Efficient Bayesian Active Learning with Langevin Dynamics for Reservoir Porosity Inversion

The remaining useful life (RUL) estimation is an important metric that helps in condition-based maintenance. Damage data obtained from the diagnostics techniques are often noisy, and the RUL estimated from the data is less reliable. Estimating the probabilistic RUL by quantifying the uncertainty in the predictive model parameters using the noisy data increases confidence in the predicted values. In this work, Bayesian inference is used to inversely quantify the uncertainty in the model parameters of the predictive damage model in adhesively bonded joints, and quantified parameter uncertainty is represented by a probability distribution function (PDF). It is difficult to obtain a closed-form solution for the RUL from the PDF of model parameters due to the nonlinearity of the damage models. Instead, statistical simulations are used to generate the model parameter samples from the PDF, and the RUL is estimated from the samples. In the statistical simulations, the predictive damage model is evaluated for each parameter sample. Using a physics-based model as the predictive model increases computational time, which makes the statistical techniques to be computationally expensive. It is essential to reduce the computational time to estimate the RUL in a feasible time. In this work, real-time probabilistic RUL estimation is demonstrated in adhesively bonded joints using the Sequential Monte Carlo (SMC) sampling method and cloud-based computations. The SMC sampling method is an alternative to traditional Markov Chain Monte Carlo (MCMC) methods, which enables generating statistical parameter samples in parallel. The parallel computational capabilities of the SMC methods are exploited by running the SMC simulation on multiple cloud calls. This approach is demonstrated by estimating fatigue RUL in the adhesively bonded joint. The accuracy of probabilistic RUL estimated by SMC is validated by comparing it with RUL estimated by the MCMC and the experimental values. The SMC simulation is run on the cloud and the computational speedup of the SMC is demonstrated.

Satellite‐based quantitative precipitation estimates (QPE), such as NASA's Integrated Multi‐satellitE Retrievals for GPM (IMERG), provide easily accessible continental‐to‐global precipitation forcings for flood prediction and other hydrologic applications. Nevertheless, when used in hydrologic prediction, uncertainty in satellite‐based QPE often leads to significant bias. This forcing uncertainty is further blended with other error sources, including process representation, parameter values, and their interactions. The identification and decoupling of these uncertainties can enhance our understanding of their respective impacts, thereby improving hydrologic prediction. Addressing this issue worldwide is challenging, however, largely due to the scarcity of precipitation ground truth and complex uncertainty interactions. Therefore, we propose an efficient uncertainty quantification framework for ensemble streamflow prediction, which keeps different uncertainty sources separable through hierarchical Bayesian inference. Satellite‐based QPE uncertainty is characterized by a novel near‐realtime quasi‐global satellite‐only ensemble precipitation data set (STREAM‐Sat), which is completely independent of ground‐based precipitation measurements. Model parameter uncertainty in a distributed physics‐based hydrologic model is inferred by an Iterative Ensemble Smoother (IES). To illustrate the impact and limitations of precipitation uncertainty, we compared ensemble streamflow predictions driven by both model parameter and satellite precipitation uncertainties and ensemble streamflow predictions driven by model parameter uncertainty and deterministic QPE. We demonstrate that the quantification of satellite‐based QPE uncertainty notably improves the accuracy and reliability of near‐realtime streamflow predictions in data scarce regions. This study also lays a foundation for satellite‐based streamflow prediction in ungauged regions.

The focus of this work is on the development of a framework permitting the unification of generalized polynomial chaos (gPC) with the linear moment propagation equations, to accurately characterize the state distribution for linear systems subject to initial condition uncertainty, Gaussian white noise excitation and parametric uncertainty which is not required to be Gaussian. For a fixed value of parameters, an ensemble of moment propagation equations characterize the distribution of the state vector resulting from Gaussian initial conditions and stochastic forcing, which is modeled as Gaussian white noise. These moment equations exploit the gPC approach to describe the propagation of a combination of uncertainties in model parameters, initial conditions and forcing terms. Sampling the uncertain parameters according to the gPC approach, and integrating via quadrature, the distribution for the state vector can be obtained. Similarly, for a fixed realization of the stochastic forcing process, the gPC approach provides an output distribution resulting from parametric uncertainty. This approach can be further combined with moment propagation equations to describe the propagation of the state distribution, which encapsulates uncertainties in model parameters, initial conditions and forcing terms. The proposed techniques are illustrated on two benchmark problems to demonstrate the techniques’ potential in characterizing the non-Gaussian distribution of the state vector.

