Uncertainty Quantification Analysis Research Articles

Competing mechanisms in bacterial invasion of human colon mucus probed with agent-based modeling

The gastrointestinal tract is inhabited by a vast community of microorganisms, termed the gut microbiota. Large colonies can pose a health threat, but the gastrointestinal mucus system protects epithelial cells from microbiota invasion. The human colon features a bilayer of mucus lining. Due to imbalances in intestinal homeostasis, bacteria may successfully penetrate the inner mucus layer, which can lead to severe gut diseases. However, it is hard to tease apart the competing mechanisms that lead to this penetration. To probe the conditions that permit bacteria penetration into the inner mucus layer, we develop an agent-based model consisting of bacteria and an inner mucus layer subject to a constant flux of nutrient fields feeding the bacteria. We find that there are three important variables that determine bacterial invasion: the bacterial reproduction rate, the contact energy between bacteria and mucus, and the rate of bacteria degrading the mucus. Under healthy conditions, all bacteria are naturally eliminated by the constant removal of mucus. In diseased states, imbalances between the rates of bacterial degradation and mucus secretion lead to bacterial invasion at certain junctures. We conduct uncertainty quantification and sensitivity analysis to compare the relative impact between these parameters. The contact energy has the strongest influence on bacterial penetration, which, in combination with bacterial degradation rate and growth rate, greatly accelerates bacterial invasion of the human gut mucus lining. Our findings will serve as predictive indicators for the etiology of intestinal diseases and highlight important considerations when developing gut therapeutics.

Empirical loss weight optimization for PINN modeling laser bio-effects on human skin for the 1D heat equation

The application of deep neural networks towards solving problems in science and engineering has demonstrated encouraging results with the recent formulation of physics-informed neural networks (PINNs). Through the development of refined machine learning techniques, the high computational cost of obtaining numerical solutions for partial differential equations governing complicated physical systems can be mitigated. However, solutions are not guaranteed to be unique, and are subject to uncertainty caused by the choice of network model parameters. For critical systems with significant consequences for errors, assessing and quantifying this model uncertainty is essential. In this paper, an application of PINN for laser bio-effects with limited training data is provided for uncertainty quantification analysis. Additionally, an efficacy study is performed to investigate the impact of the relative weights of the loss components of the PINN and how the uncertainty in the predictions depends on these weights. Network ensembles are constructed to empirically investigate the diversity of solutions across an extensive sweep of hyper-parameters to determine the model that consistently reproduces a high-fidelity numerical simulation.

Enhancement of Reflood Test Prediction by Integrating Machine Learning and Data Assimilation Technique

Data assimilation (DA) was revealed as a highly efficient approach to enhance the prediction’s accuracy, demonstrating the reliability of the simulation through uncertainty quantification analysis. However, in the numerical simulations, most of the tasks are highly nonlinear relationships between the parameters that directly affect the efficiency of the DA such as the large search space dimension, resulting in significant computational costs. This limitation can be overcome by implementing machine learning (ML) predictions that can efficiently expand the DA search space. Therefore, this study is aimed at enhancing the performance of DA by integrating ML and DA (IMD), proposing a new method to overcome the stand-alone DA limitations. The approach involved implementing a stand-alone DA using the multidimensional analysis of reactor safety (MARS) code to enhance the prediction of reflood tests. The output datasets obtained from the stand-alone DA were then used to train the deep neural networks (DNNs), and the accuracy of the DNN’s prediction was thoroughly evaluated with varying dataset sizes. This DNN subsequently can predict the enormous unobserved samples, enabling the identification and investigation of the prospective candidates for the subsequent DA process. The results demonstrated that the stand-alone DA achieved an accuracy enhancement of up to 41.3% in reflood test predictions, while the IMD yielded even more significant improvements, with a performance enhancement of 47.0%. These findings reveal that the IMD approach outperformed the stand-alone DA approach, particularly in the case of high flooding rate tests. In this context, the proposed integrating system can effectively overcome the high computational cost and enhance the performance of stand-alone DA.

