We develop a moment method based on the Hermite series of arbitrary order to calculate viscous-slip, thermal-slip, and temperature-jump coefficients for general gas-surface scattering kernels. Under some usual assumptions of scattering kernels, the solvability is obtained by showing the positive definiteness of the symmetric coefficient matrix in the boundary conditions. For gas flows with the Cercignani-Lampis gas-surface interaction and inverse-power-law intermolecular potentials, the model can capture the slip and jump coefficients accurately with elegant analytic expressions. On the one hand, the proposed method can apply to the cases of arbitrary order moments with increasing accuracy. On the other hand, the explicit formulae for low-order situations are simpler and more accurate than some existing results in references. Therefore, one may apply these formulae in slip and jump conditions to improve the accuracy of macroscopic fluid dynamic models for gas flows.
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Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it is often hard to interpret the meaning of the latent factors. This paper formally introduces a class of sparse DFMs whereby the loading matrices are constrained to have few non-zero entries, thus increasing interpretability of factors. We present a regularised M-estimator for the model parameters, and construct an efficient expectation maximisation algorithm to enable estimation. Synthetic experiments demonstrate consistency in terms of estimating the loading structure, and superior predictive performance where a low-rank factor structure may be appropriate. The utility of the method is further illustrated in an application forecasting electricity consumption across a large set of smart meters.
Most continual learning (CL) algorithms have focused on tackling the stability-plasticity dilemma, that is, the challenge of preventing the forgetting of previous tasks while learning new ones. However, they have overlooked the impact of the knowledge transfer when the dataset in a certain task is biased - namely, when some unintended spurious correlations of the tasks are learned from the biased dataset. In that case, how would they affect learning future tasks or the knowledge already learned from the past tasks? In this work, we carefully design systematic experiments using one synthetic and two real-world datasets to answer the question from our empirical findings. Specifically, we first show through two-task CL experiments that standard CL methods, which are unaware of dataset bias, can transfer biases from one task to another, both forward and backward, and this transfer is exacerbated depending on whether the CL methods focus on the stability or the plasticity. We then present that the bias transfer also exists and even accumulate in longer sequences of tasks. Finally, we propose a simple, yet strong plug-in method for debiasing-aware continual learning, dubbed as Group-class Balanced Greedy Sampling (BGS). As a result, we show that our BGS can always reduce the bias of a CL model, with a slight loss of CL performance at most.
Semantically coherent out-of-distribution (SCOOD) detection aims to discern outliers from the intended data distribution with access to unlabeled extra set. The coexistence of in-distribution and out-of-distribution samples will exacerbate the model overfitting when no distinction is made. To address this problem, we propose a novel uncertainty-aware optimal transport scheme. Our scheme consists of an energy-based transport (ET) mechanism that estimates the fluctuating cost of uncertainty to promote the assignment of semantic-agnostic representation, and an inter-cluster extension strategy that enhances the discrimination of semantic property among different clusters by widening the corresponding margin distance. Furthermore, a T-energy score is presented to mitigate the magnitude gap between the parallel transport and classifier branches. Extensive experiments on two standard SCOOD benchmarks demonstrate the above-par OOD detection performance, outperforming the state-of-the-art methods by a margin of 27.69% and 34.4% on FPR@95, respectively.
The paper focuses on a new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable velocity-pressure space pairs to Navier-Stokes equations and the N\'ed\'elec's edge element for the magnetic field. The methods have been widely used in various numerical simulations in the last several decades, while the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order N\'ed\'elec's edge approximation in analysis. In terms of a newly modified Maxwell projection we establish new and optimal error estimates. In particular, we prove that the method based on the commonly-used Taylor-Hood/lowest-order N\'ed\'elec's edge element is efficient and the method provides the second-order accuracy for numerical velocity. Two numerical examples for the problem in both convex and nonconvex polygonal domains are presented. Numerical results confirm our theoretical analysis.
