Pattern-based calibration of complex subsurface flow models against dynamic response data

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

Construction of predictive subsurface flow models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias in predicting the flow and transport behavior of these systems. In particular, the uncertainty in the facies distribution in complex geologic environments, such as alluvial/fluvial channels, can be consequential for forecasting the dynamic response of these systems to perturbations due to pumping and development activities. Conventional model calibration techniques that are designed to update continuous model parameters cannot be used to estimate discrete parameters from flow and pressure data. We present a distance transform approach for converting discrete facies models to continuous parameters that can be updated using continuous model calibration methods. Distance transforms are widely used in discrete image processing, where the discrete values in each pixel are replaced with their distance (i.e., a continuous variable) to the nearest boundary cell. After updating the continuous distance maps during model calibration, a back transformation is applied to retrieve the updated facies maps. To preserve large‐scale facies connectivity, truncated singular value decomposition (SVD) parametrization may be used to represent the distance maps with low‐rank parameters. A variant of the ensemble smoother, ES‐MDA is used to update the continuous parameters of the inversion (either distance maps or their SVD coefficients if used). The distance transform method addresses an important problem in facies model calibration where model updating can result in losing facies connectivity and discreteness.

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

Efficient calibration of microscopic car-following models for large-scale stochastic network simulators

Numerical groundwater flow and solute transport models are usually subject to model structural error due to simplification and/or misrepresentation of the real system, which raises questions regarding the suitability of conventional least squares regression‐based (LSR) calibration. We present a new framework that explicitly describes the model structural error statistically in an inductive, data‐driven way. We adopt a fully Bayesian approach that integrates Gaussian process error models into the calibration, prediction, and uncertainty analysis of groundwater flow models. We test the usefulness of the fully Bayesian approach with a synthetic case study of the impact of pumping on surface‐ground water interaction. We illustrate through this example that the Bayesian parameter posterior distributions differ significantly from parameters estimated by conventional LSR, which does not account for model structural error. For the latter method, parameter compensation for model structural error leads to biased, overconfident prediction under changing pumping condition. In contrast, integrating Gaussian process error models significantly reduces predictive bias and leads to prediction intervals that are more consistent with validation data. Finally, we carry out a generalized LSR recalibration step to assimilate the Bayesian prediction while preserving mass conservation and other physical constraints, using a full error covariance matrix obtained from Bayesian results. It is found that the recalibrated model achieved lower predictive bias compared to the model calibrated using conventional LSR. The results highlight the importance of explicit treatment of model structural error especially in circumstances where subsequent decision‐making and risk analysis require accurate prediction and uncertainty quantification.

Sensitivity analysis is an important tool that can be used for calibration of river flow models. Generally, friction coefficient is used as a calibration parameter for steady-state one-dimensional shallow water flow models. In this study, the local sensitivity analysis is used to derive a general rule for calibration of prismatic open channel models. For this, the sensitivity of the water depth to the friction coefficient is analytically derived for one-dimensional steady flow conditions in a wide rectangular channel. Also, the parameter of influence distance is defined to calibrate a channel reach using stage measurement at a given location. This characteristic distance allows 90% of the maximum possible variation in the sensitivity of the water depth to the friction coefficient to be captured. This parameter estimates the optimal length of a channel reach over which the friction coefficient can be calibrated from stage measurement. This length locates downstream of the stage measurement point in subcrit...

Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against measured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo (MCMC) methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identifiability: a basic SIR model, an influenza model with vaccination and treatment and a HIV–Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV–Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The presented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.

As a result of the highly heterogeneous tumor microenvironment and a series of complex phenomena that occur at different scales, several modeling approaches have emerged. The tumor growth models can be categorized by the behaviors they aim to capture, the hallmarks of cancer that are being considered, and the temporal and biological scales represented. Moreover, these models can also be differentiated according to the mathematical framework that is being employed, being either discrete models, continuum models, or hybrid models. Therefore, with this large set of possible models, and with each model choice having many unknown parameters, it is important to develop an adaptive model selection and validation framework in order to choose the best model for the desired application. In this work, we employ the Occam Plausibility Algorithm (OPAL) framework [1] for model selection and validation of a large body of tumor growth models. We select several continuum tumor growth models, half of them using the phase-field modeling approach, derived from the models developed in [2], and the other half being reaction-diffusion type models derived from [3]. The OPAL framework brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Firstly, we identify the model classes and compute the sensitivity of the quantity of interest (QoI), here the tumor volume as a function of time. The models with parameters that do not influence the QoI are eliminated. The next step consists in dividing the models into Occam categories according to their number of parameters, where the models with fewer parameters are assembled to category 1. Following the principle of Occam's Razor, one of main goals of OPAL is to select the simplest model among the several models that leads to the same prediction. The models from the first category are calibrated using Bayes' rule for a specific calibration scenario. The next step is to compute the plausibilities for the models in this category and choose the most plausible model. Finally, with the most plausible model known, we solve the problem in the validation scenario. The model is valid depending on the accuracy with which the model predictions of the QoI agree with experimental data. If the model is not valid, we move to the next category; otherwise, we select this model as being the simplest and the most plausible valid model. We demonstrate that the OPAL is able to assist in the selection of the best tumor growth model from a defined set of models. The model selected is valid for particular scenarios. In this work, we consider avascular tumor growth models to reproduce the data obtained in a murine model of glioma growth. The brain data is generated with diffusion weighted magnetic resonance imaging over a period of ten days. The methodologies and results confirm that the OPAL strategy provides a powerful framework for model selection, parameters estimation, and model validation in the presence of uncertainties.

