Turbulence parametrizations will remain a necessary building block in kilometer-scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass flux parametrizations for the typically asymmetric up- and downdrafts in the atmospheric boundary layer. In this work, we present a parametrization for a dry convective boundary layer based on a generative adversarial network. The model incorporates the physics of self-similar layer growth following from the classical mixed layer theory by Deardorff. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer. The algorithm training is based on fully three-dimensional direct numerical simulation data. Differently to stochastic parametrizations, our model is able to predict the highly non-Gaussian transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two-equation or multi-plume stochastic mass-flux schemes. The present parametrization provides additionally the granule-type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our work paves the way to efficient data-driven convective parametrizations in other natural flows, such as moist convection, upper ocean mixing, or convection in stellar interiors.
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Recent advancements in evaluating matrix-exponential functions have opened the doors to the practical use of exponential time-integration methods in numerical weather prediction (NWP). The success of exponential methods in shallow water simulations has led to the question of whether they can be beneficial in a 3D atmospheric model. In this paper, we take the first step forward by evaluating the behavior of exponential time-integration methods in the Navy's compressible deep-atmosphere nonhydrostatic global model (NEPTUNE-Navy Environmental Prediction sysTem Utilizing a Nonhydrostatic Engine). Simulations are conducted on a set of idealized test cases designed to assess key features of a nonhydrostatic model and demonstrate that exponential integrators capture the desired large and small-scale traits, yielding results comparable to those found in the literature. We propose a new upper boundary absorbing layer independent of reference state and shown to be effective in both idealized and real-data simulations. A real-data forecast using an exponential method with full physics is presented, providing a positive outlook for using exponential integrators for NWP.
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In the common situation that the components of the vector have different distributions, the rank transformation offers a convenient and robust way of standardizing data in order to build an empirical version of the angular measure based on the most extreme observations. We provide a functional asymptotic expansion for the empirical angular measure in the bivariate case based on the theory of weak convergence in the space of bounded functions. From the expansion, not only can the known asymptotic distribution of the empirical angular measure be recovered, it also enables to find expansions and weak limits for other statistics based on the associated empirical process or its quantile version.
We present a nonparametric graphical model. Our model uses an undirected graph that represents conditional independence for general random variables defined by the conditional dependence coefficient (Azadkia and Chatterjee (2021)). The set of edges of the graph are defined as $E=\{(i,j):R_{i,j}\neq 0\}$, where $R_{i,j}$ is the conditional dependence coefficient for $X_i$ and $X_j$ given $(X_1,\ldots,X_p) \backslash \{X_{i},X_{j}\}$. We propose a graph structure learning by two steps selection procedure: first, we compute the matrix of sample version of the conditional dependence coefficient $\widehat{R_{i,j}}$; next, for some prespecificated threshold $\lambda>0$ we choose an edge $\{i,j\}$ if $ \left|\widehat{R_{i,j}} \right| \geq \lambda.$ The graph recovery structure has been evaluated on artificial and real datasets. We also applied a slight modification of our graph recovery procedure for learning partial correlation graphs for the elliptical distribution.
A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.
Distributed formation control of end-effector of mixed planar fully- and under-actuated manipulators
This paper addresses the problem of end-effector formation control for a mixed group of two-link manipulators moving in a horizontal plane that comprises of fully-actuated manipulators and underactuated manipulators with only the second joint being actuated (referred to as the passive-active (PA) manipulators). The problem is solved by extending the distributed end-effector formation controller for the fully-actuated manipulator to the PA manipulator moving in a horizontal plane by using its integrability. This paper presents stability analysis of the closed-loop systems under a given necessary condition, and we prove that the manipulators' end-effector converge to the desired formation shape. The proposed method is validated by simulations.
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit residual-based error estimator as well as a separate marking strategy based on the alternative error estimator and an optimal data approximation algorithm. This paper reviews and discusses available convergence results. In addition, all three strategies are investigated empirically for a set of benchmarks examples of second-order elliptic partial differential equations in two spatial dimensions. Particular interest is on the choice of the marking and refinement parameters and the approximation of the given data. The numerical experiments are reproducible using the author's software package octAFEM available on the platform Code Ocean.
This paper introduces novel bulk-surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system. This means that the bulk and surface dynamics are modeled separately and connected through a coupling constraint. This allows the implementation of splitting schemes, which show first-order convergence in numerical experiments. On the other hand, acoustic boundary conditions naturally separate bulk and surface dynamics. Here, Lie and Strang splitting schemes reach first- and second-order convergence, respectively, as we reveal numerically.
Epidemiological models must be calibrated to ground truth for downstream tasks such as producing forward projections or running what-if scenarios. The meaning of calibration changes in case of a stochastic model since output from such a model is generally described via an ensemble or a distribution. Each member of the ensemble is usually mapped to a random number seed (explicitly or implicitly). With the goal of finding not only the input parameter settings but also the random seeds that are consistent with the ground truth, we propose a class of Gaussian process (GP) surrogates along with an optimization strategy based on Thompson sampling. This Trajectory Oriented Optimization (TOO) approach produces actual trajectories close to the empirical observations instead of a set of parameter settings where only the mean simulation behavior matches with the ground truth.
When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the geometry is complex, in particular in 3D. In this work, we develop an efficient technique for a non-conforming finite-element treatment of weak discontinuities by using laminated microstructures. The approach is inspired by the so-called composite voxel technique that has been developed for FFT-based spectral solvers in computational homogenization. The idea behind the method is rather simple. Each finite element that is cut by an interface is treated as a simple laminate with the volume fraction of the phases and the lamination orientation determined in terms of the actual geometrical arrangement of the interface within the element. The approach is illustrated by several computational examples relevant to the micromechanics of heterogeneous materials. Elastic and elastic-plastic materials at small and finite strain are considered in the examples. The performance of the proposed method is compared to two alternative, simple methods showing that the new approach is in most cases superior to them while maintaining the simplicity.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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