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Cycle life regression model, cycle life prediction model, and acceleration factors are discussed. A method was presented to: (1) select a mathematical model; (2) determine model coefficients using accelerated test data; (3) test model fit of the accelerated test data; and (4) predict normal packs.
Enhanced characterization and phase identification of post-PUREX Pu Oxalates (PuOXA) are pivotal for nonproliferation and pre-detonation nuclear forensics. Despite significant advances in the characterization of PuO 2 samples, little is known about the impact of both the chemical structure and oxidation states of PuOXA (i.e., Pu(III) and Pu(IV)) have on optical emission signatures. Here, we demonstrate the analytical capabilities of laser-induced breakdown spectroscopy (LIBS) applied to Fe(II) and Fe(III) oxalate samples as surrogates for PuOXA, highlighting the discriminating features in the LIBS emission spectra arising from differences in the oxidation states within mixed FeOXA samples. We report the enhancement of spectral feature selection using Principal Component Analysis (PCA), which enables the analytical superiority of machine learning algorithms such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and Random Forest Regression (RFR) over conventional univariate techniques for phase discrimination and chemometric analysis. Cluster analysis revealed how both matrix effects and laser ablation influence cluster separability by introducing spectral artifacts that misdirect the maximization of variance. PCA-selected emission lines were used in the regression models, demonstrating that both univariate and multivariate linear regression models (i.e., PLSR and SVR) can achieve acceptable performance, with machine learning models outperforming conventional calibration regressions. Furthermore, the application of non-linearly activated PCA-selected emission lines illustrates how simplifying the data while retaining captured variance enables the use of less complex and more computationally efficient models. Furthermore, this is particularly evident in the underperformance of RFR, which suffers from increased computational costs and overfitting owing to its high complexity.
Material creep under high-temperature conditions limits the lifetime and safety of structural systems such as advanced nuclear reactors. Conventional creep testing is slow and often produces inconsistent results across nominally identical experiments, making lifetime prediction uncertain. Here, to address these challenges, this work develops a data-driven symbolic regression (SR) model that consolidates results from duplicate creep tests and predicts the remaining strain-time curve of an ongoing experiment. The method uses piece-wise multi-objective SR with physical constraints to generate analytic, interpretable functions describing transient creep strain. Applied to Inconel Alloy 617 data, the approach achieved relative mean absolute errors of 1.0–9.5%, providing closed-form predictions of strain evolution. These results demonstrate a first step toward reducing the duration and cost of long-term creep testing while retaining physically interpretable model forms.
Radon is a naturally occurring radioactive gas that poses a serious health risk as the primary cause of lung cancer in non-smokers. Despite the well-known adverse association with health outcomes, current radon exposure assessments are limited to county-level or average-level estimates, which fail to capture regional variability. This study uses Machine Learning models, including Random Forest (RF) and Quantile Regression Forest (QRF), to estimate the indoor radon concentrations at the ZCTA (Zip code tabulation area)-level and characterize uncertainties in model estimates. Incorporating geological, meteorological, and building-specific data, the models aim to improve radon risk assessment by capturing mean exposure, variability, and extreme concentration levels. Processed radon test data (n = 718,111) were analyzed using average, variability, and quantile prediction methods. Models that estimate the average radon exposure at the ZCTA-level can yield promising model-fit results, but they do not capture the underlying variability of indoor radon exposure within a ZCTA. We utilize volatility analyses to identify characteristics indicative of high variability of indoor radon exposure. We also show that a QRF model can be used to estimate upper quantiles of residential radon exposure, thereby uncovering localized areas of elevated exposure that were not apparent in mean estimates. The results highlighted the need for a deep characterization of exposure risk and show that regions with moderate average exposure levels could still harbor extreme outliers with implications for evaluating health risks. Utilizing multiple radon exposure models allows for a deeper characterization of radon risk within a geographic area and can better identify high-risk areas. The results from this study provide a foundation for developing mitigation strategies and examining associations between radon exposure and health outcomes at fine scales. Future research should extend the geographic scope and incorporate additional environmental risk factors to establish a comprehensive framework for risk assessment.
