在概述中，引入了通用数学对象（映射），并解释了其与模型物理参数化的关系。引入了可用于模拟和/或近似映射的机器学习（ML）工具。ML的应用在模拟现有参数化，开发新的参数化，确保物理约束和控制开发应用程序的准确性。讨论了一些允许开发人员超越标准参数化范式的ML方法。

The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed laboratory setup with MEMS sensors on a sealed platform with the ability to adjust its tilt angles. To assess the effectiveness of the models, test curves were constructed with different values of the parameters of these models for each core in the case of a linear, polynomial radial basis function. The inverse regularization parameter was used as a parameter. The proposed algorithm based on MO has demonstrated its ability to correctly classify in the presence of noise typical for MEMS sensors, where good classification results were obtained when choosing the optimal values of hyperpa-rameters.

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational inference is now the preferred choice for many high-dimensional models and large datasets. This tutorial introduces variational inference from the parametric perspective that dominates these recent developments, in contrast to the mean-field perspective commonly found in other introductory texts.

Knowledge graphs (KG) have served as the key component of various natural language processing applications. Commonsense knowledge graphs (CKG) are a special type of KG, where entities and relations are composed of free-form text. However, previous works in KG completion and CKG completion suffer from long-tail relations and newly-added relations which do not have many know triples for training. In light of this, few-shot KG completion (FKGC), which requires the strengths of graph representation learning and few-shot learning, has been proposed to challenge the problem of limited annotated data. In this paper, we comprehensively survey previous attempts on such tasks in the form of a series of methods and applications. Specifically, we first introduce FKGC challenges, commonly used KGs, and CKGs. Then we systematically categorize and summarize existing works in terms of the type of KGs and the methods. Finally, we present applications of FKGC models on prediction tasks in different areas and share our thoughts on future research directions of FKGC.

Few Shot Instance Segmentation (FSIS) requires models to detect and segment novel classes with limited several support examples. In this work, we explore a simple yet unified solution for FSIS as well as its incremental variants, and introduce a new framework named Reference Twice (RefT) to fully explore the relationship between support/query features based on a Transformer-like framework. Our key insights are two folds: Firstly, with the aid of support masks, we can generate dynamic class centers more appropriately to re-weight query features. Secondly, we find that support object queries have already encoded key factors after base training. In this way, the query features can be enhanced twice from two aspects, i.e., feature-level and instance-level. In particular, we firstly design a mask-based dynamic weighting module to enhance support features and then propose to link object queries for better calibration via cross-attention. After the above steps, the novel classes can be improved significantly over our strong baseline. Additionally, our new framework can be easily extended to incremental FSIS with minor modification. When benchmarking results on the COCO dataset for FSIS, gFSIS, and iFSIS settings, our method achieves a competitive performance compared to existing approaches across different shots, e.g., we boost nAP by noticeable +8.2/+9.4 over the current state-of-the-art FSIS method for 10/30-shot. We further demonstrate the superiority of our approach on Few Shot Object Detection. Code and model will be available.

Unsupervised domain adaptation (UDA) for semantic segmentation is a promising task freeing people from heavy annotation work. However, domain discrepancies in low-level image statistics and high-level contexts compromise the segmentation performance over the target domain. A key idea to tackle this problem is to perform both image-level and feature-level adaptation jointly. Unfortunately, there is a lack of such unified approaches for UDA tasks in the existing literature. This paper proposes a novel UDA pipeline for semantic segmentation that unifies image-level and feature-level adaptation. Concretely, for image-level domain shifts, we propose a global photometric alignment module and a global texture alignment module that align images in the source and target domains in terms of image-level properties. For feature-level domain shifts, we perform global manifold alignment by projecting pixel features from both domains onto the feature manifold of the source domain; and we further regularize category centers in the source domain through a category-oriented triplet loss and perform target domain consistency regularization over augmented target domain images. Experimental results demonstrate that our pipeline significantly outperforms previous methods. In the commonly tested GTA5$\rightarrow$Cityscapes task, our proposed method using Deeplab V3+ as the backbone surpasses previous SOTA by 8%, achieving 58.2% in mIoU.

The development of social media user stance detection and bot detection methods rely heavily on large-scale and high-quality benchmarks. However, in addition to low annotation quality, existing benchmarks generally have incomplete user relationships, suppressing graph-based account detection research. To address these issues, we propose a Multi-Relational Graph-Based Twitter Account Detection Benchmark (MGTAB), the first standardized graph-based benchmark for account detection. To our knowledge, MGTAB was built based on the largest original data in the field, with over 1.55 million users and 130 million tweets. MGTAB contains 10,199 expert-annotated users and 7 types of relationships, ensuring high-quality annotation and diversified relations. In MGTAB, we extracted the 20 user property features with the greatest information gain and user tweet features as the user features. In addition, we performed a thorough evaluation of MGTAB and other public datasets. Our experiments found that graph-based approaches are generally more effective than feature-based approaches and perform better when introducing multiple relations. By analyzing experiment results, we identify effective approaches for account detection and provide potential future research directions in this field. Our benchmark and standardized evaluation procedures are freely available at: https://github.com/GraphDetec/MGTAB.

The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.

Designing experiments often requires balancing between learning about the true treatment effects and earning from allocating more samples to the superior treatment. While optimal algorithms for the Multi-Armed Bandit Problem (MABP) provide allocation policies that optimally balance learning and earning, they tend to be computationally expensive. The Gittins Index (GI) is a solution to the MABP that can simultaneously attain optimality and computationally efficiency goals, and it has been recently used in experiments with Bernoulli and Gaussian rewards. For the first time, we present a modification of the GI rule that can be used in experiments with exponentially-distributed rewards. We report its performance in simulated 2- armed and 3-armed experiments. Compared to traditional non-adaptive designs, our novel GI modified design shows operating characteristics comparable in learning (e.g. statistical power) but substantially better in earning (e.g. direct benefits). This illustrates the potential that designs using a GI approach to allocate participants have to improve participant benefits, increase efficiencies, and reduce experimental costs in adaptive multi-armed experiments with exponential rewards.

Given the increasingly intricate forms of partial differential equations (PDEs) in physics and related fields, computationally solving PDEs without analytic solutions inevitably suffers from the trade-off between accuracy and efficiency. Recent advances in neural operators, a kind of mesh-independent neural-network-based PDE solvers, have suggested the dawn of overcoming this challenge. In this emerging direction, Koopman neural operator (KNO) is a representative demonstration and outperforms other state-of-the-art alternatives in terms of accuracy and efficiency. Here we present KoopmanLab, a self-contained and user-friendly PyTorch module of the Koopman neural operator family for solving partial differential equations. Beyond the original version of KNO, we develop multiple new variants of KNO based on different neural network architectures to improve the general applicability of our module. These variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier-Stokes equation and the Bateman-Burgers equation) and ERA5 (i.e., one of the largest high-resolution data sets of global-scale climate fields). These demonstrations suggest the potential of KoopmanLab to be considered in diverse applications of partial differential equations.