Quad meshes are essential in geometric modeling and computational mechanics. Although learning-based methods for triangle mesh demonstrate considerable advancements, quad mesh generation remains less explored due to the challenge of ensuring coplanarity, convexity, and quad-only meshes. In this paper, we present Point2Quad, the first learning-based method for quad-only mesh generation from point clouds. The key idea is learning to identify quad mesh with fused pointwise and facewise features. Specifically, Point2Quad begins with a k-NN-based candidate generation considering the coplanarity and squareness. Then, two encoders are followed to extract geometric and topological features that address the challenge of quad-related constraints, especially by combining in-depth quadrilaterals-specific characteristics. Subsequently, the extracted features are fused to train the classifier with a designed compound loss. The final results are derived after the refinement by a quad-specific post-processing. Extensive experiments on both clear and noise data demonstrate the effectiveness and superiority of Point2Quad, compared to baseline methods under comprehensive metrics.

Gradient descent based optimization methods are the methods of choice to train deep neural networks in machine learning. Beyond the standard gradient descent method, also suitable modified variants of standard gradient descent involving acceleration techniques such as the momentum method and/or adaptivity techniques such as the RMSprop method are frequently considered optimization methods. These days the most popular of such sophisticated optimization schemes is presumably the Adam optimizer that has been proposed in 2014 by Kingma and Ba. A highly relevant topic of research is to investigate the speed of convergence of such optimization methods. In particular, in 1964 Polyak showed that the standard gradient descent method converges in a neighborhood of a strict local minimizer with rate (x - 1)(x + 1)^{-1} while momentum achieves the (optimal) strictly faster convergence rate (\sqrt{x} - 1)(\sqrt{x} + 1)^{-1} where x \in (1,\infty) is the condition number (the ratio of the largest and the smallest eigenvalue) of the Hessian of the objective function at the local minimizer. It is the key contribution of this work to reveal that Adam also converges with the strictly faster convergence rate (\sqrt{x} - 1)(\sqrt{x} + 1)^{-1} while RMSprop only converges with the convergence rate (x - 1)(x + 1)^{-1}.

An adaptive physics-informed model design strategy for machine-learning interatomic potentials (MLIPs) is proposed. This strategy follows an iterative reconfiguration of composite models from single-term models, followed by a unified training procedure. A model evaluation method based on the Fisher information matrix (FIM) and multiple-property error metrics is proposed to guide model reconfiguration and hyperparameter optimization. Combining the model reconfiguration and the model evaluation subroutines, we provide an adaptive MLIP design strategy that balances flexibility and extensibility. In a case study of designing models against a structurally diverse niobium dataset, we managed to obtain an optimal configuration with 75 parameters generated by our framework that achieved a force RMSE of 0.172 eV/Å and an energy RMSE of 0.013 eV/atom.

This paper introduces a geometric Quaternion-based Unscented Particle Filter for Visual-Inertial Navigation (QUPF-VIN) specifically designed for a vehicle operating with six degrees of freedom (6 DoF). The proposed QUPF-VIN technique is quaternion-based capturing the inherently nonlinear nature of true navigation kinematics. The filter fuses data from a low-cost inertial measurement unit (IMU) and landmark observations obtained via a vision sensor. The QUPF-VIN is implemented in discrete form to ensure seamless integration with onboard inertial sensing systems. Designed for robustness in GPS-denied environments, the proposed method has been validated through experiments with real-world dataset involving an unmanned aerial vehicle (UAV) equipped with a 6-axis IMU and a stereo camera, operating with 6 DoF. The numerical results demonstrate that the QUPF-VIN provides superior tracking accuracy compared to ground truth data. Additionally, a comparative analysis with a standard Kalman filter-based navigation technique further highlights the enhanced performance of the QUPF-VIN.

Accurate localization is a challenging task for autonomous vehicles, particularly in GPS-denied environments such as urban canyons and tunnels. In these scenarios, simultaneous localization and mapping (SLAM) offers a more robust alternative to GPS-based positioning, enabling vehicles to determine their position using onboard sensors and surrounding environment's landmarks. Among various vehicle SLAM approaches, Rao-Blackwellized particle filter (RBPF) stands out as one of the most widely adopted methods due to its efficient solution with logarithmic complexity relative to the map size. RBPF approximates the posterior distribution of the vehicle pose using a set of Monte Carlo particles through two main steps: sampling and importance weighting. The key to effective sampling lies in solving a distribution that closely approximates the posterior, known as the sampling distribution, to accelerate convergence. Existing methods typically derive this distribution via linearization, which introduces significant approximation errors due to the inherent nonlinearity of the system. To address this limitation, we propose a novel vehicle SLAM method called \textit{N}atural Gr\textit{a}dient Gaussia\textit{n} Appr\textit{o}ximation (NANO)-SLAM, which avoids linearization errors by modeling the sampling distribution as the solution to an optimization problem over Gaussian parameters and solving it using natural gradient descent. This approach improves the accuracy of the sampling distribution and consequently enhances localization performance. Experimental results on the long-distance Sydney Victoria Park vehicle SLAM dataset show that NANO-SLAM achieves over 50\% improvement in localization accuracy compared to the most widely used vehicle SLAM algorithms, with minimal additional computational cost.