Correlations between fundamental microscopic properties computable from first principles, which we term canonical properties, and complex large-scale quantities of interest (QoIs) provide an avenue to predictive materials discovery. Here, we propose that such correlations can be efficiently discovered through simulations utilizing approximate interatomic potentials (IPs), which serve as an ensemble of “synthetic materials”. As a proof of principle we build a regression model relating canonical properties to the symmetric tilt grain boundary (GB) energy curves in face-centered cubic crystals, characterized by the scaling factor in the universal lattice matching model of Runnels et al. (2016), which we take to be our QoI. Our analysis recovers known correlations of GB energy to other properties and discovers new ones. We also demonstrate, using available density functional theory (DFT) GB energy data, that the regression model constructed from IP data is consistent with DFT results, confirming the assumption that the IPs and DFT belong to same statistical pool and thereby validating the approach. Regression models constructed in this fashion can be used to predict large-scale QoIs based on first-principles data and provide a general method for training IPs for QoIs beyond the scope of first-principles calculations.
Weather-induced spatio-temporal degradation limits outdoor PV inverter lifetime and reliability, necessitating advanced data analysis. This study employs a top-down, data-driven approach utilizing multiple machine learning (ML) algorithms to estimate inverter reliability in a 1.4 MW PV power plant, considering factors such as irradiance, humidity, temperature, time of day, and weather conditions. An extensive alert dataset from 17 identical inverters, including alert types, propagation, and frequency, reveals significant correlations with environmental factors and inverter output power, enabling the construction of a performance reliability model. Dual-stage supervised-ML models are evaluated for accuracy, with the ‘classification-regression’ model by an artificial neural network (ANN) tested on the averaged “Alert-Ambient” dataset, which is outperformed by ‘clustering-regression’ models using random forest (RF) and K-Nearest Neighbors (KNN) on individual inverter datasets. K-means clustering applies principal component analysis to reduce dimensions, achieving improved accuracy beyond the 80% achieved by ANN on the averaged dataset. Second-stage regression estimates inverter reliability with a mean square error of 0.0195 on the averaged dataset and as low as 0.002 on individual inverter datasets using RF. Furthermore, these findings highlight the method's suitability for estimating PV inverter output reliability under ambient conditions, essential for digital twin development and related applications.
A unique approach to remotely quantify Cm(III) (0–100 µg mL −1 ) in HNO 3 (1–12 M) using steady-state laser fluorescence spectroscopy and multivariate regression models was developed. Photoluminescence is amenable to remote measurements using fiber-optic cables and is sensitive to numerous lanthanide and actinide species. In-line measurements can provide feedback to support complex processing in harsh environments (e.g., hot cells) to help guide and optimize radiochemical separations. In this work, Cm(III) spectra were acquired remotely in a glove box as a function of HNO 3 concentration to better understand spectral characteristics and evaluate the utility of multivariate regression models in this system. Furthermore, the Cm(III) fluorescence peak shape, width, position, and intensity changed significantly as a function of HNO 3 concentration, likely because of the displacement of emission quenching inner-sphere water molecules and complexation with nitrate ions. Despite significant covariance and nonlinearity in the data, a D-optimal design strategy successfully minimized training set sample size and was used to build effective partial least squares regression models for Cm(III) and HNO 3 concentrations without a priori knowledge of solution conditions. Chemometrics for modeling complex fluorescence spectra are promising and may find widespread applicability for online analysis in numerous chemical systems found in the nuclear field.
