annual runoff, estimated from monthly precipitation and evaporation within the lake basin. Strong evidence for both summer- and winter-biased sources exists, however, with winter bias pervasive in most snow-prone regions. Furthermore, the new analytical framework should improve the rigor of iSW E in ecohydrology and related sciences, and our initial results from US lakes suggest that previous interpretations of lakes as unbiased isotope integrators may only be valid in certain climate regimes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2012

General Diffuse-Interface Theories and an Approach to Predictive Tumor Growth Modeling

While a large and growing literature exists on mathematical and computational models of tumor growth, to date tumor growth models are largely qualitative in nature, and fall far short of being able to provide predictive results important in life-and-death decisions. This is largely due to the enormous complexity of evolving biological and chemical processes in living tissue and the complex interactions of many cellular and vascular constituents in living organisms. Several new technologies have emerged, however, which could lead to significant progress in this important area: (i) the development of so-called phase-field, or diffuse-interface models, which can be developed using continuum mixture theory, and which provide a general framework for modeling the action of multiple interacting constituents. These are based on generalizations of the Cahn–Hilliard models for spinodal decomposition, and have been used recently in certain tumor growth theories; (ii) the emergence of predictive computational methods based on the use of statistical methods for calibration, model validation, and uncertainty quantification; (iii) advances in imaging, experimental cell biology, and other medical observational methodologies; and (iv) the advent of petascale computing that makes possible the resolution of features at scales and at speeds that were unattainable only a short time in the past. Here we develop a general phenomenological thermomechanical theory of mixtures that employs phase-field or diffuse interface models of surface energies and reactions and which provides a framework for generalizing existing theories of the types that are in use in tumor growth modeling. In principle, the framework provides for the effects of M solid constituents, which may undergo large deformations, and for the effect of N - M fluid constituents, which could include highly nonlinear, non-Newtonian fluids. We then describe several special cases which have the potential of providing acceptable models of tumor growth. We then describe the beginning steps of the development of Bayesian methods for statistical calibration, model validation, and uncertainty quantification, which, with further work, could produce a truly predictive tool for studying tumor growth. In particular, we outline the processes of statistical calibration and validation that can be employed to determine if tumor growth models, drawn from the broad class of models developed here, are valid for prediction of key quantities of interest critical to making decisions on various medical protocols. We also describe how uncertainties in such key quantities of interest can be quantified in ways that can be used to establish confidence in predicted outcomes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