The electrification of powertrains is rising as the objective for a more viable future is intensified. To ensure continuous and reliable operation without undesirable malfunctions, it is essential to monitor the internal temperatures of machines and keep them within safe operating limits. Conventional modeling methods can be complex and usually require expert knowledge. With the amount of data collected these days, it is possible to use information models to assess thermal behaviors. This paper investigates artificial intelligence techniques for monitoring the cooling efficiency of induction machines. Experimental data was collected under specific operating conditions, and three machine-learning models have been developed. The optimal configuration for each approach was determined through rigorous hyperparameter searches, and the models were evaluated using a variety of metrics. The three solutions performed well in monitoring the condition of the machine even under transient operation, highlighting the potential of data-driven methods in improving the thermal management.

We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions centered at each integer, and (2) normalized weighted sums of sigmoid derivatives representing local densities. The first method approximates the step-like behavior of rounding through differences of shifted sigmoids, while the second method achieves smooth interpolation between integers via density-based weighting. Both methods converge pointwise to the classical rounding function as the sharpness parameter k tends to infinity, and allow controlled trade-offs between smoothness and approximation accuracy. We demonstrate that by restricting the summation to a small set of nearest integers, the computational cost remains low without sacrificing precision. These constructions provide fully differentiable alternatives to hard rounding, which are valuable in contexts where gradient-based methods are essential.

This paper investigates the structural dynamics of stock market volatility through the Financial Chaos Index, a tensor- and eigenvalue-based measure designed to capture realized volatility via mutual fluctuations among asset prices. Motivated by empirical evidence of regime-dependent volatility behavior and perceptual time dilation during financial crises, we develop a regime-switching framework based on the Modified Lognormal Power-Law distribution. Analysis of the FCIX from January 1990 to December 2023 identifies three distinct market regimes, low-chaos, intermediate-chaos, and high-chaos, each characterized by differing levels of systemic stress, statistical dispersion and persistence characteristics. Building upon the segmented regime structure, we further examine the informational forces that shape forward-looking market expectations. Using sentiment-based predictors derived from the Equity Market Volatility tracker, we employ an elastic net regression model to forecast implied volatility, as proxied by the VIX index. Our findings indicate that shifts in macroeconomic, financial, policy, and geopolitical uncertainty exhibit strong predictive power for volatility dynamics across regimes. Together, these results offer a unified empirical perspective on how systemic uncertainty governs both the realized evolution of financial markets and the anticipatory behavior embedded in implied volatility measures.

This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often suffer from oscillatory updates and slow convergence in high-dimensional, noisy landscapes. TFGD addresses these limitations by incorporating a tempered memory mechanism, where historical gradients are weighted by fractional coefficients $|w_j| = \binomα{j}$ and exponentially decayed via a tempering parameter $λ$. Theoretical analysis establishes TFGD's convergence guarantees: in convex settings, it achieves an $\mathcal{O}(1/K)$ rate with alignment coefficient $d_{α,λ} = (1 - e^{-λ})^{-α}$, while stochastic variants attain $\mathcal{O}(1/k^α)$ error decay. The algorithm maintains $\mathcal{O}(n)$ time complexity equivalent to SGD, with memory overhead scaling as $\mathcal{O}(d/λ)$ for parameter dimension $d$. Empirical validation on the Breast Cancer Wisconsin dataset demonstrates TFGD's superiority, achieving 98.25\% test accuracy (vs. 92.11\% for SGD) and 2$\times$ faster convergence. The tempered memory mechanism proves particularly effective in medical classification tasks, where feature correlations benefit from stable gradient averaging. These results position TFGD as a robust alternative to conventional optimizers in both theoretical and applied machine learning.

A BSTRACT We propose PyViT -FUSE, a foundation model for earth observation data explicitly designed to handle multi-modal imagery by learning to fuse an arbitrary number of mixed-resolution input bands into a single representation through an attention mechanism. The learned patch tokens are further processed by a stack of vision transformers with a novel pyramidal structure. We train the model on a globally sampled dataset in a self-supervised manner, leveraging core concepts of the SwA V algorithm. We show the interpretability of the fusion mechanism by visualization of the attention scores and the models applicability to downstream tasks. 1 I NTRODUCTION Foundation models (FM) for earth observations (EO) have gained traction following the success of large language models (LLM) and their demonstration of scaling laws (Kaplan et al., 2020). The premise is that training larger models on vast datasets enhances performance. This idea has been central to computer vision, where datasets like ImageNet (Deng et al., 2009) have enabled pre-training in both supervised and unsupervised settings, leading to breakthroughs in model design and training.