Uncertainty Quantification in Modeling Mold Heat Transfer in Steel Continuous Slab Casting with CON1D

Computational models are powerful tools to quantify physical phenomena to gain valuable insights into a manufacturing process. Their accuracy is hindered, however, by uncertainty in the input data. Furthermore, when calibrating models with plant measurements, it helps to understand which variables have greatest effect on the critical model outputs. This work applies uncertainty quantification and sensitivity analysis to determine the most influential input parameters in the CON1D model of heat transfer and solidification in steel continuous casting with slag. Results show that the slag rim greatly affects heat flux near the meniscus, so control of its size is important. Heat flux and temperature down the mold depend greatly on velocity of the solid slag layer, and slag solidification temperature, which control the slag layer thickness, which in turn affects the interfacial resistance that controls heat transfer in the process. Scale formation on the mold coldface greatly increases mold temperatures. Based on the results presented here, models of heat transfer in continuous casting such as CON1D would benefit from plant measurements such as slag rim size and solid slag velocity, and lab measurements such as slag viscosity at lower temperatures, to better characterize this important slag property.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics.

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Uncertainty quantification and global sensitivity analysis of bearing capacity of push-out specimen considering randomness in bond-slip behaviour

As an artificial composite material, the uncertainty in mechanical property of concrete significantly impacts the bond-slip behaviour of the shaped steel concrete structure. To investigate the effect of the uncertainty of concrete mechanical properties on the bearing capacity of push-out specimens, based on the data of a small number of push-out test with identical design parameters, the improved Bootstrap method is utilized to execute sample augmentation for the bond stress-slip curves, and the stochastic bond slip constitutive model is established after considering five parameters (K1, …, K5) in the deterministic bond-slip model as random variables. Simultaneously, considering the randomness in elastic modulus of concrete (Ec), uncertainty quantification (UQ) of the bearing capacities of the push-out specimens is conducted using the arbitrary polynomial chaos (aPC) method. Subsequently, the global sensitivity analysis of the ultimate and residual bearing capacities is accomplished through the aPC surrogate model. The results indicate that the probability distribution types of the parameters in the stochastic bond-slip constitutive model can be arbitrary when considering the randomness of concrete material, and the aPC method with at least a third-order expansion is recommended to execute UQ for the push-out test due to the strong nonlinearty between the bearing capacities and the random parameters. The ultimate bearing capacity is primarily affected by the parameter K2, followed by K4, K3, and K5. Whereas the residual bearing capacity is predominantly influenced by the parameter K4, followed by K5, the remaining parameters exhibit negligible influence. In contrast, K1 and Ec have the greatest influence on equivalent plastic strain of the concrete near the loading end of the push-out specimen.

Large-Eddy Simulations with remeshed Vortex methods: An assessment and calibration of subgrid-scale models

This study assesses various subgrid-scale models within the framework of Large Eddy Simulation (LES) using a remeshed Vortex method (RVM). RVM is a semi-Lagrangian method discretizing the vorticity-velocity Navier–Stokes equations that has proven to be a stable and less dissipative alternative to more classical Eulerian methods. The subgrid-scale models are first tested on the well-known Taylor–Green Vortex case at Re=5000. Notably, the Variational Multiscale (VMS) variant of the Smagorinsky model and the Spectral Vanishing Viscosity (SVV) approaches emerge as the best-suited to the RVM, as they add diffusion to only the smallest resolved vorticity scales. Then, a stochastic uncertainty quantification analysis is conducted for both selected models, and the model coefficients are calibrated against direct numerical simulation. These coefficients are then applied to additional cases (different regimes, grid resolutions and test cases), showing the robustness of the calibration within the RVM-LES framework.

