Uncertainty quantification of single and multi-parameter full-waveform inversion through a variational autoencoder
This poster will be presented at IMAGE as well as for a Sandia-UT student poster session next week
Elmeliegy, Abdelrahman M↗
SEARCH · Search NASA
Results for “Inverse uncertainty quantification”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Inverse Modeling of Hydrologic Parameters in CLM4 via Generalized Polynomial Chaos in the Bayesian Framework
In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great uncertainty in the Community Land Model (CLM) for a given value of the output LH. The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We set up the inversion problem in the Bayesian framework in two steps: (i) building a surrogate model expressing the input–output mapping, and (ii) performing inverse modeling and computing the posterior distributions of the input parameters using observation data for a given value of the output LH. The development of the surrogate model is carried out with a Bayesian procedure based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and, hence, all of the input parameters, via the associated posterior probabilities.
97 MATHEMATICS AND COMPUTING↗
Combining Data with Physical Knowledge for Uncertainty Quantification in Certification and Reliability Analysis
Unifying empirical data with predictive models can enable engineering cost-savings through certification by analysis and reliability-based design. Both concepts require rigorous uncertainty quantification (UQ) and robust understanding and treatment of relevant physics. Combining sampling-based UQ algorithms with high-fidelity simulations creates a computational bottleneck that is often alleviated through the use of machine learning (ML). ML can be used to create computationally efficient surrogates for simulations of complex or high-dimensional physical interactions (e.g., multi-phase interactions associated with melt pools in laser powder bed fusion or spatially-dependent material properties in functionally graded materials). However, negative side effects of ML may include a lack of interpretability and negative correlation between event rarity and simulation accuracy due to a lack of training data. As such, it is important to infuse ML algorithms with physics-based guardrails to provide confidence in their predictions. This talk will provide a brief review of recent NASA research at this intersection of physics-based simulation, ML, and UQ with a focus on certification and reliability analysis.
uncertainty quantification↗
Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM
This paper investigates the use of the inverse first-order reliability method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example.
Sankararaman, Shankar↗
Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction
Abstract We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.
Instruments & Instrumentation↗
Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry
Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.
54 ENVIRONMENTAL SCIENCES↗
NASA’s Prototype Spectral Water Inversion Processor and Emulator (SWIPE): Towards Global Coastal and Inland Water Quality and Algal Biodiversity Monitoring
Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will provide updates on NASA’s prototype open-source aquatic modeling platform, Spectral Water Inversion Processor and Emulator (SWIPE), which is a comprehensive, multi-faceted modeling platform for both forward and inverse modeling of diverse aquatic ecosystems from the benthos to top-of-atmosphere (TOA). SWIPE provides a cohesive application which leverages recent advancements in particle modeling, Big Data analytics, and machine learning to develop a high-fidelity synthetic training ground for sensitivity studies and algorithm development for multispectral or upcoming hyperspectral missions. Some of the prominent features of SWIPE to be discussed include: 1. Advanced hyperspectral modeling of globally diverse algal and non-algal particles using a novel two-layer coated sphere scattering model and radiative transfer modeling, 2. Massive, highly detailed synthetic spectral libraries of Analysis-Ready-Data (ARD) which include spectral libraries of particle microphysics, water biogeophysical and optical properties, as well as surface and TOA reflectances at 1 nm resolution, 3. An ensemble of pre-built analytic, machine learning, and deep learning inversion algorithms for various water quality and biodiversity related retrieval parameters and uncertainty quantification, 4. Sensor-agnostic water quality inversion at wide ranging spatial and spectral resolutions including a codebase for seamless application in the Google Earth Engine and NASA Earth Exchange (NEX) for planetary scale analysis. SWIPE will be a fully open-source platform based in python with comprehensive documentation, tutorials, and options for distributed computing on high performance computing clusters or on single, local machines. Further, we will discuss how we envision SWIPE contributing towards a global analysis of coastal and inland water quality dynamics.
