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DOE OSTI2022

Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiments is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data, such as large time series, due to the difficulty in building an emulator and the nonidentifiability between effects from input parameters and data-model discrepancy. To overcome these challenges, we, in this work, propose a new calibration framework based on a deep neural network (DNN) with long short-term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the “learning with noise” idea, we train our DNN model to filter out the effects from data-model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with the Weather Research and Forecasting Model Hydrological modeling system (WRF-Hydro), we show our approach can yield accurate point estimates and well-calibrated interval estimates for input parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference↗

DOE OSTI2022

Transformer Health Monitoring Using Dissolved Gas Analysis

As integral components of any power plant, transformers supply the generated electricity to the grid. However, a transformer’s cellulose-based paper insulation and the mineral oil in which it is immersed break down over time under standard operating conditions—or more rapidly due to potential faults within the system. As the transformer’s mineral oil breaks down, gases are released that can be measured and monitored. This technical brief exhibits a collection of diagnostic and prognostic techniques that utilities can adopt in lieu of labor-intensive periodic preventive maintenance routines. Furthermore, prognostic models have been incorporated using the latest version of the Institute of Electrical and Electronics Engineers (IEEE) standard (IEEE, 2019) for dissolved gas analysis (DGA), thus expanding it to include estimation of the time to maintenance. Overall, four different methodologies are explained, each of which aids in determining a transformer’s state of health. These methodologies include the Chendong model, the IEEE thermal life consumption model (IEEE, 2012), a diagnostic model for DGA, and a prognostic model for DGA that uses an autoregressive integrated moving average (ARIMA) model. An additional improvement for estimating missing system parameters by using monitoring data (i.e., a tool for parameter estimation utilizing Powell’s method) is presented, enabling the IEEE thermal life consumption model to benefit not only the collaborating power plant, but also the power industry at large.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Toward Improved Regional Hydrological Model Performance Using State-Of-The-Science Data-Informed Soil Parameters

Accurate soil moisture and streamflow data are an aspirational need of many hydrologically relevant fields. Model simulated soil moisture and streamflow hold promise but models require validation prior to application. Calibration methods are commonly used to improve model fidelity but misrepresentation of the true dynamics remains a challenge. In this study, we leverage soil parameter estimates from the Soil Survey Geographic (SSURGO) database and the probability mapping of SSURGO (POLARIS) to improve the representation of hydrologic processes in the Weather Research and Forecasting Hydrological modeling system (WRF-Hydro) over a central California domain. Our results show WRF-Hydro soil moisture exhibits increased correlation coefficients ( r ), reduced biases, and increased Kling-Gupta Efficiencies (KGEs) across seven in situ soil moisture observing stations after updating the model's soil parameters according to POLARIS. Compared to four well-established soil moisture data sets including Soil Moisture Active Passive data and three Phase 2 North American Land Data Assimilation System land surface models, our POLARIS-adjusted WRF-Hydro simulations produce the highest mean KGE (0.69) across the seven stations. More importantly, WRF-Hydro streamflow fidelity also increases, especially in the case where the model domain is set up with SSURGO-informed total soil thickness. The magnitude and timing of peak flow events are better captured, r increases across nine United States Geological Survey stream gages, and the mean KGE across seven of the nine gages increases from 0.12 to 0.66. Our pre-calibration parameter estimate approach, which is transferable to other spatially distributed hydrological models, can substantially improve a model's performance, helping reduce calibration efforts and computational costs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Capital Structure for Techno-Economic Analysis of Hydrogen Projects

This report provides updated generally accepted accounting principles (GAAP) parameter estimates of assumptions that may be used to reflect the cost of financing hydrogen infrastructure deployment. The report also provides parameter estimation for more streamlined financial analysis frameworks such as discounted cash flow and annualized financial models. Parameter values are derived from industry feedback and are reflective of current macro-economic factors such as higher interest rates and higher risk profile of emerging hydrogen technologies, given a myriad of factors such as projects’ construction inexperience, capital costs, and rising inflation, among others.