Advice on fishing opportunities is based on stock assessment models. Modern stock assessment frameworks are designed to account for uncertainty in model parameters. However, some parameters are often fixed at specific values and assumed to be known precisely. Paradoxically, these fixed values often relate to parameters we understand the least—such as the natural mortality rate. For example, in the assessment of Norwegian Spring-Spawning Herring, the natural mortality rate is assumed to be exactly 0.9 for age 2 fish and 0.15 for older fish. In this study, we investigate how sensitive the assessment results—and, more specifically, the resulting fishing quotas (total allowable catch, TAC)—are to assumptions regarding natural mortality and maturity-at-age for both Norwegian Spring-Spawning Herring and North-East Arctic Cod. The assessment models for both stocks are formulated within the SAM framework. Furthermore, we explore a simple approach for adjusting harvest control rules that seeks to preserve the TACs when fundamental fixed assumptions are altered. Our intention is that this serves as an exploratory tool to investigate sensitivity to new assumptions, and is not intended to replace a more formal process for defining new biological reference points and harvest control rules. The results indicate that, under the current harvest control rules, the TACs for both herring and cod may be sensitive to assumptions regarding natural mortality rates and maturity-at-age. For herring, sensitivity to natural mortality is significantly greater than is reflected by the estimation uncertainty in model parameters. However, when basic assumptions are changed, it is also natural to consider corresponding adjustments to the harvest control rules. Our proposed simple adjustments to the control rules reduce sensitivity to these assumptions in many cases, though not in all.

Metamodeling may substantially reduce the computational expense of individual-level state transition simulation models (IL-STM) for calibration, uncertainty quantification, and health policy evaluation. However, because of the lack of guidance and readily available computer code, metamodels are still not widely used in health economics and public health. In this study, we provide guidance on how to choose a metamodel for uncertainty quantification. We built a simulation study to evaluate the prediction accuracy and computational expense of metamodels for uncertainty quantification using life-years gained (LYG) by treatment as the IL-STM outcome. We analyzed how metamodel accuracy changes with the characteristics of the simulation model using a linear model (LM), Gaussian process regression (GP), generalized additive models (GAMs), and artificial neural networks (ANNs). Finally, we tested these metamodels in a case study consisting of a probabilistic analysis of a lung cancer IL-STM. In a scenario with low uncertainty in model parameters (i.e., small confidence interval), sufficient numbers of simulated life histories, and simulation model runs, commonly used metamodels (LM, ANNs, GAMs, and GP) have similar, good accuracy, with errors smaller than 1% for predicting LYG. With a higher level of uncertainty in model parameters, the prediction accuracy of GP and ANN is superior to LM. In the case study, we found that in the worst case, the best metamodel had an error of about 2.1%. To obtain good prediction accuracy, in an efficient way, we recommend starting with LM, and if the resulting accuracy is insufficient, we recommend trying ANNs and eventually also GP regression.

The traditional treatment of uncertainty in hydrological modelling primarily attributes it to model parameters, but rarely systematically considers meteorological input errors, especially in quantifying the impact of meteorological input errors on parameter uncertainty. This study developed a Bayesian‐based integrated approach to quantitatively investigate uncertainties in meteorological inputs (precipitation and temperature) and model parameters as well as the variation in parameter uncertainty due to meteorological input errors. Additionally, we analysed the propagation from these uncertainties to runoff response in snowmelt and non‐snowmelt periods. The applicability and advantages of this approach were presented by applying of the Soil and Water Assessment Tool to the Shitoukoumen Reservoir Catchment. Differential Evolution Adaptive Metropolis‐Markov Chain Monte Carlo was applied for the straightforward Bayesian inference the uncertainties of meteorological inputs and model parameters. On this basis, multilevel factorial analysis technology was used to quantitatively investigate the specific impact of the model parameters' individual and interactive effects due to meteorological input errors. Finally, the impact of meteorological input errors and model parameter uncertainty on the model performance were analysed and quantified systematically. The results showed that the meteorological input errors could affect the random characteristics of multiple model parameters. Moreover, meteorological input errors could further affect the model parameters' effects on annual average runoff. Overall, the above results have significant implications in enhancing hydrological model to simulate/predict runoff and understanding hydrological processes during different periods.

