Framework for Optimization, Quantification of Uncertainty, and Surrogates (FOQUS) – Demonstration
Presented at the 2022 Carbon Management Project Review Meeting in Pittsburgh, PA
Deshpande, Anuja↗
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Framework for Optimization, Quantification of Uncertainty and Surrogates – Updated Capabilities
This poster presents updated capabilities within the FOQUS Toolset, covering core features as well as project-based applications. Specifically, the poster highlights advancements in FOQUS integration with cloud-based clients, plugin support for machine learning tools and external simulations, sequential design of experiments, and advanced support for dynamic process models. The applications demonstrate the breadth of FOQUS predictive capabilities for chemical, energy and economic system analysis.
Paul, Brandon↗
Model Structural Inference Using Local Dynamic Operators
This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Here, we (1) define a discrete, local representation of the structure of a partial differential equation, which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.
97 MATHEMATICS AND COMPUTING↗
Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield
The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.
Baurle, Robert A.↗
A Neural Optimizer With Decision-Focused Learning for Optimal Energy Storage Operation
Here, this article introduces a neural optimizer-based framework for optimizing battery energy storage system (BESS) control for grid services, including demand charge and energy cost reduction. By leveraging decision-focused learning (DFL), the proposed framework ensures seamless integration and adaptation, significantly enhancing control performance. A patch time-series transformer is employed for peak load forecasting, incorporating aleatoric uncertainty quantification to account for forecasting uncertainties within the decision-making process. The framework utilizes a solver-in-the-loop approach to generate optimal BESS actions, which are then used to train the neural optimizer-based agent. By co-optimizing both BESS operational modes and output power within the NN, the system achieves improved performance and robustness. After initial training, the forecasting and control models are jointly fine-tuned to account for forecasting errors, further improving decision precision and efficiency through DFL. Case studies are performed to validate the performance of the framework using multiple real-world datasets, demonstrating superior performance in monthly peak load forecasting compared to state-of-the-art models. In addition, the results are compared against existing decision-making approaches. The results demonstrate a reduction in monthly peak forecasting error by approximately 15% across various performance measures and achieve an optimization gap for BESS operation that is about three times smaller compared to existing methods.
Kim, Hyeonjin [Pacific Northwest National Laborato↗
Examples of Mission-driven Data Science from Jefferson Lab and ACES
This presentation details mission-driven data science initiatives at Jefferson Lab and the Joint Institute for Advanced Computing on Environmental Studies (ACES). JLab, a U.S. Department of Energy Office of Science national laboratory, operates the Continuous Electron Beam Accelerator Facility (CEBAF), and is the lead institute for the new High Performance Data Facility (HPDF) Hub. The Joint Institute for ACES brings together interdisciplinary teams in health informatics, climate modeling, computer science, and physics to address environmental challenges, including flood modeling. The Hampton Roads region, particularly Norfolk and Virginia Beach, faces increasing flood risks, motivating the need for rapid, reliable, and risk-aware decision support. ACES’s flooding work has a focus on uncertainty quantification (UQ) and machine learning (ML) for coastal flood management. The work is motivated by the increasing vulnerability of communities such as Norfolk and Virginia Beach, Virginia, to frequent coastal flooding events, and the need for rapid, reliable decision support. The research develops computationally efficient ML surrogate models to forecast water levels and flooding risk. A central theme is the quantification and calibration of predictive uncertainty, especially for out-of-distribution (OOD) scenarios, using techniques such as Monte Carlo Dropout, Deep Ensembles, Gaussian Processes, and Deep Quantile Regression (DQR). The study demonstrates that distance-aware UQ is critical for reliable scientific AI, particularly in high-dimensional, safety-critical, and real-time applications.
McSpadden, Diana [Thomas Jefferson National Accele↗
Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method
Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.
Uncertainty Quantification↗
Adaptive learning-driven high-throughput synthesis of oxygen reduction reaction Fe–N–C electrocatalysts
Reducing human reliance on inefficient energy systems and fossil fuels has become more urgent due to the consequences of global climate change. However, traditional trial-and-error approaches have hampered our ability to accelerate the discovery and implementation of functional materials for efficient energy conversion devices, such as polymer electrolyte fuel cells (PEFCs). To address this, we develop an adaptive learning framework that integrates machine learning and state-of-the-art capabilities in high-throughput synthesis to achieve expedited optimization of iron-nitrogen-carbon PEFC oxygen reduction reaction (ORR) electrocatalysts. We use statistical inference, uncertainty quantification, and global optimization to build a computational design-of-experiment tool that identifies the optimum compositions to be investigated next to reduce the demands placed on experimental materials discovery. We benchmark the ability of the proposed strategy to discover optimum catalyst synthesis conditions in a six-dimensional search space when starting with a thirty-six-sample database. By following the adaptive learning strategy, we synthesize fourteen new catalysts from approximately ten billion unique compositions and discover four catalysts that outperform all original samples. The best machine learning-optimized catalyst is 33% more active than the highest-performing one in the initial database, showing an ORR activity seven times larger than those typically reported for the same class of materials.
