Inverse Modeling Approach Research Articles

Determining the Unsaturated Hydraulic Properties of Cohesionless Soils: An Integrated Experimental and Inverse Modeling Approach

Abstract A simple, inexpensive and quick method for measuring the van Genuchten soil water retention curve (SWRC) model parameters for cohesionless soil is presented. The proposed method is an integration of laboratory testing and numerical modeling. The experimental testing consists of multistage bottom-top water imbibition of a dry sand column while recording pore pressure at the inlet. The experiment is then simulated numerically using Hydrus 1D, and the van Genuchten SWRC model parameters are determined through inverse modeling to match the recorded pore pressures. The soil column flushing includes multiple flow stoppages and resumptions, all before permeating one pore volume of water. The flow stoppage results in a time-dependent redistribution of moisture near the waterfront that is controlled by the unsaturated hydraulic properties of the soil and is reflected by changes in the pore pressure measurements. The uniqueness of this method comes from the simple experimental setup and the multistage flushing that can reduce the testing time by a factor of 30 compared with other methods. The results from testing three different sands with different grain size distributions are presented. The new method generated consistent results from multiple specimens tested at a range of flow rates for the three sands. The hypothesis behind moisture redistribution during flow stoppage was confirmed through a combination of experimental and numerical observations. The van Genuchten SWRC parameters obtained from the new method were comparable to those obtained using the conventional hanging column test for Sands B and C and available data in the literature. Sand A could not be tested using the hanging column test because of its large particle size, which demonstrates the wide range of soils that can be tested using the new proposed method.

Inverse Procedural Modeling of Branching Structures by Inferring L-Systems

We introduce an inverse procedural modeling approach that learns L-system representations of pixel images with branching structures. Our fully automatic model generates a compact set of textual rewriting rules that describe the input. We use deep learning to discover atomic structures such as line segments or branchings. Orientation and scaling of these structures are determined and the detected structures are combined into a tree. The initial representation is analyzed, and repeating parts are encoded into a small grammar by using greedy optimization while the user can control the size of the detected rules. The output is an L-system that represents the input image as a simple text and a set of terminal symbols. We apply our approach to a variety of examples, demonstrate its robustness against noise and blur, and we show that it can detect user sketches and complex input structures.

Variability of Ammonia and Methane Emissions from Animal Feeding Operations in Northeastern Colorado.

Concentrated animal feeding operations (CAFOs) are major emitters of both ammonia (NH3) and methane (CH4). However, current emission inventories have limited temporal resolution and use data derived from a small subset of farms. To this end, we deployed three mobile laboratories during the DISCOVER-AQ campaign in summer 2014 with a focus on northeastern Colorado. Observations of NH3 and CH4 plumes downwind of 43 CAFOs were used to investigate the diurnal and site-to-site variability of emissions with an inverse area source plume modeling approach. Ammonia emissions scaled to all permitted animals in Weld, Morgan, and Larimer counties were estimated at 1.9 Gg month-1, 50% greater than the U.S. NEI 2014 and 360% greater than EDGAR for the month of August. Methane emissions were likewise estimated at 10.6 Gg month-1, consistent with the U.S. GHGI but 99% greater than EDGAR. Significant differences between individual CAFOs with repeat observations were also observed for both CH4 and NH3 emissions. The large subfarm, site-to-site, and diurnal variabilities observed show the importance of measurements taken across these scales in order to derive representative emission factors.

Air quality impacts of the 2018 Mt. Kilauea Volcano eruption in Hawaii: A regional chemical transport model study with satellite-constrained emissions

