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1. Conditional Gaussian nonlinear system: A fast preconditioner and a cheap surrogate model for complex nonlinear systems

   https://doi.org/https://doi.org/10.1063/5.0081668  

   Chen, N. ; Li, Y. ; Liu, H. ( May 2022 , Chaos)

   Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian nonlinear system (CGNS), as both a cheap surrogate model and a fast preconditioner for facilitating many computationally challenging tasks. The CGNS preserves the underlying physics to a large extent and can reproduce intermittency, extreme events, and other non-Gaussian features in many complex systems arising from practical applications. Three interrelated topics are studied. First, the closed analytic formulas of solving the conditional statistics provide an efficient and accurate data assimilation scheme. It is shown that the data assimilation skill of a suitable CGNS approximate forecast model outweighs that by applying an ensemble method even to the perfect model with strong nonlinearity, where the latter suffers from filter divergence. Second, the CGNS allows the development of a fast algorithm for simultaneously estimating the parameters and the unobserved variables with uncertainty quantification in the presence of only partial observations. Utilizing an appropriate CGNS as a preconditioner significantly reduces the computational cost in accurately estimating the parameters in the original complex system. Finally, the CGNS advances rapid and statistically accurate algorithms for computing the probability density function and sampling the trajectories of the unobserved state variables. These fast algorithms facilitate the development of an efficient and accurate data-driven method for predicting the linear response of the original system with respect to parameter perturbations based on a suitable CGNS preconditioner. 

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2. Field fluctuations viscoplastic self-consistent crystal plasticity: Applications to predicting texture evolution during deformation and recrystallization of cubic polycrystalline metals

   https://doi.org/10.1016/j.actamat.2023.119395  

   Riyad, Iftekhar A. ; Knezevic, Marko ( December 2023 , Acta Materialia)

   Recent advances pertaining to modeling of grain fragmentation during deformation and recrystallization of polycrystalline metals using viscoplastic self-consistent (VPSC) polycrystal plasticity are combined into a field fluctuations VPSC (FF-VPSC) model. The FF-VPSC model is a higher-order formulation calculating the second moments of lattice rotation rates based on the second moments of stress fields inside grains and resulting intragranular misorientation distributions. The misorientation distributions are used to define a grain fragmentation sub-model for improving predictions of deformation texture evolution and to formulate kinetics sub-models for nucleation as well as to influence the stored energy governing grain growth for the predictions of recrystallization texture evolution. Formation of a copper-like texture in moderately high stacking fault energy (SFE) Cu and a brass-like texture in low SFE brass during rolling to very large strains are successfully predicted using the model. Remarkably, the model also predicts recrystallization textures from the deformation textures of the two metals after adjusting tradeoffs between transition-bands and grain boundary nucleation mechanisms. Additionally, rolling and recrystallization of an interstitial-free steel, tension and recrystallization of AA5182-O, and recrystallization of an additively manufacturing cobalt-based alloy MarM-509 are simulated to predict texture evolution. Through these case studies involving multiple alloys and thermo-mechanical processes we show that, in addition to being predictive with good accuracy, the key advantage of the model lies in its versatility. The FF-VPSC model, simulation results, and insights from the results are presented and discussed in this paper. 

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3. A Statistical Hypothesis Testing Strategy for Adaptively Blending Particle Filters and Ensemble Kalman Filters for Data Assimilation

   https://doi.org/10.1175/MWR-D-22-0108.1  

   Kurosawa, Kenta ; Poterjoy, Jonathan ( January 2023 , Monthly Weather Review)

   Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. 

