A hybrid adaptive MCMC algorithm in function spaces

The preconditioned Crank-Nicolson (pCN) method is a Markov Chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in function spaces. Unlike many standard MCMC algorithms, the pCN method can preserve the sampling efficiency under the mesh refinement, a property referred to as being dimension independent. In this work we consider an adaptive strategy to further improve the efficiency of pCN. In particular we develop a hybrid adaptive MCMC method: the algorithm performs an adaptive Metropolis scheme in a chosen finite dimensional subspace, and a standard pCN algorithm in the complement space of the chosen subspace. We show that the proposed algorithm satisfies certain important ergodicity conditions. Finally with numerical examples we demonstrate that the proposed method has competitive performance with existing adaptive algorithms.Comment: arXiv admin note: text overlap with arXiv:1511.0583

2D Spatial Distributions for Measures of Random Sequences Using Conjugate Maps

Advanced visual tools are useful to provide additional information for modern information warfare. 2D spatial distributions of random sequences play an important role to understand properties of complex sequences. This paper proposes time-sequences from a given logical function of 1D Cellular Automata in both Poincare map and conjugate map. Multiple measure sequences of Markov chains can be used to display spatial distributions using conjugate maps. Measure sequences recursively produced by different logical functions generating maps. Possible complementary feature exits between pair functions, Conjugate symmetry relationships between a pair of logical functions in conjugate maps can be observed

Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems

Combining the strengths of model-based iterative algorithms and data-driven deep learning solutions, deep unrolling networks (DuNets) have become a popular tool to solve inverse imaging problems. While DuNets have been successfully applied to many linear inverse problems, nonlinear problems tend to impair the performance of the method. Inspired by momentum acceleration techniques that are often used in optimization algorithms, we propose a recurrent momentum acceleration (RMA) framework that uses a long short-term memory recurrent neural network (LSTM-RNN) to simulate the momentum acceleration process. The RMA module leverages the ability of the LSTM-RNN to learn and retain knowledge from the previous gradients. We apply RMA to two popular DuNets -- the learned proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods, resulting in LPGD-RMA and LPD-RMA respectively. We provide experimental results on two nonlinear inverse problems: a nonlinear deconvolution problem, and an electrical impedance tomography problem with limited boundary measurements. In the first experiment we have observed that the improvement due to RMA largely increases with respect to the nonlinearity of the problem. The results of the second example further demonstrate that the RMA schemes can significantly improve the performance of DuNets in strongly ill-posed problems

Deep unrolling networks with recurrent momentum acceleration for nonlinear inverse problems

Combining the strengths of model-based iterative algorithms and data-driven deep learning solutions, deep unrolling networks (DuNets) have become a popular tool to solve inverse imaging problems. Although DuNets have been successfully applied to many linear inverse problems, their performance tends to be impaired by nonlinear problems. Inspired by momentum acceleration techniques that are often used in optimization algorithms, we propose a recurrent momentum acceleration (RMA) framework that uses a long short-term memory recurrent neural network (LSTM-RNN) to simulate the momentum acceleration process. The RMA module leverages the ability of the LSTM-RNN to learn and retain knowledge from the previous gradients. We apply RMA to two popular DuNets—the learned proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods, resulting in LPGD-RMA and LPD-RMA, respectively. We provide experimental results on two nonlinear inverse problems: a nonlinear deconvolution problem, and an electrical impedance tomography problem with limited boundary measurements. In the first experiment we have observed that the improvement due to RMA largely increases with respect to the nonlinearity of the problem. The results of the second example further demonstrate that the RMA schemes can significantly improve the performance of DuNets in strongly ill-posed problems

Combination of sonic wave velocity, density and electrical resistivity for joint estimation of gas-hydrate reservoir parameters and their uncertainties

Gas-hydrate saturation and porosity are the most crucial reservoir parameters for gas-hydrate resource assessment. Numerous academics have put forward elastic and electrical petrophysical models for calculating the saturation and porosity of gas-hydrate. However, owing to the limitations of a single petrophysical model, the estimation of gas-hydrate saturation and porosity using single elastic or electrical measurement data appears to be inconsistent and uncertain. In this study, the sonic wave velocity, density and resistivity well log data are combined with a Bayesian linear inversion method for the simultaneous estimation of gas-hydrate saturation and porosity. The sonic wave velocity, density and resistivity data of the Shenhu area in the South China Sea are used to estimate the gas-hydrate saturation and porosity. To validate the accuracy of this method, the estimation results are compared with the saturation obtained from pore water chemistry and porosity obtained from density logs. The well log data examples show that the joint estimation method not only provides a rapid estimation of the gas-hydrate reservoir parameters but also improves the accuracy of results and determines their uncertainty.Document Type: Original articleCited as: Zhang, X., Li, Q., Li, L., Fan, Q., Geng, J. Combination of sonic wave velocity, density and electrical resistivity for joint estimation of gas-hydrate reservoir parameters and their uncertainties. Advances in Geo-Energy Research, 2023, 10(2): 133-140. https://doi.org/10.46690/ager.2023.11.0

The Non-Perturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and the nature of dislocation-phonon resonance. Here by introducing a fully quantized dislocation field, the "dislon"[1], a phonon is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime that is reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. In particular, a renormalized phonon naturally resolves the decades-long debate between dynamic and static dislocation-phonon scattering approaches.Comment: 5 pages main text, 3 figures, 10 pages supplemental material

Between Attention and Portfolio Adjustment: Insights from Machine Learning-based Risk Preference Assessment

Financial firms recommend products to customers, intending to gain their attention and change their portfolios. Based on behavioral decision-making theory, we argue attention’s effect on portfolio adjustment is through the risk deviation between portfolio risk and their risk preference. Thus, to fully understand the adjustment process, it is necessary to assess customers’ risk preferences. In this study, we use machine learning methods to measure customers’ risk preferences. Then, we build a dynamic adjustment model and find that attention’s impact on portfolio adjustment speed is stronger when customers’ risk preference is higher than portfolio risk (which needs an upward adjustment) and when customers’ risk preference is within historical portfolio risk experience. We conducted a field experiment and found that directing customers’ attention to products addressing the risk deviation would lead to more portfolio adjustment activities. Our study illustrates the role of machine learning in enhancing our understanding of financial decision-making