Abstract Volcanic eruptions could bring a vast amount of sulfur dioxide (SO2) and ash into the air, often imposing substantial impacts on air quality and the ecosystem. Quantifying its impacts, however, is difficult due to the uncertainties in estimating the strength and variations of volcanic emissions. Here we developed and evaluated a new approach to combine satellite SO2 detection and chemical transport modeling to assess the impact of the 2018 Mt. Kilauea eruption on air quality over Hawaii. During the sustained eruption of the Kilauea Volcano in Hawaii's Big Island from May to July 2018, considerable SO2 and PM2.5 enhancements were observed both from the ground and from space. We studied this case using an experimental version of the NOAA National Air Quality Forecast Capability (NAQFC) modeling system. Daily emissions of SO2 and ash were estimated using a combination of SO2 column density retrieved by Ozone Mapping and Profiling Suite (OMPS) Nadir-Mapper (NM) aboard the Suomi-NPP satellite and the NAQFC model with an inverse emission modeling approach. We found that the volcanic SO2 emission rates peaked at 15,000 mol/s from the Kilauea's East Rift zone and Summit. The formation and transport of volcanic smog, or Vog, was highly dependent upon the vertical distribution of the volcanic emission, controlled by the heat flux of emission sources. We conducted four model simulations with various emission settings, and compared them to satellite data (CALIOP, OMPS and VIIRS) and in-situ measurements. All the runs tended to underpredict the peak values of surface SO2 and PM2.5 (particulate matter smaller than 2.5 μm in diameter). The “No Plume Rise” run underestimated the Vog plume rise and downstream transport. Using fixed emission rate or removing the temporal variations (”3-Day Mean”) led to miss peak Vog effects or inconsistent transport pattern compared to the observations. Therefore, the Base simulation with daily-varying emission and plume rise was used to quantify the air quality effects of the Kilauea eruption. We found that the volcanic eruption elevated surface PM2.5 concentration by 30–40 μg/m3 in the southeast part of the Big Island, with peak values up to 300 μg/m3. The Vog effect on trace gases, such as O3, NOx, and non-methane hydrocarbons, were much weaker (

Identification of anomalous diffusion sources by unsupervised learning

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim t^{\alpha}$, where the diffusion exponent $\alpha$ characterizes whether the transport is subdiffusive, ($\alpha<1$), diffusive ($\alpha = 1$), or superdiffusive, ($\alpha >1$). Due to the abundance of fBm processes in nature, significant efforts have been devoted to the identification and characterization of fBm sources in various phenomena. In practice, the identification of the fBm sources often relies on solving a complex and ill-posed inverse problem based on limited observed data. In the general case, the detected signals are formed by an unknown number of release sources, located at different locations and with different strengths, that act simultaneously. This means that the observed data is composed of mixtures of releases from an unknown number of sources, which makes the traditional inverse modeling approaches unreliable. Here, we report an unsupervised learning method, based on Nonnegative Matrix Factorization, that enables the identification of the unknown number of release sources as well the anomalous diffusion characteristics based on limited observed data and the general form of the corresponding fBm Green's function. We show that our method performs accurately for different types of sources and configurations with a predetermined number of sources with specific characteristics and introduced noise.

Parameter subset reduction for patient-specific modelling of arrhythmogenic cardiomyopathy-related mutation carriers in the CircAdapt model.

Arrhythmogenic cardiomyopathy (AC) is an inherited cardiac disease, clinically characterized by life-threatening ventricular arrhythmias and progressive cardiac dysfunction. Patient-specific computational models could help understand the disease progression and may help in clinical decision-making. We propose an inverse modelling approach using the CircAdapt model to estimate patient-specific regional abnormalities in tissue properties in AC subjects. However, the number of parameters (n = 110) and their complex interactions make personalized parameter estimation challenging. The goal of this study is to develop a framework for parameter reduction and estimation combining Morris screening, quasi-Monte Carlo (qMC) simulations and particle swarm optimization (PSO). This framework identifies the best subset of tissue properties based on clinical measurements allowing patient-specific identification of right ventricular tissue abnormalities. We applied this framework on 15 AC genotype-positive subjects with varying degrees of myocardial disease. Cohort studies have shown that atypical regional right ventricular (RV) deformation patterns reveal an early-stage AC disease. The CircAdapt model of cardiovascular mechanics and haemodynamics has already demonstrated its ability to capture typical deformation patterns of AC subjects. We, therefore, use clinically measured cardiac deformation patterns to estimate model parameters describing myocardial disease substrates underlying these AC-related RV deformation abnormalities. Morris screening reduced the subset to 48 parameters. qMC and PSO further reduced the subset to a final selection of 16 parameters, including regional tissue contractility, passive stiffness, activation delay and wall reference area.This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

Source estimation of an unexpected release of Ruthenium-106 in 2017 using an inverse modelling approach