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4. Data-Driven Calibration of Multifidelity Multiscale Fracture Models Via Latent Map Gaussian Process

   https://doi.org/10.1115/1.4055951  

   Deng, Shiguang ; Mora, Carlos ; Apelian, Diran ; Bostanabad, Ramin ( January 2023 , Journal of Mechanical Design)

   Abstract Fracture modeling of metallic alloys with microscopic pores relies on multiscale damage simulations which typically ignore the manufacturing-induced spatial variabilities in porosity. This simplification is made because of the prohibitive computational expenses of explicitly modeling spatially varying microstructures in a macroscopic part. To address this challenge and open the doors for the fracture-aware design of multiscale materials, we propose a data-driven framework that integrates a mechanistic reduced-order model (ROM) with a calibration scheme based on random processes. Our ROM drastically accelerates direct numerical simulations (DNS) by using a stabilized damage algorithm and systematically reducing the degrees of freedom via clustering. Since clustering affects local strain fields and hence the fracture response, we calibrate the ROM by constructing a multifidelity random process based on latent map Gaussian processes (LMGPs). In particular, we use LMGPs to calibrate the damage parameters of an ROM as a function of microstructure and clustering (i.e., fidelity) level such that the ROM faithfully surrogates DNS. We demonstrate the application of our framework in predicting the damage behavior of a multiscale metallic component with spatially varying porosity. Our results indicate that microstructural porosity can significantly affect the performance of macro-components and hence must be considered in the design process. 

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5. A coupled model for phase mixing, grain damage and shear localization in the lithosphere: comparison to lab experiments

   https://doi.org/10.1093/gji/ggac428  

   Bercovici, David ; Mulyukova, Elvira ; Girard, Jennifer ; Skemer, Philip ( November 2022 , Geophysical Journal International)

   SUMMARY The occurrence of plate tectonics on Earth is rooted in the physics of lithospheric ductile weakening and shear-localization. The pervasiveness of mylonites at lithospheric shear zones is a key piece of evidence that localization correlates with reduction in mineral grain size. Most lithospheric mylonites are polymineralic and the interaction between mineral phases, such as olivine and pyroxene, especially through Zener pinning, impedes normal grain growth while possibly enhancing grain damage, both of which facilitate grain size reduction and weakening, as evident in lab experiments and field observations. The efficacy of pinning, however, relies on the mineral phases being mixed and dispersed at the grain scale, where well-mixed states lead to greater mylonitization. To model grain mixing between different phases at the continuum scale, we previously developed a theory treating grain-scale processes as diffusion between phases, but driven by imposed compressive stresses acting on the boundary between phases. Here we present a new model for shearing rock that combines our theory for diffusive grain mixing, 2-D non-Newtonian flow and two-phase grain damage. The model geometry is designed specifically for comparison to torsional shear-deformation experiments. Deformation is either forced by constant velocity or constant stress boundary conditions. As the layer is deformed, mixing zones between different mineralogical units undergo enhanced grain size reduction and weakening, especially at high strains. For constant velocity boundary experiments, stress drops towards an initial piezometric plateau by a strain of around 4; this is also typical of monophase experiments for which this initial plateau is the final steady state stress. However, polyphase experiments can undergo a second large stress drop at strains of 10–20, and which is associated with enhanced phase mixing and resultant grain size reduction and weakening. Model calculations for polyphase media with grain mixing and damage capture the experimental behaviour when damage to the interface between phases is moderately slower or less efficient than damage to the grain boundaries. Other factors such as distribution and bulk fraction of the secondary phase, as well as grain-mixing diffusivity also influence the timing of the second stress drop. For constant stress boundary conditions, the strain rate increases during weakening and localization. For a monophase medium, there is theoretically one increase in strain rate to a piezometric steady state. But for the polyphase model, the strain rate undergoes a second abrupt increase, the timing for which is again controlled by interface damage and grain mixing. The evolution of heterogeneity through mixing and deformation, and that of grain size distributions also compare well to experimental observations. In total, the comparison of theory to deformation experiments provides a framework for guiding future experiments, scaling microstructural physics to geodynamic applications and demonstrates the importance of grain mixing and damage for the formation of plate tectonic boundaries. 

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