top-of-atmosphere (TOA)↗
Learning-Based Inversion-Free Model-Data Integration to Advance Ecosystem Model Prediction
Ecosystem model prediction is important for understanding ecosystem responses to climate change and for management support. Model prediction and quantification of predictive uncertainty of ecosystems have long been investigated. The traditional workflow, which calibrates models to match observations and then uses the calibrated models for predictions, relies heavily on inverse modeling to constrain uncertain parameters in complex forward models. This inversion-based prediction approach is infeasible for complex models with heterogeneous parameter uncertainties and incapable of rapid integration of streaming and multiple sources of data because of the difficulty and computational cost in the model inversion, which is typically ill-posed and can require hundreds of thousands of expensive forward simulations to be performed iteratively. We propose to circumvent inverse modeling by precomputing an ensemble of unconstrained forward simulations and then using machine learning (ML) methods to learn the statistical relationship between simulated observation and prediction quantities. Once the ML model has learned the relationship, it can be used to make predictions of future system behavior with uncertainty quantification based on observations. The proposed learningbased inversion-free model prediction (LIMP) framework is computationally efficient which only requires a few thousands of fully parallelizable forward simulations. Additionally, LIMP can continually update predictions based on streaming observations from multiple locations and sources without necessarily requiring extra model simulations. In this study, we apply LIMP to a regional terrestrial ecosystem model with 47 parameters for testing, refining, and evaluating the approach. We demonstrate that LIMP can be used for efficient model prediction, rapid data assimilation, and cost-effective experimental design for improving robust predictive understanding of ecosystems.
Lu, Dan↗
A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate
SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.
58 GEOSCIENCES↗
A Bayesian Approach for Quantifying Data Scarcity when Modeling Human Behavior via Inverse Reinforcement Learning
Computational models that formalize complex human behaviors enable study and understanding of such behaviors. However, collecting behavior data required to estimate the parameters of such models is often tedious and resource intensive. Thus, estimating dataset size as part of data collection planning (also known as Sample Size Determination) is important to reduce the time and effort of behavior data collection while maintaining an accurate estimate of model parameters. In this paper, we present a sample size determination method based on Uncertainty Quantification (UQ) for a specific Inverse Reinforcement Learning (IRL) model of human behavior, in two cases: 1) pre-hoc experiment design—conducted in the planning stage before any data is collected, to guide the estimation of how many samples to collect; and 2) post-hoc dataset analysis—performed after data is collected, to decide if the existing dataset has sufficient samples and whether more data is needed. Here, we validate our approach in experiments with a realistic model of behaviors of people with Multiple Sclerosis (MS) and illustrate how to pick a reasonable sample size target. Our work enables model designers to perform a deeper, principled investigation of effects of dataset size on IRL.
97 MATHEMATICS AND COMPUTING↗
Accurate and Rapid Forecasts for Geologic Carbon Storage via Learning-Based Inversion-Free Prediction
Carbon capture and storage (CCS) is one approach being studied by the U.S. Department of Energy to help mitigate global warming. The process involves capturing CO 2 emissions from industrial sources and permanently storing them in deep geologic formations (storage reservoirs). However, CCS projects generally target “green field sites,” where there is often little characterization data and therefore large uncertainty about the petrophysical properties and other geologic attributes of the storage reservoir. Consequently, ensemble-based approaches are often used to forecast multiple realizations prior to CO 2 injection to visualize a range of potential outcomes. In addition, monitoring data during injection operations are used to update the pre-injection forecasts and thereby improve agreement between forecasted and observed behavior. Thus, a system for generating accurate, timely forecasts of pressure buildup and CO 2 movement and distribution within the storage reservoir and for updating those forecasts via monitoring measurements becomes crucial. This study proposes a learning-based prediction method that can accurately and rapidly forecast spatial distribution of CO 2 concentration and pressure with uncertainty quantification without relying on traditional inverse modeling. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO 2 storage site operators with an effective tool for timely and informative decision making based on limited simulation and monitoring data.
58 GEOSCIENCES↗
LaSDI: Parametric Latent Space Dynamics Identification
Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.