Physics-based reduced order modeling for uncertainty quantification of guided wave propagation using Bayesian optimization

Guided wave propagation (GWP) is commonly employed for the design of SHM systems. However, GWP is sensitive to variations in the material properties, often leading to false alarms. To address this issue, uncertainty quantification (UQ) is employed to improve the reliability of the predictions. Computational structural mechanics is a useful tool for the simulation of GWP. Even so, the application of UQ methods requires numerous solutions, while large-scale, transient GWP simulations increase the computational cost. In this paper, we propose a machine learning (ML)-based reduced order model (ROM), annotated as BO-ML-ROM, to decrease the computational time of the GWP simulation. The ROM is integrated with a Bayesian optimization (BO) framework to adaptively sample the data for the ROM training. The results showed that BO outperforms one-shot sampling methods, both in terms of accuracy and speed. The developed ROM, which is orders of magnitude faster than the original solver, is then applied for forward uncertainty quantification of the GWP in an aluminum plate and a composite panel under varying material properties. The UQ analysis reveals the higher impact of the uncertainties in the wave reflections. Furthermore, to compute the influence of the material properties on the predictions, a sensitivity analysis (SA) is performed using the variance-based Sobol’ indices and the Shapley additive explanations, where it is shown that the uncertainties in the elastic properties have a varying influence across time. The predicted results reveal the efficiency of BO-ML-ROM for the simulation of the GWP and demonstrate its utility for UQ and SA.

An efficient sparse surrogate model for aerodynamic characteristics of a supersonic compressor cascade with uncertain geometric deformations

The increasing demand for high-load compressors necessitates research and design of supersonic compressor blades. Geometric deformations of the blades resulting from manufacturing errors introduce uncertainties in their aerodynamic characteristics. For uncertainty analysis, Polynomial Chaos Expansion (PCE) has gained popularity among engineers in various disciplines. However, as the number of random variables used to describe uncertainties increases, the efficiency of the PCE method diminishes. To overcome this limitation, an Efficient Sparse Surrogate Model (ESSM) was first proposed. The ESSM combines PCE to approximate global characteristics and Gaussian process modeling to capture local variability, resulting in a highly accurate model. Additionally, by utilizing an iteratively diffeomorphic modulation under observable response preserving homotopy, important PCE basis functions are adaptively selected, leading to a sparse surrogate model that significantly reduces the required training samples. Then using the ESSM, efficient Uncertainty Quantification (UQ) and global sensitivity analysis were conducted to evaluate the impact of uncertain geometric deformations on the aerodynamic characteristics of a supersonic compressor cascade. Principal Component Analysis (PCA) was employed in conjunction with an Improved Class Shape Transformation (ICST) to characterize geometric deformations caused by manufacturing errors. The proposed ICST method exhibits enhanced accuracy in fitting near the leading and trailing edges compared to the CST method. PCA enables a 50% reduction in the number of random variables needed to describe geometric deformations. The UQ results establish a quantitative correlation between geometric deformations and supersonic aerodynamics, and the sensitivity analysis identifies some specific forms of geometric deformations that significantly impact the aerodynamics. Finally, the study investigated the flow mechanisms associated with typical geometric deformation forms, further providing recommendations for manufacturing and testing of supersonic blades to prevent performance deterioration.

Uncertainty quantification for high-temperature flame sensing using wavelength modulation spectroscopy

In this study, we explore the uncertainty of the wavelength modulation spectroscopy (WMS) technique applied to water profile measurement in a flat flame. The scanned WMS-2f/1f method is used to measure the water profile in a C2H4-O2-Ar flame, using an absorption transition line near 1391.7 nm. The Monte Carlo sampling method is used for the uncertainty quantification (UQ) analysis. The results show a non-negligible uncertainty on the water concentration with an uncertainty range from 10% to 30%, depending on the uncertainty level considered for the input parameters of the spectroscopic model. Further sensitivity analyses show that the lower state energy (E′′), the line strength, and the temperature are the most important uncertainty sources. When multiple transition lines are involved, the line strength value controls the overall influence of the other parameters associated with these specific lines. We also compared the uncertainty obtained when applying the direct absorption spectroscopy (DA) and WMS techniques for a similar flame configuration. Only a slight advantage is observed for the WMS.