36 MATERIALS SCIENCE↗
Quantifying the impact of temporal analysis of products reactor initial state uncertainties on kinetic parameters
The temporal analysis of products (TAP) reactor, a transient kinetic tool, provides users with information as the catalyst state evolves. However, the state of the art for TAP uncertainty quantification only considers the experimental noise present in the outlet flow signal. Additional sources of uncertainty, including, but not limited to, initial surface coverages, the catalyst zone location, the inert void fraction, and the gas pulse intensity and pulse delay, are not included. For this reason, a framework for quantifying all uncertainty sources present in TAP experiments is presented and applied to a carbon monoxide oxidation case study. Herein, two methods for quantifying these sources of uncertainty are introduced. The first utilizes initial state sensitivities to approximate the parameter variances, as well as to provide insights into the structural certainty of the model. The second generates parameter confidence distributions through an ensemble-based sampling algorithm. This initial state covariance matrix can ultimately be merged with the experimental noise covariance matrix, providing a unified description of the parameter uncertainties for a single TAP experiment.
36 MATERIALS SCIENCE↗
Surrogate-driven Variance-based Sensitivity Analysis of Thermal Storage Tanks in Integrated Energy Systems
Sensitivity analysis and uncertainty quantification are essential steps for enhancing the accuracy of computational models by identifying and mitigating uncertainties. This study focuses on these steps for the Thermal Energy Delivery System at Idaho National Laboratory, specifically targeting the thermocline tank. Using a Modelica/Dymola simulation model, the study perturbed various design parameters and boundary conditions, including shape factor, porosity, outlet temperature, inlet mass flow rate, and system pressure, to predict and quantify uncertainty in the tank’s ax- ial temperature. A dataset of over 1,000 simulations was generated, and surrogate models were developed using the pyMAISE (Michigan Artificial Intelligence Standard Environment) library, which is an Automatic Machine Learning library for nuclear engineering applications. The optimal model, a feedforward neural network with two hidden layers, achieved an R2 score above 0.99 and a mean absolute error below 1 Kelvin. Sensitivity analyses using Sobol indices and Fourier amplitude sensitivity testing methods on this surrogate model revealed that the inlet mass flow rate at initial timestamps and porosity significantly impacts predicted temperatures across all sensors and time steps.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Sensitivity Analysis of Genome-Scale Metabolic Flux Prediction
TRIMER, Transcription Regulation Integrated with MEtabolic Regulation, is a genome-scale modeling pipeline targeting at metabolic engineering applications. Using TRIMER, regulated metabolic reactions can be effectively predicted by integrative modeling of metabolic reactions with a Transcription Factor (TF)-gene regulatory network (TRN), which is modeled via a Bayesian network (BN). In this paper, we focus on sensitivity analysis of metabolic flux prediction for uncertainty quantification of BN structures for TRN modeling in TRIMER. We propose a computational strategy to construct the uncertainty class of TRN models based on the inferred regulatory order uncertainty given transcriptomic expression data. With that, we analyze the prediction sensitivity of the TRIMER pipeline for the metabolite yields of interest. The obtained sensitivity analyses can guide Optimal Experimental Design (OED) to help acquire new data that can enhance TRN modeling and achieve specific metabolic engineering objectives, including metabolite yield alterations. Here we have performed small- and large-scale simulated experiments, demonstrating the effectiveness of our developed sensitivity analysis strategy for BN structure learning to quantify the edge importance in terms of metabolic flux prediction uncertainty reduction and its potential to effectively guide OED.
59 BASIC BIOLOGICAL SCIENCES↗
Probabilistic reliability assessment and case studies for predicted energy savings in residential buildings
This study aims to (1) investigate the key influential parameters (KIPs) in estimating the uncertainty of energy savings using a residential building energy simulation model and (2) perform uncertainty quantification for energy savings for several different scenarios. The proposed methodology was successfully applied to the calculation of uncertainties associated with residential energy retrofits using two test houses designed for pre- and post-retrofit cases. Uncertainties were determined using basic parameters that might be supplied to an energy model and then reevaluated based on an audit of the KIPs identified, resulting in substantially reduced uncertainty. Of four different scenarios, the most uncertain scenario estimated the annual energy savings from the retrofit would be between 18% and 51% at a 95% confidence level, and the least uncertain scenario estimated the annual savings would be between 26% and 40% at a 95% confidence level. The actual measured annual savings from the two test houses was 28%, which shows an agreement with the uncertainty analysis.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Consistency Analysis for Massively Inconsistent Datasets in Bound-to-Bound Data Collaboration
Bound-to-Bound Data Collaboration (B2BDC) provides a natural framework for addressing both forward and inverse uncertainty quantification problems. In this approach, QOI (quantity of interest) models are constrained by related experimental observations with interval uncertainty. A collection of such models and observations is termed a dataset and carves out a feasible region in the parameter space. If a dataset has a nonempty feasible set, it is said to be consistent. In real-world applications, it is often the case that collections of models and observations are inconsistent. Revealing the source of this inconsistency, i.e., identifying which models and/or observations are problematic, is essential before a dataset can be used for prediction. To address this issue, we introduce a constraint relaxation-based approach, entitled the vector consistency measure, for investigating datasets with numerous sources of inconsistency. Here, the benefits of this vector consistency measure over a previous method of consistency analysis is demonstrated in two realistic gas combustion examples.