Executive Summary Project Background The Industrial Technology Validation (ITV) program aims to identify and demonstrate the performance of new, emerging, and underutilized energy-saving technologies in the industrial sector to help inform decisions to help accelerate their commercialization and deployment, as well as to help make industries more competitive. This ITV demonstration evaluated a thermoelectric generation (TEG) technology at a cement plant, aiming to reduce energy demand in the cement industry. A median cement plant consumes 5.73 million British thermal units per ton of clinker production (resulting in 0.838 metric tons of carbon dioxide [CO₂] emissions per ton of clinker) (Boyd and Zhang 2011, EPA 2021), equivalent to approximately 6.9 trillion British thermal units (TBtu) per year in energy consumption at a cement plant producing 3,300 tons of clinker per day.¹ Collaborating with Holcim, Advanced Thermovoltaic Systems (ATS) developed and deployed a pilot-scale thermoelectric power system to efficiently capture and convert waste heat to electricity. The system leverages the Seebeck effect to convert temperature differences on two sides of semiconductor cartridges into electrical power (ScienceDirect, n.d.). This generation is realized with minimal moving parts compared to existing waste-heat-to-generation solutions and allows capture from heat sources with temperatures as low as 150°C. This project aimed to validate a scalable solution applicable for capturing medium-temperature waste heat, including ambient losses from other high-temperature processes, and high-temperature sources less suitable for other waste-heat-to-power solutions. By recovering this otherwise wasted heat, this project intends to validate improvements to overall process efficiency through reduction in purchased electricity, thereby reducing operational costs while enhancing resiliency and competitiveness. Description and Scope This study evaluated the performance of a TEG system from ATS as a solution to convert waste heat into useful power at a Holcim cement plant in Alpena, Michigan. This plant is a fully integrated cement plant that has been operating since 1907. The facility operates continuously (24/7/365) with approximately 250 employees and five long dry kilns, yielding a total production capacity of 7,852 tons of cement per day (EPA 2023). Currently, the Alpena plant uses waste heat boilers to convert waste heat from the exhaust of each kiln into steam, which drives steam turbine generators. The ATS TEG is being evaluated for its potential to supplement the steam turbines by capturing the remaining lower grade heat. This technology is also being considered for other Holcim plants where steam turbines are not a viable option. ATS installed a pilot-scale TEG unit with an array of 582 individual thermoelectric semiconductor cartridges, of which 573 were operational. The cartridges are sandwiched between 48 hot plates and 49 cold plates. Each cartridge is designed to generate 20 watts (W) of gross power at a hot-side temperature of 240°C and cold-side temperature of 20°C. As such, the total gross generation capacity of the installed system is 11.5 kilowatts (kW) at design conditions. The system configuration for the evaluation was designed to prioritize convenience of installation and minimize disruption to production at the site, while ensuring that the heat required can be obtained for evaluating the TEG system at various operational conditions. To accomplish this, a portion of the steam supplied to Alpena’s steam turbine generation system was diverted to be used as the heat source for the TEG system, while water was supplied to the cold side of the system from nearby Lake Huron. This configuration was designed for the evaluation of the pilot-scale system to assess the performance at different conditions. A commercial-scale system will likely vary from the pilot system depending on typical configurations, including both scale and application. Future commercial applications of the ATS system would involve integrating the system into the exhaust from kiln preheaters, clinker coolers, or radiant heat capture from kiln shells for the heat source. For the cold source, a range of cooling solutions can be considered, including a mechanical cooling system, depending on the location and the application. To increase the generation capacity for commercial applications, the technology provider is working toward developing a commercial-scale TEG system, which would combine multiple TEG units (each similar in design to the pilot system) together. The scope of this evaluation includes the pilot-scale TEG system and all impacted equipment including pumps, controllers, and power handling equipment. Study Objectives The evaluation's goal was to assess the potential of the ATS TEG system to generate useful electrical power by capturing waste heat from cement production kilns. The objectives of this study are to evaluate and verify the following claims made by ATS regarding the pilot-scale system installed at the Holcim Alpena plant. The following design parameters and claims are also outlined in Table ES- 1 and Table ES- 2: • Gross Power: The thermoelectric system converts heat into power to create gross power, the total measured power generated by the system. The 573 active cartridge pilot-scale system is expected to generate 