Systematic quantification of modeling uncertainties in tank–foundation coupled systems

Traditionally, uncertainty quantification in the context of liquid storage tanks has primarily focused on ground motion record-to-record variability, along with partial consideration of material randomness. This paper presents a comprehensive framework for addressing “modeling uncertainty” in the seismic analysis of rectangular tanks, including the influence of foundation interactions. The framework encompasses uncertainties inherent in both general finite element and mathematical modeling techniques, as well as uncertainty in modeling parameters (e.g., hydrodynamic mass and concrete constitutive model). This is achieved through the implementation of an efficient design of experiments. By employing an innovative intensifying artificial acceleration, over 26,000 transient simulations are conducted, spanning the full spectrum of structural behavior from linear to nonlinear regimes. Through a series of uncertainty quantification and sensitivity analyses, this study assesses bias and dispersion arising from diverse model assumptions. Furthermore, fragility analysis and machine learning post-processing techniques are employed to extract latent insights from the generated data. The outcomes underscore that numerical and mathematical modeling uncertainties can bear comparable significance to ground motion record-to-record variability. The adoption of distinct modeling strategies introduces biases in fragility curves, particularly within higher damage states. Consequently, it is advised to account for modeling randomness directly (via simulation) or approximately (leveraging the insights from this study) in any uncertainty quantification related to storage tanks.

Review of Sources of Uncertainty and Techniques Used in Uncertainty Quantification and Sensitivity Analysis to Estimate Greenhouse Gas Emissions from Ruminants

Uncertainty quantification and sensitivity analysis are essential for improving the modeling and estimation of greenhouse gas emissions in livestock farming to evaluate and reduce the impact of uncertainty in input parameters to model output. The present study is a comprehensive review of the sources of uncertainty and techniques used in uncertainty analysis, quantification, and sensitivity analysis. The search process involved rigorous selection criteria and articles retrieved from the Science Direct, Google Scholar, and Scopus databases and exported to RAYYAN for further screening. This review found that identifying the sources of uncertainty, implementing quantifying uncertainty, and analyzing sensitivity are of utmost importance in accurately estimating greenhouse gas emissions. This study proposes the development of an EcoPrecision framework for enhanced precision livestock farming, and estimation of emissions, to address the uncertainties in greenhouse gas emissions and climate change mitigation.

Uncertainty Quantification in Geochemical Mapping: A Review and Recommendations

AbstractGeochemical mapping is a crucial tool that can provide valuable insights for a wide range of applications, including mineral resources prospecting, environmental impact assessment, geological process understanding, and climate change research. Despite its significance, geochemical mapping requires spatial modeling based on sparse, heterogeneous, and potentially inaccurate data sets. Moreover, the underlying geological processes are often imperfectly understood. Therefore, uncertainty quantification (UQ) is vital in geochemical mapping to ensure accurate and reliable results, ultimately facilitating well‐informed decision‐making. In this contribution, we distinguish two primary types of uncertainties: systemic and stochastic. We identify the key sources of uncertainties in geochemical mapping and review the techniques that have been employed or hold potential for uncertainty quantification, communication, visualization, and sensitivity analysis. This contribution also illustrates the general procedure of UQ in geochemical mapping by a case study of mapping geochemical anomalies associated with gold mineralization in northwestern Sichuan Province, China. We also explore potential strategies for mitigating the critical uncertainties, such as gathering more geochemical data, developing more effective models, enhancing our understanding of the geochemical dispersion process, or leveraging other thematic information or knowledge. Future research should prioritize addressing underexplored uncertainties and implementing more practical applications to validate the UQ procedure in geochemical mapping.

