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Abstract State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface observations. Directly implementing an ensemble Kalman filter based on the full forecast model is usually expensive. One widely used method in practice projects the information of the observed layer to other layers via linear regression. However, large errors appear when nonlinearity in the highly turbulent flow field becomes dominant. In this paper, we develop a multi-step nonlinear data assimilation method that involves the sequential application of nonlinear assimilation steps across layers. Unlike traditional linear regression approaches, a conditional Gaussian nonlinear system is adopted as the approximate forecast model to characterize the nonlinear dependence between adjacent layers. At each step, samples drawn from the posterior of the current layer are treated as pseudo-observations for the next layer. Each sample is assimilated using analytic formulae for the posterior mean and covariance. The resulting Gaussian posteriors are then aggregated into a Gaussian mixture. Therefore, the method can capture strongly turbulent features, particularly intermittency and extreme events, and more accurately quantify the inherent uncertainty. Applications to the two-layer quasi-geostrophic system with Lagrangian data assimilation demonstrate that the multi-step method outperforms the one-step method, particularly as the tracer number and ensemble size increase. Results also show that the multi-step CGDA is particularly effective for assimilating frequent, high-accuracy observations, which are scenarios where traditional EnKF methods may suffer from catastrophic filter divergence. 

The central complex (CX) plays a key role in many higher-order functions of the insect brain including navigation and activity regulation. Genetic tools for manipulating individual cell types, and knowledge of what neurotransmitters and neuromodulators they express, will be required to gain mechanistic understanding of how these functions are implemented. We generated and characterized split-GAL4 driver lines that express in individual or small subsets of about half of CX cell types. We surveyed neuropeptide and neuropeptide receptor expression in the central brain using fluorescent in situ hybridization. About half of the neuropeptides we examined were expressed in only a few cells, while the rest were expressed in dozens to hundreds of cells. Neuropeptide receptors were expressed more broadly and at lower levels. Using our GAL4 drivers to mark individual cell types, we found that 51 of the 85 CX cell types we examined expressed at least one neuropeptide and 21 expressed multiple neuropeptides. Surprisingly, all co-expressed a small molecule neurotransmitter. Finally, we used our driver lines to identify CX cell types whose activation affects sleep, and identified other central brain cell types that link the circadian clock to the CX. The well-characterized genetic tools and information on neuropeptide and neurotransmitter expression we provide should enhance studies of the CX. 

Abstract Constructing sparse, effective reduced-order models (ROMs) for high-dimensional dynamical data is an active area of research in applied sciences. In this work, we study an efficient approach to identifying such sparse ROMs using an information-theoretic indicator called causation entropy. Given a feature library of possible building block terms for the sought ROMs, the causation entropy ranks the importance of each term to the dynamics conveyed by the training data before a parameter estimation procedure is performed. It thus allows for an efficient construction of a hierarchy of ROMs with varying degrees of sparsity to effectively handle different tasks. This article examines the ability of the causation entropy to identify skillful sparse ROMs when a relatively high-dimensional ROM is required to emulate the dynamics conveyed by the training dataset. We demonstrate that a Gaussian approximation of the causation entropy still performs exceptionally well even in presence of highly non-Gaussian statistics. Such approximations provide an efficient way to access the otherwise hard to compute causation entropies when the selected feature library contains a large number of candidate functions. Besides recovering long-term statistics, we also demonstrate good performance of the obtained ROMs in recovering unobserved dynamics via data assimilation with partial observations, a test that has not been done before for causation-based ROMs of partial differential equations. The paradigmatic Kuramoto–Sivashinsky equation placed in a chaotic regime with highly skewed, multimodal statistics is utilized for these purposes. 

Abstract Doping of organic semiconductors has served as an effective method to achieve high electrical conductivity and large thermoelectric power factor. This is of importance to the development of flexible/wearable electronics and green energy‐harvesting technologies. The doping impact of the Lewis acid tris (pentafluorophenyl) borane (BCF) on the thermoelectric performance of poly(2‐(4,4′‐bis(2‐methoxyethoxy)‐5′‐methyl‐[2,2′‐bithiophen]‐5‐yl)‐5‐methylthieno[3,2‐b]thiophene (pgBTTT), a thiophene‐based polymer featuring oligoethylene glycol side chains is investigated. Tetrafluorotetracyanoquinodimethane (F4TCNQ), a well‐established dopant, is utilized as a comparison; however, its inability to co‐dissolve with pgBTTT in less polar solvents hinders the attainment of higher doping levels. Consequently, a comparative study is performed on the thermoelectric behavior of pgBTTT doped with BCF and F4TCNQ at a very low doping level. Subsequent investigation is carried out with BCF at higher doping levels. Remarkably, at 50 wt% BCF doping level, the highest power factor of 223 ± 4 µW m⁻¹K²is achieved with an electrical conductivity of 2180 ± 360 S cm⁻¹and a Seebeck coefficient of 32 ± 1.3 µV K⁻¹. This findings not only contribute valuable insights to the dopant interactions with oxygenated side chain polymers but also open up new avenues for high conductivity thermoelectric polymers in flexible electronic applications. 

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. 

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.