For the first time since the Chernobyl accident, detectable concentrations of ruthenium-106 were measured across Europe in September and October 2017. The source of this radioactive cloud remains unconfirmed. In this paper we present a forensic inverse modelling study to simultaneously estimate the source location, timing and magnitude of the unexpected ruthenium-106 release using 473 measurements of atmospheric concentration. To do this, we introduce a novel method, which estimates the uncertainty in the often unknown transport error using a Markov chain Monte Carlo approach. We corroborate the conclusions of other studies which suggest the source location is in the Southern Ural region of Russia, where the Mayak nuclear complex is located. Assuming that the Mayak nuclear complex is the most plausible release location, the method estimates that 441±13 TBq was released 12:00–18:00 UTC 24 September 2017, assuming a six hour release window.

Validation of pyrolysis model in transient heating scenarios and diverse spectral boundary conditions

This study aims to provide a robust validation to the condensed-phase pyrolysis model approach used in the FireFOAM CFD code. Firstly, bench-scale pyrolysis tests were conducted for two engineering wood products (EWPs), namely plywood and medium density fiberboard (MDF), at three constant heat flux levels. These tests were used to derive model-effective material properties via inverse modeling and optimization approaches. For MDF, a better model fit was obtained when the virgin material density was allowed to vary along its thickness, which is consistent with its known anisotropic nature. Next, three test cases were developed for the purpose of pyrolysis model validation by subjecting the EWPs to fire-relevant dynamic heating scenarios. In two tests, the materials were exposed to transient heating conditions where the heat flux to the materials increased over the duration of pyrolysis. In the remaining test, the spectral emissivity boundary condition of the sample material was altered significantly. Very good agreement was observed between the validation experimental data and the model predictions for all three scenarios. The validation studies provide confidence that the model-effective material properties, determined using inverse modeling and optimization for constant heating conditions, can be confidently applied to fire-relevant dynamic heating scenarios and boundary conditions.

Warmback analysis to determine fracture geometry of a single-stage hydraulic fracturing stimulation

Significant variation in hydraulic fracturing efficiency over the length of horizontal wells has been observed in the field. Monitoring and diagnosis of the fracture treatment is a critical step to evaluate the efficiency of the fracturing stimulation and the fracture geometry. Different diagnostic tools have been used to determine fracture placement and fracture effectiveness such as pressure decline analysis, microseismic, and tiltmeter fracture mapping technology. Recently, temperature monitoring has been evolved as a new technique can be analyzed to infer fracturing zone and fracture characteristics. Temperature behavior during fracture propagation and the subsequent warmback period can reveal important information about the dimensions and flow characteristics of developed fracture. In this work, we present forward and inverse modelling approaches to determine the fracture geometry using the temperature measured at the horizontal lateral. An analytical model is first developed to obtain the transient temperature in the fracture-matrix system during injection/propagation and the subsequent warmback period. The analytical solutions are developed by solving mass conservation equation along with energy balance equation in the fracture and the surrounding matrix assuming linear fluid flow and negligible leak-off effect which can be feasible for ultra-tight formations with low filtration coefficient. The developed solutions are validated against a thermally coupled numerical reservoir simulator as well as published field data. The solutions for warmback period are obtained and presented in the form of graphical type curves. The temperature measurements obtained during warmback period along with the developed solutions are used to estimate fracture width, fracture half-length, and geothermal reservoir temperature. The analytical results provide good agreement with the numerical results during forward and inverse modelling.

A Direct Inverse Model for Hysteresis Compensation

The feedforward inverse compensation is a typical approach to compensate for the hysteresis nonlinearity in smart materials based actuators, which often requires to develop a hysteresis model first and to compute the parameters of the inverse compensator based on the hysteresis model. Different from the above method, a direct inverse model (DIM) constructed by newly proposed clockwise relay operators is developed in this article. The direct inverse modeling approach is free from constructing the inverse compensator, and can be directly used as the inverse compensator. The parameters of DIM can be obtained via the model identification using the experimental data. In order to facilitate the numerical implementation and reduce the model complexity of DIM, a QR factorization based selection mechanism is employed to select the dominant clockwise relay operators. The reduced DIM is capable of preserving the accuracy of the full DIM. The simulation study and experiments are conducted to validate the effectiveness of the developed compensation approach.