Probabilistic Design Method for Aircraft Thermal Protective Layers Based on Surrogate Models

In this study, a probabilistic method was proposed for an aircraft’s thermal protective layers. The uncertainties of material properties, geometric dimensions, and incoming flow environments were considered for the design inputs. To accelerate the design efficiency, Latin hypercube sampling and surrogate models were built based on finite element method calculations to enhance the simulation efficiency. Thus, the Monte Carlo method can be implemented with such a fast simulation method and produce a massive number of samples for the uncertainty quantification and sensitivity analysis, exploring their impact on the back temperature of the thermal protection layer. Compared to the deterministic method with the extreme deviation design, the probabilistic design yields a weight reduction of 15.61%. This indicates that probabilistic design is an efficient approach to enhance the performance of aircraft and reduce the overall weight of the aircraft. The general goal of this study is to provide a new design method for the coating film of thermal protection systems by considering multiple sources of uncertainties.

Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Uncertainty quantification and sensitivity analysis of an unsteady axisymmetric reacting solid particle

Simulations of unsteady solid fuel particle combustion involve a variety of complex phenomena, which can be numerically predicted using models with varying levels of fidelity. These models in turn rely on parameters obtained from experiments or small-scale simulations. It is therefore essential to quantify the uncertainties in the prediction of different quantities of interest with respect to these model parameters to ensure robustness. This is particularly important when combustion under different freestream compositions (for example, air or oxy atmospheres) are analyzed. The first step is to determine the most sensitive parameters of the model. However the large dimension of the parameter space makes traditional methods such as finite difference (brute force) unfeasible. This work addressed this bottleneck by employing a semi-discrete adjoint method to determine sensitivities. This study also examines the evolution of these sensitivities in time for a single unsteady axisymmetric particle undergoing devolatilization, where a methane mechanism is used to the gas phase chemical reactions. The dominant model parameters are identified for several quantities of interest, including particle temperature and burning rate, and under two freestream compositions (i.e. air and oxy atmospheres). Additionally, the impact of various devolatilization models on the extracted sensitivities is analyzed. In addition to sensitivities, an adjoint-based active sub-space method (AASM) Hassan et al. (2023) is also utilized to quantify the underlying uncertainties in the predictions. This provides a general assessment of model predictability with respect to the identified quantities of interest. Using AASM uncertainties are extracted for both air and oxy atmospheres and compared in the context of a single particle undergoing devolatilization. Comparisons reveal that particle parameters yield significantly greater uncertainties and sensitivities than gas phase reaction rates. Additionally, model parameter uncertainties are larger in the oxy atmosphere than in air, highlighting the impact of the freestream composition on the resulting predictions.Novelty and significance statementQuantifying the uncertainties and sensitivities associated with solid fuel combustion model parameters is unfeasible using traditional methods due to the large number of model parameters, which is known as the ‘curse of dimensionality’ However, by combining adjoint techniques with dimension reduction approaches in a single method, AASM, this issue can be overcome. AASM offers a general assessment of model predictability for various quantities of interest (QoIs), defining the most sensitive parameters in a global context rather than a local one, and shows the time evolution of uncertainties for these QoIs in different atmospheric conditions, revealing the role of the free-stream composition on the resulting predictions.

Quantifying Drivers of Methane Hydrobiogeochemistry in a Tidal River Floodplain System

The influence of coastal ecosystems on global greenhouse gas (GHG) budgets and their response to increasing inundation and salinization remains poorly constrained. In this study, we have integrated an uncertainty quantification (UQ) and ensemble machine learning (ML) framework to identify and rank the most influential processes, properties, and conditions controlling methane behavior in a freshwater floodplain responding to recently restored seawater inundation. Our unique multivariate, multiyear, and multi-site dataset comprises tidal creek and floodplain porewater observations encompassing water level, salinity, pH, temperature, dissolved oxygen (DO), dissolved organic carbon (DOC), total dissolved nitrogen (TDN), partial pressure of carbon dioxide (pCO2), nitrous oxide (pN2O), methane (pCH4), and the stable isotopic composition of methane (δ13CH4). Additionally, we incorporated topographical data, soil porosity, hydraulic conductivity, and water retention parameters for UQ analysis using a previously developed 3D variably saturated flow and transport floodplain model for a physical mechanistic understanding of factors influencing groundwater levels and salinity and, therefore, CH4. Principal component analysis revealed that groundwater level and salinity are the most significant predictors of overall biogeochemical variability. The ensemble ML models and UQ analyses identified DO, water level, salinity, and temperature as the most influential factors for porewater methane levels and indicated that approximately 80% of the total variability in hourly water levels and around 60% of the total variability in hourly salinity can be explained by permeability, creek water level, and two van Genuchten water retention function parameters: the air-entry suction parameter α and the pore size distribution parameter m. These findings provide insights on the physicochemical factors in methane behavior in coastal ecosystems and their representation in local- to global-scale Earth system models.

UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF SEISMIC FRAGILITY CURVES USING KRIGING

Seismic fragility curves have been introduced as key components of seismic probabilistic risk assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into account various sources of uncertainties, the so-called epistemic uncertainties (i.e., coming from the uncertainty on the mechanical parameters of the structure) and the aleatory uncertainties (i.e., coming from the randomness of the seismic ground motions). For simulation-based approaches we propose a methodology to build and calibrate a Gaussian process surrogate model to estimate a family of nonparametric seismic fragility curves for a mechanical structure by propagating both the surrogate model uncertainty and the epistemic ones. Gaussian processes have indeed the main advantage to propose both a predictor and an assessment of the uncertainty of its predictions. In addition, we extend this methodology to sensitivity analysis. Global sensitivity indices such as aggregated Sobol' indices and kernel-based indices are proposed to know how the uncertainty on the seismic fragility curves is apportioned according to each uncertain mechanical parameter. This comprehensive uncertainty quantification framework is finally applied to an industrial test case consisting of a part of a piping system of a pressurized water reactor.

Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests

The reflooding phase, a crucial recovery process after a loss of coolant accident (LOCA) in reactors, involves cooling overheated fuel rods with subcooled water. Its complex nature, notably in its flow regime and heat transfer, makes prediction challenging, resulting in high uncertainty and computation cost. In this study, we utilized the data assimilation (DA) technique to enhance the prediction of reflooding phenomena and subsequently deployed machine learning models to predict the accuracy of the safety and performance analysis code (SPACE) simulation. To generate the dataset for the machine learning model, we employed the sampling method for highly nonlinear system uncertainty analysis (STARU), providing a high-quality dataset for a complex problem such as a reflooding simulation. In this dataset, the physical models were assimilated under their selected uncertainty bands and utilized the effective sampling approach of STARU, generating the high-quality output and efficient enhancement of SPACE predictions. Consequently, the implemented machine learning model can be used to enhance model development and uncertainty quantification (UQ) analysis using the system code.

A Physics-Informed Spatial-Temporal Neural Network for Reservoir Simulation and Uncertainty Quantification

Summary Surrogate models play a vital role in reducing computational complexity and time burden for reservoir simulations. However, traditional surrogate models suffer from limitations in autonomous temporal information learning and restrictions in generalization potential, which is due to a lack of integration with physical knowledge. In response to these challenges, a physics-informed spatial-temporal neural network (PI-STNN) is proposed in this work, which incorporates flow theory into the loss function and uniquely integrates a deep convolutional encoder-decoder (DCED) with a convolutional long short-term memory (ConvLSTM) network. To demonstrate the robustness and generalization capabilities of the PI-STNN model, its performance was compared against both a purely data-driven model with the same neural network architecture and the renowned Fourier neural operator (FNO) in a comprehensive analysis. Besides, by adopting a transfer learning strategy, the trained PI-STNN model was adapted to the fractured flow fields to investigate the impact of natural fractures on its prediction accuracy. The results indicate that the PI-STNN not only excels in comparison with the purely data-driven model but also demonstrates a competitive edge over the FNO in reservoir simulation. Especially in strongly heterogeneous flow fields with fractures, the PI-STNN can still maintain high prediction accuracy. Building on this prediction accuracy, the PI-STNN model further offers a distinct advantage in efficiently performing uncertainty quantification, enabling rapid and comprehensive analysis of investment decisions in oil and gas development.