Stochastic long-term mine planning has evolved to account for different sources of uncertainty. Typically, the uncertainty and local variability of boundaries in geological domains have been overlooked by experts through their deterministic interpretation of available data. Categorical attributes are used to model geological domains, and their stochastic simulation accounts for the mentioned issues. The ability of two-points simulation methods to reproduce complex patterns or the requirement of a training image in multiple-points simulation methods has limited their implementation in mining environments. The high-order simulation of categorical attributes presents a mathematically consistent framework that overcomes these limitations by using high-order spatial statistics from sample data. The case study at a gold mining complex shows two stochastic mine plans based on two sets of geological realisations: geological domains in the first set are modelled using conventional wireframes, while, in the second, they are simulated through the high-order method. The resulting mine plans are substantially different; while both plans present a similar quantity of metal recovered and lifespan, risk profiles are up to 40% wider, and the expected NPV is 20% higher for the case of simulated geological domains, given the decrease of waste handling costs and the corresponding reduction in environmental footprint.

In-flight wavefront measurements around a flat-window turret at subsonic Mach numbers are analyzed in instantaneous and time-averaged sense. In addition to the root-mean-squared levels of aero-optical distortions, higher-order spatial statistics are calculated, and their dependence as a function of the viewing angle is discussed. Given the optical data obtained, the applicability of the commonly used large aperture approximation (LAA) is revisited. We show that, for all angles, the LAA consistently underestimates the time-averaged Strehl ratio, so the LAA should be used very cautiously. Some reasons for these discrepancies are traced to non-Gaussian spatial distribution of the optical wavefronts. A different approximation for computing time-averaged Strehl ratios is proposed, and the results are discussed.

Transport models based on calibrated flow models may often yield wrong predictions unless recalibrated with the aid of environmental tracers because migration velocity depends on the ratio of hydraulic conductivity to porosity whereas flow rates depend on transmissivity. An environmental tracer (SF6) was used to improve calibration of transport and flow models in a sandy aquifer. Simulated and measured 3 H contents showed that further improvement of the conceptual model and recalibration of flow and migration models are needed for some parts of the aquifer. Residence time distributions obtained from lumped-parameter and numerical models are shown to serve for a better understanding of the groundwater system.

The self-potential (SP) method relies on passive measurements of the ambient electrical potential at the ground surface or in boreholes. When the electrokinetic effect is the dominant contribution, the resulting signal is called the streaming potential and contains information about groundwater fluxes that can be useful for calibration of groundwater flow models. The streaming potential forward equation was implemented in the HydroGeoSphere model, which simulates 3D groundwater flow and solute transport in porous media, including fractured geological formations. HydroGeoSphere is able to calculate the streaming potential given a distribution of Darcy velocity and electrical resistivity. Since groundwater flow modelling relies on a conceptual model, prior information on the distribution of the geological units and hydraulic conductivity at the site is mandatory. However, this information is often scarce or missing. In this work, we use the electrical resistivity tomography (ERT) and the SP methods as an additional source of information for building the groundwater flow model. ERT is used to identify the location of fractured zones in a fractured and karstified calcareous aquifer of South Belgium. The SP signal is used with PEST in order to calibrate the groundwater flow model and better constrain the hydraulic conductivity of the fractured zones.

Microscopic simulation models are becoming increasingly important tools in modeling transport systems. A large number of models are used in many countries. The most difficult stage in the development and use of such models is the calibration and validation of the microscopic submodels such as the car-following and gap acceptance models. This difficulty results from the lack of suitable methods for adapting models to empirical data. Recent progress has been made in calibrating a number of microscopic traffic flow models. Ten very different models have been tested with data collected via Differential Global Positioning System-equipped cars on a test track in Japan. To calibrate the models, the data of the leading car are fed into the model under consideration, and the model is used to compute the headway time series of the following car. The deviations between the measured and the simulated headways are then used to calibrate and validate the models. The calibration results agree with earlier studies as there are errors of 12% to 17% for all models, and no model can be denoted to be the best. The differences between individual drivers are larger than the differences between different models. The validation process gives acceptable errors from 17% to 22%. But for special data sets with validation errors up to 60%, the calibration process has reached what is known as "overfitting": because of the adaptation to a particular situation, the models are not capable of generalizing to other situations.