Abstract. The future of the Antarctic Ice Sheet in response to climate warming is one of the largest sources of uncertainty in estimates of future changes in global mean sea level (ΔGMSL). Mass loss is currently concentrated in regions of warm circumpolar deep water, but it is unclear how ice shelves currently surrounded by relatively cold ocean waters will respond to climatic changes in the future. Studies suggest that warm water could flush the Filchner–Ronne (FR) ice shelf cavity during the 21st century, but the inland ice sheet response to a drastic increase in ice shelf melt rates is poorly known. Here, we use an ice flow model and uncertainty quantification approach to project the GMSL contribution of the FR basin under RCP emissions scenarios, and we assess the forward propagation and proportional contribution of uncertainties in model parameters (related to ice dynamics and atmospheric/oceanic forcing) on these projections. Our probabilistic projections, derived from an extensive sample of the parameter space using a surrogate model, reveal that the FR basin is unlikely to contribute positively to sea level rise by the 23rd century. This is primarily due to the mitigating effect of increased accumulation with warming, which is capable of suppressing ice loss associated with ocean-driven increases in sub-shelf melt. Mass gain (negative ΔGMSL) from the FR basin increases with warming, but uncertainties in these projections also become larger. In the highest emission scenario RCP8.5, ΔGMSL is likely to range from −103 to 26 mm, and this large spread can be apportioned predominantly to uncertainties in parameters driving increases in precipitation (30 %) and sub-shelf melting (44 %). There is potential, within the bounds of our input parameter space, for major collapse and retreat of ice streams feeding the FR ice shelf, and a substantial positive contribution to GMSL (up to approx. 300 mm), but we consider such a scenario to be very unlikely. Adopting uncertainty quantification techniques in future studies will help to provide robust estimates of potential sea level rise and further identify target areas for constraining projections.

Utilizing degraded quality waters such as saline water as irrigation water with proper management methods such as leaching application is a potential answer to water scarcity in agricultural systems. Leaching application requires understanding the relationship between the amount of irrigation water and its quality with the dynamic of salts in the soil. The HYDRUS-1D model can simulate the dynamic of soil salinity under saline water irrigation conditions. However, these simulations are subject to uncertainty. A study was conducted to assess the uncertainty of the HYDRUS-1D model parameters and outputs to simulate the dynamic of salts under saline water irrigation conditions using the Markov Chain Monte Carlo (MCMC) based Metropolis-Hastings algorithm in the R-Studio environment. Results indicated a low level of uncertainty in parameters related to the advection term (water movement simulation) and water stress reduction function for root water uptake in the solute transport process. However, a higher level of uncertainty was detected for dispersivity and diffusivity parameters, possibly because of the study’s scale or some error in initial or boundary conditions. The model output (predictive) uncertainty showed a high uncertainty in dry periods compared to wet periods (under irrigation or rainfall). The uncertainty in model parameters was the primary source of total uncertainty in model predictions. The implementation of the Metropolis-Hastings algorithm for the HYDRUS-1D was able to conveniently estimate the residual water content (θr) value for the water simulation processes. The model’s performance in simulating soil water content and soil water electrical conductivity (ECsw) was good when tested with the 50% quantile of the posterior distribution of the parameters. Uncertainty assessment in this study revealed the effectiveness of the Metropolis-Hastings algorithm in exploring uncertainty aspects of the HYDRUS-1D model for reproducing soil salinity dynamics under saline water irrigation at a field scale.

Comparison of experimental data with modeling predictions is essential for making quantitative measurements of species properties, such as diffusion coefficients and species concentrations using a T-sensor. To make valid comparisons between experimental data and model predictions, it is necessary to account for uncertainty in model predictions due to uncertain values of model parameters. We present an analysis of uncertainty induced in model predictions of a T-sensor based competitive diffusion immunoassay due to uncertainty in diffusion constants, binding reaction rate constants, and inlet flow speed. We use a non-intrusive stochastic uncertainty quantification method employing polynomial chaos expansions to represent the dependence of uncertain species concentrations on the uncertainty in model parameters. Our simulations show that the uncertainties in model parameters lead to significant spatially varying uncertainty in predicted concentration. In particular, the diffusivity of fluorescently labeled probe antigen dominates the overall uncertainty. The predicted uncertainty in fluorescence intensity is minimum near the centerline of T-sensor and relatively high in the regions with gradients in fluorescence intensity. We show that using centerline fluorescence intensity instead of first derivative of fluorescence intensity as the system response for measuring sample antigen concentration in T-sensor based competitive diffusion immunoassay leads to lower uncertainty and higher detection sensitivity.

We dealt with a rather frequent and difficult situation while modelling extreme floods, namely, model output uncertainty in data sparse regions. A historical extreme flood event was chosen to illustrate the challenges involved. Our aim was to understand what the causes might have been and specifically to show how input and model parameter uncertainties affect the output. For this purpose, a conceptual model was calibrated and validated with recent data rich time period. Resulting model parameters were used to model the historical event which subsequently resulted in a rather poor hydrograph. Due to the bad model performance, a spatial simulation technique was used to invert the model for precipitation. Constraints, such as taking the precipitation values at historical observation locations in to account, with correct spatial structures and following the observed regional distributions were used to generate realistic precipitation fields. Results showed that the inverted precipitation improved the performance significantly even when using many different model parameters. We conclude that while modelling in data sparse conditions both model input and parameter uncertainties have to be dealt with simultaneously to obtain meaningful results.

