In the present work, we examine and analyze an alternative of the unfitted mesh finite element method improved by omitting computationally expensive, especially for fluids, stabilization type of penalty onto the boundary area, namely the so-called ghost penalty. This approach is based on the discontinuous Galerkin method, enriched by arbitrarily shaped boundary elements techniques. In this framework, we examine a stationary Stokes fluid system and we prove the inf/sup condition, the hp- a priori error estimates, to our knowledge for the first time in the literature, while we investigate the optimal convergence rates numerically. This approach recovers and integrates the flexibility and superiority of the unfitted methods whenever geometrical deformations are taking place, combined with the efficiency of the hp-version techniques based on arbitrarily shaped elements on the boundary.
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In this paper we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust (the constants in the error bounds are independent of the Reynolds number).
In this paper, we present a conforming discontinuous Galerkin (CDG) finite element method for Brinkman equations. The velocity stabilizer is removed by employing the higher degree polynomials to compute the weak gradient. The theoretical analysis shows that the CDG method is actually stable and accurate for the Brinkman equations. Optimal order error estimates are established in $H^1$ and $L^2$ norm. Finally, numerical experiments verify the stability and accuracy of the CDG numerical scheme.
We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $\beta$-method for the momentum equation and a $\theta$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally we present a simulation in a three dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain.
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the posterior covariance, which are useful in robust and stochastic control. However, the error bounds require knowledge of the true hyperparameters in the kernel design and are demonstrated to be inaccurate with estimated hyperparameters for lightly damped systems or in the presence of high noise. In this work, we provide reliable quantification of the estimation error when the hyperparameters are unknown. The bounds are obtained by first constructing a high-probability set for the true hyperparameters from the marginal likelihood function and then finding the worst-case posterior covariance within the set. The proposed bound is proven to contain the true model with a high probability and its validity is verified in numerical simulation.
We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and $hp$-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$\beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models.
We present a novel class of ambiguity sets for distributionally robust optimization (DRO). These ambiguity sets, called cost-aware ambiguity sets, are defined as halfspaces which depend on the cost function evaluated at an independent estimate of the optimal solution, thus excluding only those distributions that are expected to have significant impact on the obtained worst-case cost. We show that the resulting DRO method provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and demonstrate empirically that it results in less conservative solutions compared to divergence-based ambiguity sets.
Currently, inter-organizational process collaboration (IOPC) has been widely used in the design and development of distributed systems that support business process execution. Blockchain-based IOPC can establish trusted data sharing among participants, attracting more and more attention. The core of such study is to translate the graphical model (e.g., BPMN) into program code called smart contract that can be executed in the blockchain environment. In this context, a proper smart contract plays a vital role in the correct implementation of block-chain-based IOPC. In fact, the quality of graphical model affects the smart con-tract generation. Problematic models (e.g., deadlock) will result in incorrect contracts (causing unexpected behaviours). To avoid this undesired implementation, this paper explores to generate smart contracts by using the verified formal model as input instead of graphical model. Specifically, we introduce a prototype framework that supports the automatic generation of smart contracts, providing an end-to-end solution from modeling, verification, translation to implementation. One of the cores of this framework is to provide a CSP#-based formalization for the BPMN collaboration model from the perspective of message interaction. This formalization provides precise execution semantics and model verification for graphical models, and a verified formal model for smart contract generation. Another novelty is that it introduces a syntax tree-based translation algorithm to directly map the formal model into a smart contract. The required formalism, verification and translation techniques are transparent to users without imposing additional burdens. Finally, a set of experiments shows the effectiveness of the framework.
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques based on sparse spectrum Gaussian processes, we focus on models given by regularized trigonometric linear regression. This paper provides an analysis of the performance of such an estimation set-up within the statistical learning framework. In particular, we derive a novel bound for the sample error in finite-dimensional spaces, accounting for noise with potentially unbounded support. Next, we study the approximation error and discuss the bias-variance trade-off as a function of the regularization parameter by combining the two bounds.
Intelligent reflecting surface (IRS) is envisioned to become a key technology for the upcoming six-generation (6G) wireless system due to its potential of reaping high performance in a power-efficient and cost-efficient way. With its disruptive capability and hardware constraint, the integration of IRS imposes some fundamental particularities on the coordination of multi-user signal transmission. Consequently, the conventional orthogonal and non-orthogonal multiple-access schemes are hard to directly apply because of the joint optimization of active beamforming at the base station and passive reflection at the IRS. Relying on an alternating optimization method, we develop novel schemes for efficient multiple access in IRS-aided multi-user multi-antenna systems in this paper. Achievable performance in terms of the sum spectral efficiency is theoretically analyzed. A comprehensive comparison of different schemes and configurations is conducted through Monte-Carlo simulations to clarify which scheme is favorable for this emerging 6G paradigm.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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