11.5 kW of gross power at the designed hot-side temperature of 240°C and cold-side temperature of 20°C. Power production is dependent on the temperature difference between the heat source (ultimately from the waste heat) and cold temperature supply source. • Net Power: The net power is the total usable power provided to the site by the TEG system after deducting parasitic power loads from the gross generated power. Supplementary equipment is required to operate the TEG system including pumps, controllers, and, in certain anticipated applications, mechanical cooling, which introduce parasitic loads to system operation. After deducting the parasitic loads from the gross power generation, ATS anticipates achieving a net power generation of 7.5 kW from the pilot-scale system. • Thermal Efficiency: The thermal efficiency is the percent of the total heat transferred to the TEG system that is converted to gross power. Historically, TEGs have a thermal efficiency of 2%–5% (DOE 2008). Prior industrial-scale TEG systems, such as the E1 TEG offered by Alphabet Energy, operated at an efficiency of 2.5% (Lamonica, 2014). ATS anticipates achieving an average efficiency of 4.8% or higher in converting heat energy to usable electricity. • Cartridge Performance: The TEG system comprises 573 active individual semiconductor cartridges, each of which generates a portion of the total power. Cartridge optimization and selection is an important design consideration for potential future TEG system design performance. Therefore, understanding the distribution of gross power and efficiency within the pilot system is vital to understanding what is achievable. At a design hot-side temperature of 240°C and cold-side temperature of 20°C, ATS anticipates a cartridge performance of 20 W of gross power per cartridge at an efficiency of 4.8% per cartridge. In addition to evaluating the claimed performance of the TEG pilot-scale unit, the study estimated the potential annual impacts of a scaled-up commercial system used to capture kiln waste heat over annual operations. The evaluation estimated the gross and net annual electric generation achievable by capturing heat from the two proposed tap-in points: the kiln exhaust and the clinker cooler exhaust; see Section 2.1 for details. Two use cases were examined: • Holcim Alpena: The Holcim Alpena site consists of long dry kilns with superheater boilers, which differs from the rest of Holcim’s cement plant portfolio and results in lower waste heat temperatures. The study estimates gross and net annual generation using the superheater boiler exhaust and clinker cooler exhaust, based on 2023 operational data. • Typical Installation: Common cement plants have preheater kilns with higher exhaust temperatures than Holcim Alpena across a range of production rates. The study estimates gross and net annual generation using the preheater exhaust and clinker cooler exhaust, with a sensitivity analysis to account for the typical range of preheater exhaust temperatures, clinker cooler exhaust temperatures, and clinker production rates. Methodology The evaluation methodology followed a measurement and verification (M&V) strategy based on the International Performance Measurement and Verification Protocol Option B through comprehensive measurements and analyses of the affected systems. Evaluation data was collected from March 9 to March 11, 2024, the test period of the pilot TEG system. During the test period, in coordination with the ITV team, the ATS team adjusted system operations to capture the range of variability expected for each of the variables pertinent to performance of the system. The methodology consisted of two parts: evaluating the performance of the pilot unit's TEG system and estimating the annual TEG impact in terms of gross and net power based on a given waste heat profile. First, the evaluation of the thermoelectric generation performance of the pilot unit relative to the claims was performed by analyzing the collected test data. Gross power of the pilot TEG system was directly measured. Net power was determined by deducting the measured parasitic power from the gross power. The gross power generation was compared to heat transferred to the system by the working fluid (which was heated by steam generated from the kiln waste heat) to calculate the thermal efficiency achieved by the system. Performance of individual semiconductor cartridges within the pilot array was also assessed in terms of measured gross cartridge power and calculated cartridge thermal efficiency. The second part of the evaluation estimated the annual TEG impacts in terms of gross power and net power (calculated from the difference between gross power and parasitic power). This analysis comprised development of mathematical regression models for gross power and parasitic power, with assessment of each model’s goodness-of-fit characteristics to ensure satisfaction of statistical requirements. The models predicted the gross power generation, the parasitic load based on the temperature difference between the hot working fluid and the cold-side fluid (cold water from Lake Huron) entering the system, the volumetric flow rate of the cold-side fluid at the inlet, and the volumetric flow rate of the hot working fluid at the inlet. The annual impact analysis considered a theoretical commercial-scale system sized to capture