97 MATHEMATICS AND COMPUTING↗
Quantifying uncertainty in the process-structure relationship for Al–Cu solidification
Phase field method (PFM) is a simulation tool to predict microstructural evolution during solidification and is helpful to establish the process-structure relationship for alloys. The robustness of the relationship however is affected by model-form and parameter uncertainties in PFM. In this paper, the uncertainty associated with the thermodynamic and process parameters of PFM is studied and quantified. Surrogate modeling is used to interpolate four quantities of interests (QoIs), including dendritic perimeter, area, primary arm length, and solute segregation, as functions of thermodynamic and process parameters. A sparse grid approach is applied to mitigate the curse-of-dimensionality computational burden in uncertainty quantification. Polynomial chaos expansion is employed to obtain the probability density functions of the QoIs. The effect of parameter uncertainty on the Al–Cu dendritic growth during solidification simulation are investigated. Here, the results show that the dendritic morphology varies significantly with respect to the interface mobility and the initial temperature.
36 MATERIALS SCIENCE↗
The Effect of the Ill-posed Problem on Quantitative Error Assessment in Digital Image Correlation
Here, this work explores the effect of the ill-posed problem on uncertainty quantification for motion estimation using digital image correlation (DIC) (Sutton et al. 2009). We develop a correction factor for standard uncertainty estimates based on the cosine of the angle between the true motion and the image gradients, in an integral sense over a subregion of the image. This correction factor accounts for variability in the DIC solution previously unaccounted for when considering only image noise, interpolation bias, contrast, and the software settings such as subset size and spacing.
97 MATHEMATICS AND COMPUTING↗
Quantifying uncertainties in α -nucleus reaction dynamics informed from first principles
The ab initio symmetry-adapted no-core shell model is a microscopic many-body method which naturally describes challenging collective and clustering features of atomic nuclei. Wave functions and observables computed with realistic nucleon-nucleon forces in this framework are tied to first principles, and are hence well-suited for rigorous uncertainty quantification. We discuss α-deuteron and α- 12 C cluster potentials informed by symmetry-adapted calculations, and propagate uncertainties in the effective binary cluster method as well as those in the nuclear interaction to reaction observables, namely scattering phase shifts, cross sections, partial widths and resonance energies. Here, we find that the overall uncertainties are dominated by those originating in the underlying nuclear force, speaking to the need for tighter constraints on realistic nucleon-nucleon interactions.
Ab initio↗
Uncertainty-Aware Machine Learning for Small-Angle X-ray Scattering Analysis in Autonomous Experimentation
Small-angle X-ray scattering (SAXS) is a powerful high-throughput characterization tool for probing nanoscale structure in native sample environments, providing real-time morphological information such as nanoparticle size and shape during synthesis. However, automated SAXS data analysis for extracting meaningful structural parameters is non-trivial and remains a bottleneck in closed-loop experimentation towards autonomous materials discovery, which demands fast, reliable, and uncertainty-aware data analysis. Here, we develop a machine-learning approach for automated SAXS analysis tailored to closed-loop nanoparticle synthesis. A Random Forest (RF) regression model is trained on 100,000 synthetic SAXS curves generated from polydisperse spherical nanoparticles with realistic background contributions. Using normalized one-dimensional SAXS intensity profiles as input, the RF model directly predicts nanoparticle radius, size polydispersity, and background parameters, while the ensemble standard deviation across trees provides built-in uncertainty quantification (UQ). On synthetic data, we show that combining fit-quality metrics (R 2 , MAE) with thresholds on prediction uncertainty reliably identifies accurate parameter estimates without access to ground truth. We then apply the trained model to 365 experimental SAXS profiles of citrate-reduced gold nanoparticles synthesized using an automated droplet-flow microreactor with in situ SAXS at a synchrotron beamline, classifying the results into high- and low-confidence subsets based on UQ metrics. Finally, we integrate RF-based SAXS analysis into a simulated closed-loop optimization campaign using Gaussian process Bayesian optimization to minimize nanoparticle polydispersity, benchmarking against conventional automated Levenberg–Marquardt fitting. The RF-guided campaign exhibits substantially faster convergence and lower relative opportunity cost (∼0.07 vs ∼0.3), demonstrating that uncertainty-aware machine-learning SAXS analysis significantly enhances the efficiency and robustness of autonomous nanomaterials synthesis workflows.
Bayesian optimization↗
Multilevel Monte Carlo Estimators For Derivative-Free Optimization Under Uncertainty
Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. Here, in this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.
97 MATHEMATICS AND COMPUTING↗