Approximation error approach in spatiotemporally chaotic models with application to Kuramoto–Sivashinsky equation

To construct a valid model, hydrologists face challenges in determining sensitivity to the forcing data and uncertainty in model parameters. These require basin data and forcing data from different sources, which may be incommensurate. The study reported here calibrated the Variable Infiltration-Capacity (VIC) platform to quantify model result sensitivity to model parameters and uncertainty in those parameters. The modeled basin was the Diyala River in Iraq, above the Derbendikhan Dam. The study produced the first complete set of daily forcing data for the basin using different sources. Besides ground observations from the Iraqi Ministry of Water Resources, two additional data sources were tested: Tropical Rainfall Measurement Mission (TRMM) and Global Implemented Data (GIDAL). Several methods were implemented to adjust the data, and model sensitivity and parameter uncertainty were examined by Generalized Likelihood Uncertainty Estimation (GLUE) and Differential Evolution Adaptive Metropolis (DREAM). Neither of these techniques had been applied before in Iraq. The VIC model was then calibrated manually using Kling–Gupta efficiency (KGE). The analyses indicate that neither TRMM nor GIDAL data are adequate for gridded precipitation analysis in the study basin. TRMM tends to underestimate and GIDAL tends to overestimate actual data. Multiplicative random cascade and Schaake Shuffle were used to determine daily precipitation data. A set of correction equations was developed to adjust GIDAL temperature and wind speed. Results for the GLUE and DREAM analyses imply that the depth of the second soil layer is the parameter that causes the most sensitivity in the model. The VIC model outputs were calibrated on a daily timescale with a KGE average of 0.743.

Parameter uncertainty in hydrologic modeling is commonly evaluated, but assessing the impact of spatial input data uncertainty in spatially descriptive ‘distributed’ models is not common. This study compares the significance of uncertainty in spatial input data and model parameters on the output uncertainty of a distributed hydrology and sediment transport model, HYdrology Simulation using Time-ARea method (HYSTAR). The Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm was used to quantify parameter uncertainty of the model. Errors in elevation and land cover layers were simulated using the Sequential Gaussian/Indicator Simulation (SGS/SIS) techniques and then incorporated into the model to evaluate their impact on the outputs relative to those of the parameter uncertainty. This study demonstrated that parameter uncertainty had a greater impact on model output than did errors in the spatial input data. In addition, errors in elevation data had a greater impact on model output than did errors in land cover data. Thus, for the HYSTAR distributed hydrologic model, accuracy and reliability can be improved more effectively by refining parameters rather than further improving the accuracy of spatial input data and by emphasizing the topographic data over the land cover data.

One of the most important stages in addressing geophysical problems is the inversion procedure of the observed data, which involves incorporating several interdependent model parameters that describe the geophysical properties of the Earth’s subsurface. In this article, we propose a new modification to the inversion technique by applying global optimization method based on systematic search. Global optimization methods are particularly useful because geophysical inverse problems are often nonlinear making traditional local optimization methods less effective. A systematic search using the permutation method for inverting geophysical data refers to a comprehensive and methodical approach that explores different parameter combinations or configurations. The guided permutation method ensures that all possible configurations of model parameters are tested to find the best match between the geophysical model and the observed data. While this method is highly reliable in finding global solutions, its computational cost can be prohibitive for large-scale problems. This issue can be mitigated by conducting an analysis of geophysical parameter sensitivity, which helps determine which model parameters can be reliably estimated, and which are less influential. Furthermore, this analysis enhances the understanding of model uncertainties, guides the inversion process, reduces computational costs, and improves the reliability of the final geophysical model by employing this new inversion technique with the specific method used that is systematic search, permutation, sensitivity analysis. The computer program codes based on systematic search and guided permutation method demonstrates the robustness and accuracy of geophysical inversions. The inversion results from this program, applied to multimode Love wave dispersion curves, show a significant improvement in the quality of the match between the observed and modelled dispersion curves. This improvement is quantitatively confirmed by a decrease in root mean square (RMS) error from 13.435 m/s to 2.887×10-5 m/s, representing a significant reduction in misfit. Based on the obtained results, the program implementing this new inversion technique, incorporating systematic search, guided permutation, and sensitivity analysis, indicates the robustness and accuracy of geophysical inversions. Finally, we ensure that this inversion technique can be applied to solve other geophysical data problems.

Sensitivity and Uncertainty