08 HYDROGEN↗

DOE OSTI2022

Discrepancy quantification between experimental and simulated data of CO 2 adsorption isotherm using hierarchical Bayesian estimation

Here, to quantitatively analyze the inconsistencies commonly observed between experimental and simulated adsorption isotherms, parameter estimation of adsorption isotherm models was conducted by hierarchical Bayesian estimation with parameter uncertainties being quantified as probability distributions. The estimation method was implemented using Markov Chain Monte Carlo (MCMC) to analyze multiple data sets obtained from different sources, including a publicly available database. To describe the discrepancies of experimental and simulated adsorption data, the simulation data was set as the reference to which experimental measurements were compared. We applied the proposed approach to analyze CO 2 adsorption isotherms that are measured and simulated on zeolite 13X and MIL-101(Cr). In these case studies, the discrepancy of CO 2 adsorption isotherm was successfully quantified between experimental measurements and predictions given by molecular simulations using Grand Canonical Monte Carlo (GCMC), where uncertainties were quantified as probability distributions. Furthermore, experimental data sets that agree well with the GCMC simulation have been identified, providing insights into experimental and measurement methods as well as choosing the right assumptions in the molecular simulation.

42 ENGINEERING↗

DOE OSTI2023

Theory of an Automatic Seepage Meter and Ramifications for Applications

A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed. The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three-dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Estimating Drizzle Parameters by Aircraft Sampling

In-cloud supersaturation is calculated from aircraft derived measurements of the in-cloud vertical gradient of liquid water content, vertical velocity, the pt and 3 rd cloud droplet radius moments and a parameter related to the heat and mass transport during condensation and evaporation of cloud droplets. The aircraft data where taken during the VOCALS 2008 study in marine stratocumulus clouds off the coast of Chile. Approximately 16000 discrete samples, 2.5 meter in length, were used in the present analysis of in-cloud supersaturation and its variability, both of which are indicative of turbulent processes within the cloud and their significant impact on drizzle formation. Two additional drizzle parameters, the eddy persistence time and the variance of fluctuations in in-cloud droplet growth rate were also estimated from this data set. These results will help to constrain parameterizations of underlying turbulent microphysical processes of clouds and thereby advance the future development of warm cloud and precipitation models for climate simulation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Fast and Accurate Core Analysis by the Full-Immersion Pressure-Pulse Decay: Part 1—Theory

Summary Core-scale measurements are considered the ground truth that oil and gas or electric utility companies use to predict the migration of fluids such as oil, natural gas, carbon dioxide, or brine deep underground during their extraction or injection operations. To provide a greater understanding of petrophysical properties of low-permeability geologic formations such as shales and tight gas sandstones, this study introduces a novel core-analysis procedure. The technique follows conventional pressure-pulse-decay permeametry, where the pressure in an inlet chamber adjacent to a cylindrical core plug undergoes a rapid pressurization, the system is shut in, and the pressure reaches a new equilibrium. However, unlike a standard unidirectional pressure-pulse decay, the full-immersion pressure-pulse decay (Hannon 2019) applies a pressure disturbance to the entire outer surface area of the sample. This article covers the numerical simulator designed to model flow through an anisotropic porous sample in this scenario. The model assumes distinct but uniform permeabilities along the radial and axial directions of the cylindrical plug sample. When extracting a plug vertically (or perpendicular to bedding), the permeability along the radial direction associates with the horizontal permeability (i.e., parallel to bedding), whereas in the axial direction, flow occurs perpendicular to bedding (a vertical permeability). Investigations of these model outputs demonstrate an approximately 20-fold decrease in time to complete a full-immersion experiment compared with conventional pressure-pulse decay. Furthermore, the pressure-decay curves resulting from the full-immersion method have slightly different shapes than those resulting from other unidimensional transient methods. These differences begin to demonstrate that, under achievable experimental conditions, the analysis of pressure data from one full-immersion test could enable the simultaneous estimation of the apparent permeabilities parallel and perpendicular to bedding of a cylindrical sample in addition to its porosity. A follow-up article finalizes the proof of this capability with a parameter-estimation procedure and presents experimental verification through a proof-of-concept study. Described in greater detail in that article, the parameter estimator requires multiple forward simulations to analyze the data, which behooves minimizing the compute time for each simulation. By using an alternating direction implicit time-marching scheme and a structured but variably spaced grid, the numerical simulator built for this purpose provides a forward model output with suitable accuracy in approximately 0.5 seconds.