Western Greenland ice sheet retreat history reveals elevated precipitation during the Holocene thermal maximum

Abstract. We investigate changing precipitation patterns in the Kangerlussuaq region of western central Greenland during the Holocene thermal maximum (HTM), using a new chronology of ice sheet terminus position through the Holocene and a novel inverse modeling approach based on the unscented transform (UT). The UT is applied to estimate changes in annual precipitation in order to reduce the misfit between modeled and observed terminus positions. We demonstrate the effectiveness of the UT for time-dependent data assimilation, highlighting its low computational cost and trivial parallel implementation. Our results indicate that Holocene warming coincided with elevated precipitation, without which modeled retreat in the Kangerlussuaq region is more rapid than suggested by observations. Less conclusive is whether high temperatures during the HTM were specifically associated with a transient increase in precipitation, as the results depend on the assumed temperature history. Our results highlight the important role that changing precipitation patterns had in controlling ice sheet extent during the Holocene.

Integration of Pressure Transient Data into Reservoir Models Using the Fast Marching Method

SummaryCalibration of reservoir model properties by integration of well-test data remains an important research topic. Well-test data have been recognized as an effective tool to describe transient flow behavior in petroleum reservoirs. It is also closely related to the drainage volume of the well and the pressure-front propagation in the subsurface. Traditional analytic means of estimating reservoir permeability relies on an interpretation of the diagnostic plot of the well pressure and production data, which usually leads to a bulk average estimation of the reservoir permeability. When more detailed characterization is needed, a forward model that is sensitive to the reservoir heterogeneity needs to be established, and a numerical inversion technique is required.We use the concept of the diffusive time of flight (DTOF) to formulate an asymptotic solution of the diffusivity equation that describes transient flow behavior in heterogeneous petroleum reservoirs. The DTOF is obtained from the solution of the Eikonal equation using the fast marching method (FMM). It can be used as a spatial coordinate that reduces the 3D diffusivity equation to an equivalent 1D formulation. We investigate the drainage-volume evolution as a function of time in terms of the DTOF. The drainage volume might be directly related to the well-test derivative, which can be used in an inversion calculation to calibrate reservoir model parameters.The analytic sensitivity coefficients of the well-test derivative with respect to reservoir permeability are derived and incorporated into an objective function to perform model calibration. The key to formulating the sensitivity coefficients is to use the functional derivative of the Eikonal equation to derive the analytic sensitivity of the DTOF to reservoir permeability. Its solution is implemented by tracking the characteristic trajectory of the local Eikonal solver within the FMM. The major advantage of calculating the sensitivity coefficients using the FMM is its significant computational efficiency during the iterative inversion process.This inverse-modeling approach is tested on a 2D synthetic heterogeneous reservoir model and then applied to the 3D Brugge Field, where a single well with constant flow rate is simulated. The well-test derivative is shown to be inversely proportional to the drainage volume and is treated as the objective function for inversion. With an additional constraint to honor the prior model, our inverse-modeling approach will adjust the reservoir model to obtain permeability as a function of distance from the well within the drainage volume. It provides a modification of reservoir permeability both within and beyond the depth of investigation (DOI).

Optical characterization of poly-SiOx and poly-SiCx carrier-selective passivating contacts

The optical modelling for optimizing high-efficiency c-Si solar cells endowed with poly-SiOx or poly-SiCx carrier-selective passivating contacts (CSPCs) demands a thorough understanding of their optical properties, especially their absorption coefficient. Due to the mixed phase nature of these CSPCs, spectroscopic ellipsometry is unable to accurately detect the weak free carrier absorption (FCA) at long wavelengths. In this work, the absorption coefficient of doped poly-SiOx and poly-SiCx layers as function of oxygen and carbon content, respectively, was obtained for wavelengths (300–2000 nm) by means of two alternative techniques. The first approach, photothermal deflection spectroscopy (PDS), was used for layers grown on quartz substrates and is appealing from the point of view of sample fabrication. The second, a novel inverse modelling (IM) approach based on reflectance and transmittance measurements, was instead used for layers grown on textured c-Si wafer substrates to mimic symmetrical samples. Although the absorption coefficients obtained from these two techniques slightly differ due to the different used substrates, we could successfully measure weak FCA in our CSPCs layers. Using an in-house developed multi-optical regime simulator and comparing modelled reflectance and transmittance with measured counterparts from symmetrical samples, we confirmed that with increasing doping concentration FCA increases; and found that the absorption coefficients obtained from IM can now be used to perform optical simulations of these CSPCs in solar cells.