97 MATHEMATICS AND COMPUTING↗
Ensemble Kalman inversion of induced polarization data
SUMMARY This paper explores the applicability of ensemble Kalman inversion (EKI) with level-set parametrization for solving geophysical inverse problems. In particular, we focus on its extension to induced polarization (IP) data with uncertainty quantification. IP data may provide rich information on characteristics of geological materials due to its sensitivity to characteristics of the pore–grain interface. In many IP studies, different geological units are juxtaposed and the goal is to delineate these units and obtain estimates of unit properties with uncertainty bounds. Conventional inversion of IP data does not resolve well sharp interfaces and tends to reduce and smooth resistivity variations, while not readily providing uncertainty estimates. Recently, it has been shown for DC resistivity that EKI is an efficient solver for inverse problems which provides uncertainty quantification, and its combination with level set parametrization can delineate arbitrary interfaces well. In this contribution, we demonstrate the extension of EKI to IP data using a sequential approach, where the mean field obtained from DC resistivity inversion is used as input for a separate phase angle inversion. We illustrate our workflow using a series of synthetic and field examples. Variations with uncertainty bounds in both DC resistivity and phase angles are recovered by EKI, which provides useful information for hydrogeological site characterization. Although phase angles are less well-resolved than DC resistivity, partly due to their smaller range and higher percentage data errors, it complements DC resistivity for site characterization. Overall, EKI with level set parametrization provides a practical approach forward for efficient hydrogeophysical imaging under uncertainty.
Geochemistry & Geophysics↗
Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks
Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.
97 MATHEMATICS AND COMPUTING↗
Seismic Tomography 2024
Seismic tomography is the most abundant source of information about the internal structure of the Earth at scales ranging from a few meters to thousands of kilometers. It constrains the properties of active volcanoes, earthquake fault zones, deep reservoirs and storage sites, glaciers and ice sheets, or the entire globe. It contributes to outstanding societal problems related to natural hazards, resource exploration, underground storage, and many more. The recent advances in seismic tomography are being translated to nondestructive testing, medical ultrasound, and helioseismology. Nearly 50 yr after its first successful applications, this article offers a snapshot of modern seismic tomography. Focused on major challenges and particularly promising research directions, it is intended to guide both Earth science professionals and early-career scientists. The individual contributions by the coauthors provide diverse perspectives on topics that may at first seem disconnected but are closely tied together by a few coherent threads: multiparameter inversion for properties related to dynamic processes, data quality, and geographic coverage, uncertainty quantification that is useful for geologic interpretation, new formulations of tomographic inverse problems that address concrete geologic questions more directly, and the presentation and quantitative comparison of tomographic models. Finally, it remains to be seen which of these problems will be considered solved, solved to some extent, or practically unsolvable over the next decade.
58 GEOSCIENCES↗
Hardening of DOE UQ Codes for Ultra-Deep Proactive Geosteering in Oilfield Service
The primary objective of this project was to harden the DOE uncertainty quantification (UQ) code to solve the inverse problem for the geosteering service in the oilfield drilling and exploration. The primary focus is to verify the feasibility of using QUESO to solve geosteering inverse problems through statistical inversion. QUESO is a software library developed by QUEST, a DOE's Scientific Discovery through Advanced Computing (SciDAC) institute. In the process of drilling a borehole, geosteering is the act of adjusting the well trajectory on the fly to reach the geological targets or to keep the wellbore within desired formation. Geosteering inversion is to infer underground formation structure using measurements such as azimuthal resistivity logging data. The geosteering process relies on the real-time reconstruction of the subsurface earth model, and a robust and efficient inversion algorithm is always necessary to satisfy the job requirement. The new generation of azimuthal resistivity geosteering tool is capable of detecting multiple formation boundaries 20-100 ft away, and the corresponding geosteering inversion problem can be very challenging as many parameters need to be inverted within such a large depth of investigation. The success of the project will support US energy security by helping to advance subsurface modeling and characterization technologies in oilfield applications. An effective subsurface inversion algorithm and the implementation as a software package will promote the usage of ultra-deep azimuthal resistivity measurements, which can help well placement in complicated underground environments, reduce costs and risks of drilling, and increase oil and gas production. It will help medium and small size independent service companies and tool manufactures to enter the more advanced and lucrative directional drilling area. In addition, by hardening the QUESO code and building a transparent interface for easy manipulation of the QUESO functions, we provide a user-friendly tool for a larger scientific and industry communities that rely heavily on modeling and simulation tools for forecasting, parameter studies, design, and decision making. These are all activities that can strongly benefit from meaningful representations of modeling uncertainty supported by our product.
58 GEOSCIENCES↗
A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge L 1 and L 2 regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to maximum a posteriori estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement. In addition, it lends itself naturally to conduct model selection for the choice of hyperparameters. Here, we illustrate the performance of our methodology in several computed examples, including a deconvolution problem and sparse identification of dynamical systems from time series data.
Bayesian shrinkage↗
Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method
The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthal resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.
97 MATHEMATICS AND COMPUTING↗