Stochastic inversion for soil hydraulic parameters in the presence of model error: An example involving ground-penetrating radar monitoring of infiltration

Köpke, Corinna; Irving, James; Roubinet, Delphine

doi:10.1016/j.jhydrol.2018.12.016

Cited by 13 publications

(8 citation statements)

References 57 publications

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“…Traditionally, model errors are learned by evaluating modeling discrepancies using samples from the prior, yet, recent adaptive approaches in which the model error description is updated based on samples from the posterior region has shown important improvements (Cui et al, 2011;Calvetti et al, 2014). Other approaches for dealing with model errors involve estimating and removing them from the residual data term before calculating the likelihood function (Köpke et al, 2018(Köpke et al, , 2019. In such methods, the residuals are projected onto an orthogonal model-error basis, which is constructed either during the inversion using a dictionary-based K-nearest-neighbour approach, or before the inversion using principal component analysis (PCA) conducted on a suite of model-error realizations.…”

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confidence: 99%

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Levy

Hunziker

Laloy

et al. 2021

Geophysical Journal International

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Summary Most geophysical inverse problems are nonlinear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modeling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fidelity forward solvers. These representations are then used to probabilistically invert for the model error jointly with the target geophysical property field, using the computationally-cheap, low-fidelity forward solver. To this end, we combine a Markov-chain-Monte-Carlo (MCMC) inversion algorithm with a trained convolutional neural network of the spatial generative adversarial network (SGAN) type, whereby at each MCMC step, the simulated low-fidelity forward response is corrected using a proposed model-error realization. Considering the crosshole ground-penetrating radar traveltime tomography inverse problem, we train SGAN networks on traveltime discrepancy images between: (1) curved-ray (high fidelity) and straight-ray (low fidelity) forward solvers; and (2) finite-difference-time-domain (high fidelity) and straight-ray (low fidelity) forward solvers. We demonstrate that the SGAN is able to learn the spatial statistics of the model error and that suitable representations of both the subsurface model and model error can be recovered by MCMC. In comparison with inversion results obtained when model errors are either ignored or approximated by a Gaussian distribution, we find that our method has lower posterior parameter bias and better explains the observed traveltime data. Our method is most advantageous when high-fidelity forward solvers involve heavy computational costs and the Gaussian assumption of model errors is inappropriate. Unstable MCMC convergence due to nonlinearities introduced by our method remain a challenge to be addressed in future work.

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confidence: 99%

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Levy

Hunziker

Laloy

et al. 2021

Geophysical Journal International

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“…The ANN and PSO can be combined in the parameter inversion calculation process to simplify the analytical process. PCA can identify and remove the model errors introduced by the application of the ANN approximate forward model before the calculation of the likelihood function in the DREAMzs algorithm [27,28]. The detailed procedure of the algorithm is given as follows: 2.…”

Section: Procedures For the Ann-based Bayesian-mcmc Algorithmmentioning

confidence: 99%

Comparison of Two Bayesian-MCMC Inversion Methods for Laboratory Infiltration and Field Irrigation Experiments

Guo

Dai

Zhao

2020

IJERPH

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Bayesian parameter inversion approaches are dependent on the original forward models linking subsurface physical properties to measured data, which usually require a large number of iterations. Fast alternative systems to forward models are commonly employed to make the stochastic inversion problem computationally tractable. This paper compared the effect of the original forward model constructed by the HYDRUS-1D software and two different approximations: the Artificial Neural Network (ANN) alternative system and the Gaussian Process (GP) surrogate system. The model error of the ANN was quantified using a principal component analysis, while the model error of the GP was measured using its own variance. There were two groups of measured pressure head data of undisturbed loess for parameter inversion: one group was obtained from a laboratory soil column infiltration experiment and the other was derived from a field irrigation experiment. Strong correlations between the pressure head values simulated by random posterior samples indicated that the approximate forward models are reliable enough to be included in the Bayesian inversion framework. The approximate forward models significantly improved the inversion efficiency by comparing the observed and the optimized results with a similar accuracy. In conclusion, surrogates can be considered when the forward models are strongly nonlinear and the computational costs are prohibitive.

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“…To take into consideration the modeling error of the straight-ray simulator, we adopt the idea in [38] that we first calculate an orthonormal basis for the modeling error using the fine-grid FDTD and coarse-grid straight-ray solvers prior to the inversion work. Then in MCMC, we use this basis to calculate the modeling error and subtract it from the residual the between simulated and measurement data before calculating the likelihood function.In this way the modeling error is isolated outside the Bayesian inversion and no longer biases the inversion results.…”

Section: Straight-ray Model With Modeling Error Correctedmentioning

confidence: 99%

“…Yet due to the ray assumption, any scattering effects of EM waves are neglected and notable modeling errors might be produced and bias the inversion results. Before the ray-based model can be implemented successfully within the Bayesian inversion framework, the modeling errors should be carefully considered [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of a Straight-Ray Forward Model for Bayesian Inversion of Crosshole Ground Penetrating Radar Data

2019

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Bayesian inversion of crosshole ground penetrating radar (GPR) data is capable of characterizing the subsurface dielectric properties and qualifying the associated uncertainties. Markov chain Monte Carlo (MCMC) simulations within the Bayesian inversion usually require thousands to millions of forward model evaluations for the parameters to hit their posterior distributions. Therefore, the CPU cost of the forward model is a key issue that influences the efficiency of the Bayesian inversion method. In this paper we implement a widely used straight-ray forward model within our Bayesian inversion framework. Based on a synthetic unit square relative permittivity model, we simulate the crosshole GPR first-arrival traveltime data using the finite-difference time-domain (FDTD) and straight-ray solver, respectively, and find that the straight-ray simulator runs 450 times faster than its FDTD counterpart, yet suffers from a modeling error that is more than 7 times larger. We also perform a series of numerical experiments to evaluate the performance of the straight-ray model within the Bayesian inversion framework. With modeling error disregarded, the inverted posterior models fit the measurement data nicely, yet converge to the wrong set of parameters at the expense of unreasonably large number of iterations. When the modeling error is accounted for, with a quarter of the computational burden, the main features of the true model can be identified from the posterior realizations although there still exist some unwanted artifacts. Finally, a smooth constraint on the model structure improves the inversion results considerably, to the extent that it enhances the inversion accuracy approximating to those of the FDTD model, and further reduces the CPU demand. Our results demonstrate that the use of the straight-ray forward model in the Bayesian inversion saves computational cost tremendously, and the modeling error correction together with the model structure constraint are the necessary amendments that ensure that the model parameters converge correctly.

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Stochastic inversion for soil hydraulic parameters in the presence of model error: An example involving ground-penetrating radar monitoring of infiltration

Cited by 13 publications

References 57 publications

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Comparison of Two Bayesian-MCMC Inversion Methods for Laboratory Infiltration and Field Irrigation Experiments

Evaluation of a Straight-Ray Forward Model for Bayesian Inversion of Crosshole Ground Penetrating Radar Data

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