the available waste heat at a cement plant, consisting of linked pilot-scale units that receive heat from a theoretical gas-to-working-fluid heat exchanger. To estimate annual impacts at the Alpena plant, the gross power and parasitic power regression models were applied to the arrays in the theoretical commercial-scale system. The heat supplied to the unit was calculated based on the kiln run time, annual production, kiln exhaust waste heat, and clinker cooler waste heat derived from 2023 Holcim Alpena kiln operational data. Net power impacts were calculated by deducting the resulting parasitic power from the estimated gross power. Inputs for the model were generated from a combination of hourly data, assumed design considerations for TEG system scale-up from the pilot-scale unit, and assumptions regarding TEG system operations. This analysis was then used as the basis for estimating annual impacts of typical TEG installation at cement plants, by applying sensitivity analyses to key kiln operational characteristics including kiln preheater exhaust temperatures, cooler clinker exhaust temperatures, and plant daily production rates across a range of expected values. Project Results/Findings Table ES- 2 and Table ES- 2 provide a summary of the operating conditions and evaluation results compared to the stated claims from the technology provider. Key takeaways include: • Gross Power: The peak gross power achieved during the testing period was 10.0 kW, compared to the 11.5 kW expected for 573 active cartridges. The claimed gross power was associated with a target hot side of 240°C; however, the system only received a maximum hot-side mean plate temperature of 212°C during the testing period. • Net Power: The pilot-scale unit exceeded the claims for net power, achieving a peak of 7.7 kW net compared to a claim of 7.5 kW. One factor contributing to the higher achieved net power is the relatively high water pressure available through Lake Huron. The pilot TEG system did not require cold-side pumps during the test, whereas most installations would. This reduced the parasitic loads on the system, ultimately contributing to higher net power relative to the gross power. • Thermal Efficiency: The pilot-scale unit outperformed the claimed efficiency, achieving a peak system efficiency of 5.0% thermal efficiency compared to the stated 4.8%. • Cartridge Performance: To compare cartridge performance against claims, the study focused on the third day of testing, which aimed for conditions closest to the design specifications, with a hot side of 240°C and cold-side exit temperature of 6.4°–30°C. On this day, the mean gross power observed in the cartridges within the TEG array was 18.1 W/cartridge, and the peak performance was 34.7 W/cartridge. The estimated mean cartridge efficiency was 5.2%, and the estimated efficiency at peak gross cartridge power was 10%. The regression models developed for gross power generation and parasitic loads were used to estimate the generation impact for given heat input to the TEG from the working fluid (captured from the waste heat) and from the cold loop (Lake Huron) on an hourly basis for a year of operation. Based on this analysis, installation of a commercial-scale TEG system at the Holcim cement plant in Alpena, Michigan, with a waste heat exchanger of 0.85 effectiveness, would generate up to 391 kW of net power, translating to between 920,000 and 1,800,000 kilowatt-hours (kWh) in net electricity per year. Based on typical grid emissions for Alpena, this would avoid estimated net emissions by 752 metric tons of CO₂ annually.² The sensitivity analysis estimated that typical TEG system installations at cement plants could generate an average of 56–1,040 kW of net power, or between 488,000 and 9,110,000 kWh of net energy. This generation potential is most significantly affected by plant production rates and also influenced by preheater and clinker cooler exhaust temperatures. Applying the national average emission rate, typical commercial-scale installations at Holcim plants are projected to avoid between 182 and 3,401 metric tons of CO₂ annually per site. Table ES- 3 shows a summary of the estimated annual impacts.³ While parasitic loads are significant and vary by application, this analysis assumed the use of heating loop pumps and access to Lake Huron as a cold sink. This setup assumed no need for cooling loop pumps due to the available water pressure at the test site. Applications that require cooling towers or additional equipment are likely to experience higher parasitic loads. Therefore, the study’s estimates are most applicable to scenarios with similar parasitic load configurations—namely, access to a high-pressure cold sink. Applicability to other locations may be limited, as differing conditions could necessitate additional pumps and cooling systems, potentially impacting performance significantly.
In this study, we explored fusion of experiments and simulations for real time identification of pipeline defects across physical and non-physical domains. The challenges associated to data processing were addressed and a combined classification models was presented via CNN models. In addition, regression model based on XGBOOST is built to determine the defect location and defect dimension from data-driven features of guided wave signals captured by SMS fiber optic sensor.
