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Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full- field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered. 

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to stochastic noise. A practical algorithm is designed to facilitate causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure. This mitigates the curse of dimensionality and prevents the finite time blow-up issue. Numerical experiments show that the new algorithm identifies the model structure and provides suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events. 

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning model that builds a nonlinear map between the coefficients of observed and unobserved state variables for each spectral mode. A cheap low‐order nonlinear stochastic parameterized extended Kalman filter (SPEKF) model is employed as the forecast model in the ensemble Kalman filter to deal with each mode associated with the observed variables. The resulting ensemble members are then fed into the machine learning model to create an ensemble of the corresponding unobserved variables. In addition to the ensemble spread, the training residual in the machine learning‐induced nonlinear map is further incorporated into the state estimation, advancing the diagnostic quantification of the posterior uncertainty. The hybrid data assimilation algorithm is applied to a precipitating quasi‐geostrophic (PQG) model, which includes the effects of water vapor, clouds, and rainfall beyond the classical two‐level QG model. The complicated nonlinearities in the PQG equations prevent traditional methods from building simple and accurate reduced‐order forecast models. In contrast, the SPEKF forecast model is skillful in recovering the intermittent observed states, and the machine learning model effectively estimates the chaotic unobserved signals. Utilizing the calibrated SPEKF and machine learning models under a moderate cloud fraction, the resulting hybrid data assimilation remains reasonably accurate when applied to other geophysical scenarios with nearly clear skies or relatively heavy rainfall, implying the robustness of the algorithm for extrapolation.

 

Abstract El Niño-Southern Oscillation (ENSO) exhibits diverse characteristics in spatial pattern, peak intensity, and temporal evolution. Here we develop a three-region multiscale stochastic model to show that the observed ENSO complexity can be explained by combining intraseasonal, interannual, and decadal processes. The model starts with a deterministic three-region system for the interannual variabilities. Then two stochastic processes of the intraseasonal and decadal variation are incorporated. The model can reproduce not only the general properties of the observed ENSO events, but also the complexity in patterns (e.g., Central Pacific vs. Eastern Pacific events), intensity (e.g., 10–20 year reoccurrence of extreme El Niños), and temporal evolution (e.g., more multi-year La Niñas than multi-year El Niños). While conventional conceptual models were typically used to understand the dynamics behind the common properties of ENSO, this model offers a powerful tool to understand and predict ENSO complexity that challenges our understanding of the twenty-first century ENSO. 

This paper reports a new mechanism for particulate matter detection and identification. Three types of carbon particles are synthesized with different functional groups to mimic the real particulates in atmospheric aerosol. After exposing polymer‐based organic devices in organic field effect transistor (OFET) architectures to the particle mist, the sensitivity and selectivity of the detection of different types of particles are shown by the current changes extracted from the transfer curves. The results indicate that the sensitivity of the devices is related to the structure and functional groups of the organic semiconducting layers, as well as the morphology. The predominant response is simulated by a model that yielded values of charge carrier density increase and charge carriers delivered per unit mass of particles. The research points out that polymer semiconductor devices have the ability to selectively detect particles with multiple functional groups, which reveals a future direction for selective detection of particulate matter.

 

Modeling and understanding sea ice dynamics in marginal ice zones rely on measurements of sea ice. Lagrangian observations of ice floes provide insight into the dynamics of sea ice, the ocean, and the atmosphere. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of floe positions. This paper presents an efficient and statistically accurate nonlinear dynamical interpolation framework for recovering missing floe observations. It exploits a balanced physics‐based and data‐driven construction to address the challenges posed by the high‐dimensional and nonlinear nature of the coupled atmosphere‐ice‐ocean system, where effective reduced‐order stochastic models, nonlinear data assimilation, and simultaneous parameter estimation are systematically integrated. The new method succeeds in recovering the locations, curvatures, angular displacements, and the associated strong non‐Gaussian distributions of the missing floes in the Beaufort Sea. It also accurately estimates floe thickness and recovers the unobserved underlying ocean field with an appropriate uncertainty quantification, advancing our understanding of Arctic climate.