Assessing predictive models can be challenging. Modelers must navigate a wide array of evaluation methodologies implemented with incompatible interfaces across multiple packages which may give different or even contradictory results, while ensuring that their chosen approach properly estimates the performance of their model when generalizing to new observations. Assessing models fit to spatial data can be particularly difficult, given that model errors may exhibit spatial autocorrelation, model predictions are often aggregated to multiple spatial scales by end users, and models are often tasked with generalizing into spatial regions outside the boundaries of their initial training data. The waywiser package for the R language attempts to make assessing spatial models easier by providing an ergonomic toolkit for model evaluation tasks, with functions for multiple assessment methodologies sharing a unified interface. Functions from waywiser share standardized argument names and default values, making the user-facing interface simple and easy to learn. These functions are additionally designed to be easy to integrate into a wide variety of modeling workflows, accepting standard classes as inputs and returning size- and type-stable outputs, ensuring that their results are of consistent and predictable data types and dimensions. Additional features make it particularly easy to use waywiser along packages and workflows in the tidymodels ecosystem.
Future astronauts living and working on the Moon will face extreme environmental conditions impeding their operational safety and performance. While it has been suggested that Augmented Reality (AR) Head-Up Displays (HUDs) could potentially help mitigate some of these adversities, the applicability of AR in the unique lunar context remains underexplored. To address this limitation, we have produced an accurate representation of the lunar setting in virtual reality (VR) which then formed our testbed for the exploration of prospective operational scenarios with aerospace experts. Herein we present findings based on qualitative reflections made by the first 6 study participants. AR was found instrumental in several use cases, including the support of navigation and risk awareness. Major design challenges were likewise identified, including the importance of redundancy and contextual appropriateness. Drawing on these findings, we conclude by outlining directions for future research aimed at developing AR-based assistive solutions tailored to the lunar setting.
A class of implicit Milstein type methods is introduced and analyzed in the present article for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By incorporating a pair of method parameters $\theta, \eta \in [0, 1]$ into both the drift and diffusion parts, the new schemes are indeed a kind of drift-diffusion double implicit methods. Within a general framework, we offer upper mean-square error bounds for the proposed schemes, based on certain error terms only getting involved with the exact solution processes. Such error bounds help us to easily analyze mean-square convergence rates of the schemes, without relying on a priori high-order moment estimates of numerical approximations. Putting further globally polynomial growth condition, we successfully recover the expected mean-square convergence rate of order one for the considered schemes with $\theta \in [\tfrac12, 1], \eta \in [0, 1]$. Also, some of the proposed schemes are applied to solve three SDE models evolving in the positive domain $(0, \infty)$. More specifically, the particular drift-diffusion implicit Milstein method ($ \theta = \eta = 1 $) is utilized to approximate the Heston $\tfrac32$-volatility model and the stochastic Lotka-Volterra competition model. The semi-implicit Milstein method ($\theta =1, \eta = 0$) is used to solve the Ait-Sahalia interest rate model. Thanks to the previously obtained error bounds, we reveal the optimal mean-square convergence rate of the positivity preserving schemes under more relaxed conditions, compared with existing relevant results in the literature. Numerical examples are also reported to confirm the previous findings.
This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a temporal discretization algorithm capable of approximating a solution to this initial-boundary value problem. To this end, a symmetric three-layer semi-discrete scheme is employed with respect to the temporal variable, wherein the value of a nonlinear term is evaluated at the middle node point. This approach enables the numerical solutions per temporal step to be obtained by inverting the linear operators, yielding a system of second-order linear ordinary differential equations. Local convergence of the proposed scheme is established, and it achieves quadratic convergence concerning the step size of the discretization of time on the local temporal interval.
With the ever growing number of space debris in orbit, the need to prevent further space population is becoming more and more apparent. Refueling, servicing, inspection and deorbiting of spacecraft are some example missions that require precise navigation and docking in space. Having multiple, collaborating robots handling these tasks can greatly increase the efficiency of the mission in terms of time and cost. This article will introduce a modern and efficient control architecture for satellites on collaborative docking missions. The proposed architecture uses a centralized scheme that combines state-of-the-art, ad-hoc implementations of algorithms and techniques to maximize robustness and flexibility. It is based on a Model Predictive Controller (MPC) for which efficient cost function and constraint sets are designed to ensure a safe and accurate docking. A simulation environment is also presented to validate and test the proposed control scheme.
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