Energy & Fuels↗

DOE OSTI2021

Data compression and covariance matrix inspection: Cosmic shear

Covariance matrices are among the most difficult pieces of end-to-end cosmological analyses. In principle, for two-point functions, each component involves a four-point function, and the resulting covariance often has hundreds of thousands of elements. We investigate various compression mechanisms capable of vastly reducing the size of the covariance matrix in the context of cosmic shear statistics. This helps identify which of its parts are most crucial to parameter estimation. We start with simple compression methods, by isolating and “removing” 200 modes associated with the lowest eigenvalues, then those with the lowest signal-to-noise ratio, before moving on to more sophisticated schemes like compression at the tomographic level and, finally, with the massively optimized parameter estimation and data compression (MOPED). We find that, while most of these approaches prove useful for a few parameters of interest, like Ω m , the simplest yield a loss of constraining power on the intrinsic alignment (IA) parameters as well as S 8 . For the case considered—cosmic shear from the first year of data from the Dark Energy Survey—only MOPED was able to replicate the original constraints in the 16-parameter space. Finally, we apply a tolerance test to the elements of the compressed covariance matrix obtained with MOPED and confirm that the IA parameter A IA is the most susceptible to inaccuracies in the covariance matrix.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Estimating Atmospheric Parameters of DA White Dwarf Stars with Deep Learning

The determination of atmospheric parameters of white dwarf stars (WDs) is crucial for researches on them. Traditional methodology is to fit the model spectra to observed absorption lines and report the parameters with the lowest χ 2 error, which strongly relies on theoretical models that are not always publicly accessible. In this work, we construct a deep learning network to model-independently estimate T eff and log g of DA stars (DAs), corresponding to WDs with hydrogen-dominated atmospheres. The network is directly trained and tested on the normalized flux pixels of full optical wavelength range of DAs spectroscopically confirmed in the Sloan Digital Sky Survey. Experiments in test yield that the rms error for T eff and log g approaches 900 K and 0.1 dex, respectively. This technique is applicable for those DAs with T eff from 5000 to 40,000 K and log g from 7.0 to 9.0 dex. Furthermore, the applicability of this method is verified for the spectra with degraded resolution of ~200. So it is also practical for the analysis of DAs that will be detected by the Chinese Space Station Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Deep Learning At Depth: Estimating subsurface parameters from geophysical monitoring data

Geophysical imaging techniques are a non-invasive way to image the subsurface and understand both subsurface solid (rock/soil) and fluid property distributions and their evolution in time. Inversions of the geophysical data, such as Electrical Resistance Tomography (ERT) data, are solved to estimate the subsurface property distributions, such as conductivity, and many inversion techniques smooth out sharp gradients in rock or fluid property distributions. Sharp gradients in subsurface properties tend to be present in situations with complex subsurface structures, which are common in many subsurface applications. We have successfully demonstrated that it is possible to inform, or constrain, inversions with neural networks trained on synthetic data with complex subsurface structures. Initial results suggest this process may be optimizable to yield property distributions that better represent the true property distributions than the same inversion process without the neural network constraint. Future work would optimize the neural network performance for this application and then apply the synthetic-data trained neural network to real data to understand the utility and performance of this technique for real data sets.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

PrOMMiS Tutorial

This is a tutorial on using parameter estimation and process optimization in PrOMMiS. The tutorials are publicly available in the GitHub repository. The presentation attached guides through the flow of the three different tutorials. The tutorials are presented as follows: i) Parameter estimation of oxalate precipitation, ii) Optimization of precipitation model, and iii) Optimization of full process.

