arXiv subjects

Lingzao Zeng

Publications and source records attributed to Lingzao Zeng.

6 recordsLinked to original sources

arXiv2020

Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization

Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly-adopted ES method that employs the Kalman formula, that is, ES$_\text{(K)}$, does not perform well when the probability distributions involved are non-Gaussian. To address this issue, we suggest to use deep learning (DL) to derive an alternative update scheme for ES in complex data assimilation applications. Here we show that the DL-based ES method, that is, ES$_\text{(DL)}$, is more general and flexible. In this new update scheme, a high volume of training data are generated from a relatively small-sized ensemble of model parameters and simulation outputs, and possible non-Gaussian features can be preserved in the training data and captured by an adequate DL model. This new variant of ES is tested in two subsurface characterization problems with or without Gaussian assumptions. Results indicate that ES$_\text{(DL)}$ can produce similar (in the Gaussian case) or even better (in the non-Gaussian case) results compared to those from ES$_\text{(K)}$. The success of ES$_\text{(DL)}$ comes from the power of DL in extracting complex (including non-Gaussian) features and learning nonlinear relationships from massive amounts of training data. Although in this work we only apply the ES$_\text{(DL)}$ method in parameter estimation problems, the proposed idea can be conveniently extended to analysis of model structural uncertainty and state estimation in real-time forecasting studies.

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arXiv2020

Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters.

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arXiv2020

Surrogate-Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can take advantage of surrogate modeling techniques. Nevertheless, when approximation error of the surrogate model is neglected, the inversion result will be biased. In this paper, we develop a surrogate-based Bayesian inversion framework that explicitly quantifies and gradually reduces the approximation error of the surrogate. Specifically, two strategies are proposed to quantify the surrogate error. The first strategy works by quantifying the surrogate prediction uncertainty with a Bayesian method, while the second strategy uses another surrogate to simulate and correct the approximation error of the primary surrogate. By adaptively refining the surrogate over the posterior distribution, we can gradually reduce the surrogate approximation error to a small level. Demonstrated with three case studies involving high dimensionality, multimodality, and a real-world application, it is found that both strategies can reduce the bias introduced by surrogate approximation error, while the second strategy that integrates two methods (i.e., polynomial chaos expansion and Gaussian process in this work) that complement each other shows the best performance.

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arXiv2019

Physics-informed semantic inpainting: Application to geostatistical modeling

A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness in dealing with complex spatial patterns. However, the original semantic inpainting framework incorporates only information from direct measurements, while in geostatistics indirect measurements are often plentiful. To overcome this limitation, here we propose a physics-informed semantic inpainting framework, employing the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and jointly incorporating the direct and indirect measurements by exploiting the underlying physical laws. Our simulation results for a high-dimensional problem with 512 dimensions show that in the new method, the physical conservation laws are satisfied and contribute in enhancing the inpainting performance compared to using only the direct measurements.

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arXiv2018

Inverse modeling of hydrologic systems with adaptive multi-fidelity Markov chain Monte Carlo simulations

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive and high-dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU-efficient while less accurate low-fidelity model (e.g., a numerical model with a coarser discretization, or a data-driven surrogate) is usually adopted. Nowadays, multi-fidelity simulation methods that can take advantage of both the efficiency of the low-fidelity model and the accuracy of the high-fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high-fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multi-fidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high-fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process (GP) system that is adaptively constructed with multi-fidelity simulation. The error of the GP system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high-fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.

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arXiv2018

An iterative local updating ensemble smoother for estimation and uncertainty assessment of hydrologic model parameters with multimodal distributions

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

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