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In this study, we explored fusion of experiments and simulations for real time identification of pipeline defects across physical and non-physical domains. The challenges associated to data processing were addressed and a combined classification models was presented via CNN models. In addition, regression model based on XGBOOST is built to determine the defect location and defect dimension from data-driven features of guided wave signals captured by SMS fiber optic sensor.
This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.
AMLRO (Active Machine Learning Reaction Optimizer) is an open-source framework designed to accelerate chemical reaction optimization using active learning with classical machine learning regression models. AMLRO integrates space-filling sampling strategies (e.g., Sobol and Latin Hypercube sampling) with iterative model training, prediction, and experiment selection to efficiently navigate complex reaction spaces. The platform supports multiple regression models, flexible multi-objective definitions, and user-defined parameter bounds, enabling data-efficient optimization from small initial datasets. AMLRO is designed for ease of use by experimentalists and can operate as a standalone decision-support tool or be integrated into closed-loop automated experimentation workflows.
Green leaf area index (LAI) is a measure of vegetative growth and development and is frequently used as an input parameter in yield estimation and evapotranspiration models. Extensive destructive sampling is usually required to achieve accurate estimates of green LAI in natural situations. In this investigation, a statistical modeling approach was used to predict the green LAI of oats from bidirectional reflectance data collected with multiband radiometers. Stepwise multiple regression models based on two sets of spectral reflectance factors accounted for 73 percent and 65 percent of the variance in green LAI of oats. Exponential models of spectral data transformations of greenness, normalized difference, and near-infrared/red ratio accounted for more of the variance in green LAI than the multiple regression models.
Multiple regression models were studied in order to determine their yield estimation capability for any arbitrary unit area and to obtain greater responsiveness and accuracy through the use of additional data sources applied at smaller spatial and temporal scales. It was concluded that data base inadequacy was the factor limiting performance in the models studied and that each of the models has more yield predicting capability than was reached during LACIE.
The Néel temperature is a crucial yet often overlooked parameter in calculating the stacking fault energy (SFE) of austenitic alloys. Several empirical equations have been proposed to estimate the Néel temperature of austenitic alloys, which are then used to calculate the SFE and explain deformation mechanisms. However, these empirical equations, typically derived using linear regression algorithms, are often simplistic and may fail to capture the complex interactions among multiple alloying elements that influence the Néel temperature. Moreover, their applicability is usually limited to specific compositional ranges. In this study, we propose a CALPHAD based approach and develop a surrogate decision tree based regression model capable of capturing the interactions among multiple alloying elements to predict the Néel temperature. Predictions from both the CALPHAD approach and the regression model show close agreement with experimental measurements reported in the literature. In conclusion, the implications of accurate Néel temperature predictions on the calculated SFE and deformation mechanisms are also discussed.
Entrainment of surrounding cooler and drier air into convective updrafts is one of the key processes that influence deep convection initiation and growth. Numerous studies have investigated the effect of entrainment on isolated convective cloud growth in idealized simulations, but the importance of this effect in realistic conditions with many interacting convective clouds remains uncertain. We examine the impact of entrainment on the depth reached by convective clouds in realistic large-eddy simulations (LES) over central Argentina during the Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign. Cloudy updrafts and their associated properties are assigned to convective cells tracked with radar reflectivity signatures. Several thousand convective cells are tracked over two high convective available potential energy (CAPE) and two low CAPE cases that support cells of varying depths and intensities. Entrainment is calculated explicitly as the fluxes of air into the outer surface of each cloudy updraft. Single-predictor logistic regression models are used to determine the relative importance of updraft, near-updraft, and preconvective initiation atmospheric conditions in predicting whether convective cells become deep. We then build a multiple-predictor regression model pairing important updraft and meteorological metrics with fractional entrainment rate. The probability of cells transitioning to deep convection is most sensitive to ambient 600-hPa relative humidity (42% of total metric contribution to cloud depth predictability), followed by low-level CAPE (28%), cloud-base updraft width (19%), and fractional entrainment (11%). Thus, the initial width of the updraft along with potential buoyancy and its dilution through the midtroposphere collectively determine whether deep convection will result from shallower clouds.
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.