critical minerals and materials↗

DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Developing Generic Prior Distributions for Common Cause Failure Alpha Factors and Causal Alpha Factors

This report is a revision of the original report, INL/LTD-17-43723. Distribution of the original report was to the Nuclear Regulatory Commission (NRC) only, and the report was not made available to the public. The original report was revised as this report for public distribution. This report presents the latest update of generic prior distributions for common cause failure (CCF) alpha factors, as well as the development of new generic prior distributions for CCF causal alpha factors. The history of CCF treatment and parameter estimations is reviewed. The existing process for developing generic prior distributions is reviewed and used to develop new priors for CCF alpha factors and causal alpha factors. For causal alpha factors, different priors are developed for the five different CCF cause groups: Component (GC), Design (GD), Environment (GE), Human (GH), and Other (GO). These generic prior distributions could be used in the Standardized Plant Analysis Risk (SPAR) models for CCF parameter estimation. The issues and preliminary thoughts regarding prior distribution development are documented. Potential future work is then proposed for improving the process of developing priors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Three-dimensional fracture continuum characterization aided by surface time-domain electromagnetics and hydrogeophysical joint inversion—proof-of-concept

Efficient and safe production of hydraulically fractured reservoirs benefits from the prediction of their geometrical attributes. Geophysical methods have the potential to provide data that are sensitive to fracture geometries, alleviating the typically sparse nature of in situ reservoir observations. Moreover, surface-based methods can be logistically and economically attractive since they avoid operational interference with the injection well infrastructure. Here, we investigate the potential of the surface-based time-domain electromagnetic (EM) method. EM methods can play an important role owing to their sensitivity to injection-induced fluid property changes. Two other advantageous factors are the EM signal-enhancing effect of vertical steel-cased wells and the fact that injected proppants can be enhanced to produce a stronger electrical conductivity contrast with the reservoir’s connate fluid. Nevertheless, an optimal fracture characterization will no doubt require the integration of EM and reservoir injection and production data. We hence carry out our investigations within a hydrogeophysical parameter estimation framework where EM data and injection flow rates are combined in a fully coupled way. Given the interdisciplinary nature of coupled hydrogeophysical inverse modeling, we dedicate one section to laying out key aspects in a didactic manner.

58 GEOSCIENCES↗

DOE OSTI2021

Propagation of priors for more accurate and efficient spectroscopic functional fits and their application to ferroelectric hysteresis

Multi-dimensional spectral-imaging is a mainstay of the scanning probe and electron microscopies, micro-Raman, and various forms of chemical imaging. In many cases, individual spectra can be fit to a specific functional form, with the model parameter maps, providing direct insight into material properties. Since spectra are often acquired across a spatial grid of points, spatially adjacent spectra are likely to be similar to one another; yet, this fact is almost never used when considering parameter estimation for functional fits. On datasets tried here, we show that by utilizing proximal information, whether it be in the spatial or spectral domains, it is possible to improve the reliability and increase the speed of such functional fits by ~2-3x, as compared to random priors. We explore and compare three distinct new methods: (1) spatially averaging neighborhood spectra, and propagating priors based on functional fits to the averaged case, (2) hierarchical clustering-based methods where spectra are grouped hierarchically based on response, with the priors propagated progressively down the hierarchy, and (3) regular clustering without hierarchical methods with priors propagated from fits to cluster means. Our results highlight that utilizing spatial and spectral neighborhood information is often critical for accurate parameter estimation in noisy environments, which we show for ferroelectric hysteresis loops acquired on a prototypical PbTiO3 thin film with piezoresponse spectroscopy. This method is general and applicable to any spatially measured spectra where functional forms are available. Examples include exploring the superconducting gap with tunneling spectroscopy, using the Dynes formula, or current-voltage curve fits in conductive atomic force microscopy mapping. Here we explore the problem for ferroelectric hysteresis, which, given its large parameter space, constitutes a more difficult task than, for example, fitting current-voltage curves with a Schottky emission formula.

42 ENGINEERING↗