Predicting post-natal energy intake of lesser black-backed gull chicks by Dynamic Energy Budget modeling

The standard Dynamic Energy Budget (DEB) model is widely used to describe the physiology of individual animals. Here we parametrized the DEB model for the lesser black-backed gull Larus fuscus mainly on the basis of literature data. Next we performed an inverse modeling approach to predict the food intake rate of gull chicks (model input) on the basis of their growth trajectory from hatching to fledging (model output). Food intake rate and growth were also measured for this period in an aviary experiment, where three different diet treatments resulted in a large range in overall intake rate. These measured food intake rate data were not used in the parameter estimation procedure, but rather to validate model results. Model predictions of food intake rate were systematically only about 10% below the observations, but predictions and observations correlated strongly. The DEB model might be used to predict food provisioning rates in the field, which are difficult to obtain, on the basis of growth data, which are much easier to get.

Three‐Dimensional Magnetic Models of La Gomera (Canary Islands): Insights Into the Early Evolution of an Ocean Island Volcano

AbstractAn aeromagnetic data set from the island of La Gomera was studied through two inverse modeling approaches that produced complementary views of the inner structure of this volcanic island: (1) a variable magnetization model that identified the main lateral magnetization contrasts and (2) a constant magnetization model that imaged the main magnetic source by assuming that it was a uniformly magnetized body. The modeling reveals intense magnetizations beneath the northern part of La Gomera, which occupy an important portion of the northern submarine edifice, correspond well with outcrops of the submarine volcano (Basal Complex), and confirm that most of the magnetic signal revealed by aeromagnetic mapping in the Canary Islands is due to the intense magnetizations of the intrusive complexes (plutonic bodies and dike complexes) emplaced during the initial stages of growth of the volcanic edifices. The consistency of our models with the results of a previous gravimetric study suggests that these intrusive complexes are denser and more magnetic than the surrounding rocks. The location of the main magnetic source reinforces the interpretation, first suggested by geological evidence, that the submarine and early subaerial growth of La Gomera started to the north of the present island. The elongated shape of these intrusive complexes with a nearly E‐W strike agrees with the orientation of analogous structures on Tenerife and Gran Canaria, suggesting that the initial formation of the central islands of the Canary Archipelago was controlled by a set of regional fractures in a strike‐slip tectonic framework.

Inverse Data-Driven Modeling and Multiomics Analysis Reveals Phgdh as a Metabolic Checkpoint of Macrophage Polarization and Proliferation

SummaryMechanistic or mammalian target of rapamycin complex 1 (mTORC1) is an important regulator of effector functions, proliferation, and cellular metabolism in macrophages. The biochemical processes that are controlled by mTORC1 are still being defined. Here, we demonstrate that integrative multiomics in conjunction with a data-driven inverse modeling approach, termed COVRECON, identifies a biochemical node that influences overall metabolic profiles and reactions of mTORC1-dependent macrophage metabolism. Using a combined approach of metabolomics, proteomics, mRNA expression analysis, and enzymatic activity measurements, we demonstrate that Tsc2, a negative regulator of mTORC1 signaling, critically influences the cellular activity of macrophages by regulating the enzyme phosphoglycerate dehydrogenase (Phgdh) in an mTORC1-dependent manner. More generally, while lipopolysaccharide (LPS)-stimulated macrophages repress Phgdh activity, IL-4-stimulated macrophages increase the activity of the enzyme required for the expression of key anti-inflammatory molecules and macrophage proliferation. Thus, we identify Phgdh as a metabolic checkpoint of M2 macrophages.

Capillary condensation experiment for inverse modelling of porous building materials

Hygrothermal simulations are of major importance for critical problems in building physics, such as the application of internal insulation in heritage buildings. These simulations require numerous material parameters that are challenging to determine. We present measurements of typical internal insulation materials, calcium-silicate and autoclaved aerated concrete, which we expose to a warm, humid climate on one side and a cold temperature on the other side. We measure the moisture gain over time and determine the moisture profile at experiment end. In an inverse modelling approach, the measurements are used to identify material parameters, in particular vapour conductivity and capillary conductivity as a function of moisture content. We found the measurements of crucial importance for the accurate determination of these parameters. When the parameters rely only on isothermal measurements such as the drying experiment, the model fails to predict the capillary condensation process. We demonstrate this on a dataset from another study with interior insulation subjected to changing boundary conditions. The model calibrated with capillary condensation data reliably reconstructs measurements while the drying-calibrated model drastically underestimates the moisture content.

Modeling water fluxes through containerized soilless substrates using HYDRUS

AbstractContainerized crop production can enhance plant health and ensure environmental sustainability, yet proper management requires improved understanding of water fluxes and storage within soilless substrates. Numerical simulation tools developed to simulate water movement in porous media, such as HYDRUS‐3D, may help to quantify effective hydraulic properties of soilless substrates but have not yet been tested in this capacity. Therefore, this study had three main objectives: (a) to assess the accuracy of HYDRUS‐3D for simulating water flow through peat‐ and bark‐based soilless substrates by comparing measured and modeled drainage and water storage; (b) to determine sensitivity of model outputs to individual hydraulic parameters; and (c) to compare model parameterization using three laboratory characterization methods (instantaneous profile sorption, instantaneous profile desorption, and evaporation) vs. inverse modeling with HYDRUS. The results showed that the modeled water contents and drainage timing and amounts were most sensitive to saturated volumetric water content (θs) and least sensitive to saturated hydraulic conductivity (Ks). With regard to parameterization methods, the inverse modeling approach provided the most accurate water balance simulations for both substrates, followed by the sorption method. These two methods estimated lower peak water contents and greater drainage compared with simulations parameterized using desorption and evaporation measurements. Overall, the study results showed that the Richards equation, as calculated using HYDRUS, can provide accurate simulations of water flux through containers when properly calibrated, though sorption‐derived parameters may suffice when model optimization is impractical.

Hybrid neural lumped element approach in inverse modeling of RF MEMS switches

RF MEMS switches have been efficiently exploited in various applications in communication systems. As the dimensions of the switch bridge influence the switch behaviour, during the design of a switch it is necessary to perform inverse modeling, i.e. to determine the bridge dimensions to ensure the desired switch characteristics, such as the resonant frequency. In this paper a novel inverse modeling approach based on combination of artificial neural networks and a lumped element circuit model has been considered. This approach allows determination of the bridge fingered part length for the given resonant frequency and the bridge solid part length, generating at the same time values of the elements of the switch lumped element model. Validity of the model is demonstrated by appropriate numerical examples.

Continental‐Scale Landscape Evolution: A History of North American Topography

The generation and evolution of continental topography are fundamental geologic and geomorphic concerns. In particular, the history of landscape development might contain useful information about the spatiotemporal evolution of deep Earth processes, such as mantle convection. A significant challenge is to generate observations and theoretical predictions of sufficient fidelity to enable landscape evolution to be constrained at scales of interest. Here, we combine substantial inventories of stratigraphic and geomorphic observations with inverse and forward modeling approaches to determine how the North American landscape evolved. First, stratigraphic markers are used to estimate postdepositional regional uplift. Present‐day elevations of these deposits demonstrate that &gt;2 km of long‐wavelength surface uplift centered on the Colorado‐Rocky‐Mountain plateaus occurred in Cenozoic times. Second, to bridge the gaps between these measurements, an inverse modeling scheme is used to calculate the smoothest spatiotemporal pattern of rock uplift rate that yields the smallest misfit between 4,161 observed and calculated longitudinal river profiles. Our results suggest that Cenozoic regional uplift occurred in a series of stages, in agreement with independent stratigraphic observations. Finally, a landscape evolution model driven by this calculated rock uplift history is used to determine drainage patterns, denudation, and sedimentary flux from Late Cretaceous times until the present day. These patterns are broadly consistent with stratigraphic and thermochronologic observations. We conclude that a calibrated inverse modeling strategy can be used to reliably extract the temporal and spatial evolution of the North American landscape at geodynamically useful scales.