HNS: An Efficient Hermite Neural Solver for Solving Time-Fractional Partial Differential Equations

Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for addressing time-fractional derivatives within neural network solvers. However, we have discovered that neural network solvers based on L1 interpolation approximation are unable to fully exploit the benefits of neural networks, and the accuracy of these models is constrained to interpolation errors. In this paper, we present the high-precision Hermite Neural Solver (HNS) for solving time-fractional partial differential equations. Specifically, we first construct a high-order explicit approximation scheme for fractional derivatives using Hermite interpolation techniques, and rigorously analyze its approximation accuracy. Afterward, taking into account the infinitely differentiable properties of deep neural networks, we integrate the high-order Hermite interpolation explicit approximation scheme with deep neural networks to propose the HNS. The experimental results show that HNS achieves higher accuracy than methods based on the L1 scheme for both forward and inverse problems, as well as in high-dimensional scenarios. This indicates that HNS has significantly improved accuracy and flexibility compared to existing L1-based methods, and has overcome the limitations of explicit finite difference approximation methods that are often constrained to function value interpolation. As a result, the HNS is not a simple combination of numerical computing methods and neural networks, but rather achieves a complementary and mutually reinforcing advantages of both approaches. The data and code can be found at \url{https://github.com/hsbhc/HNS}.

The Analysis and Extraction of Structure from Organizational Charts

Organizational charts, also known as org charts, are critical representations of an organization's structure and the hierarchical relationships between its components and positions. However, manually extracting information from org charts can be error-prone and time-consuming. To solve this, we present an automated and end-to-end approach that uses computer vision, deep learning, and natural language processing techniques. Additionally, we propose a metric to evaluate the completeness and hierarchical accuracy of the extracted information. This approach has the potential to improve organizational restructuring and resource utilization by providing a clear and concise representation of the organizational structure. Our study lays a foundation for further research on the topic of hierarchical chart analysis.

Retargeting video with an end-to-end framework

Video holds significance in computer graphics applications. Because of the heterogeneous of digital devices, retargeting videos becomes an essential function to enhance user viewing experience in such applications. In the research of video retargeting, preserving the relevant visual content in videos, avoiding flicking, and processing time are the vital challenges. Extending image retargeting techniques to the video domain is challenging due to the high running time. Prior work of video retargeting mainly utilizes time-consuming preprocessing to analyze frames. Plus, being tolerant of different video content, avoiding important objects from shrinking, and the ability to play with arbitrary ratios are the limitations that need to be resolved in these systems requiring investigation. In this paper, we present an end-to-end RETVI method to retarget videos to arbitrary aspect ratios. We eliminate the computational bottleneck in the conventional approaches by designing RETVI with two modules, content feature analyzer (CFA) and adaptive deforming estimator (ADE). The extensive experiments and evaluations show that our system outperforms previous work in quality and running time. Visit our project website for more results at $\href{http://graphics.csie.ncku.edu.tw/RETVI}{http://graphics.csie.ncku.edu.tw/RETVI}$.

Toward Robust Recommendation via Real-time Vicinal Defense

Recommender systems have been shown to be vulnerable to poisoning attacks, where malicious data is injected into the dataset to cause the recommender system to provide biased recommendations. To defend against such attacks, various robust learning methods have been proposed. However, most methods are model-specific or attack-specific, making them lack generality, while other methods, such as adversarial training, are oriented towards evasion attacks and thus have a weak defense strength in poisoning attacks. In this paper, we propose a general method, Real-time Vicinal Defense (RVD), which leverages neighboring training data to fine-tune the model before making a recommendation for each user. RVD works in the inference phase to ensure the robustness of the specific sample in real-time, so there is no need to change the model structure and training process, making it more practical. Extensive experimental results demonstrate that RVD effectively mitigates targeted poisoning attacks across various models without sacrificing accuracy. Moreover, the defensive effect can be further amplified when our method is combined with other strategies.

Inexpensive High Fidelity Melt Pool Models in Additive Manufacturing Using Generative Deep Diffusion

Defects in laser powder bed fusion (L-PBF) parts often result from the meso-scale dynamics of the molten alloy near the laser, known as the melt pool. For instance, the melt pool can directly contribute to the formation of undesirable porosity, residual stress, and surface roughness in the final part. Experimental in-situ monitoring of the three-dimensional melt pool physical fields is challenging, due to the short length and time scales involved in the process. Multi-physics simulation methods can describe the three-dimensional dynamics of the melt pool, but are computationally expensive at the mesh refinement required for accurate predictions of complex effects, such as the formation of keyhole porosity. Therefore, in this work, we develop a generative deep learning model based on the probabilistic diffusion framework to map low-fidelity, coarse-grained simulation information to the high-fidelity counterpart. By doing so, we bypass the computational expense of conducting multiple high-fidelity simulations for analysis by instead upscaling lightweight coarse mesh simulations. Specifically, we implement a 2-D diffusion model to spatially upscale cross-sections of the coarsely simulated melt pool to their high-fidelity equivalent. We demonstrate the preservation of key metrics of the melting process between the ground truth simulation data and the diffusion model output, such as the temperature field, the melt pool dimensions and the variability of the keyhole vapor cavity. Specifically, we predict the melt pool depth within 3 $\mu m$ based on low-fidelity input data 4$\times$ coarser than the high-fidelity simulations, reducing analysis time by two orders of magnitude.

Clustering Techniques for Stable Linear Dynamical Systems with applications to Hard Disk Drives

In Robust Control and Data Driven Robust Control design methodologies, multiple plant transfer functions or a family of transfer functions are considered and a common controller is designed such that all the plants that fall into this family are stabilized. Though the plants are stabilized, the controller might be sub-optimal for each of the plants when the variations in the plants are large. This paper presents a way of clustering stable linear dynamical systems for the design of robust controllers within each of the clusters such that the controllers are optimal for each of the clusters. First a k-medoids algorithm for hard clustering will be presented for stable Linear Time Invariant (LTI) systems and then a Gaussian Mixture Models (GMM) clustering for a special class of LTI systems, common for Hard Disk Drive plants, will be presented.

Informative Priors Improve the Reliability of Multimodal Clinical Data Classification

Machine learning-aided clinical decision support has the potential to significantly improve patient care. However, existing efforts in this domain for principled quantification of uncertainty have largely been limited to applications of ad-hoc solutions that do not consistently improve reliability. In this work, we consider stochastic neural networks and design a tailor-made multimodal data-driven (M2D2) prior distribution over network parameters. We use simple and scalable Gaussian mean-field variational inference to train a Bayesian neural network using the M2D2 prior. We train and evaluate the proposed approach using clinical time-series data in MIMIC-IV and corresponding chest X-ray images in MIMIC-CXR for the classification of acute care conditions. Our empirical results show that the proposed method produces a more reliable predictive model compared to deterministic and Bayesian neural network baselines.

Mobile-Seed: Joint Semantic Segmentation and Boundary Detection for Mobile Robots

Precise and rapid delineation of sharp boundaries and robust semantics is essential for numerous downstream robotic tasks, such as robot grasping and manipulation, real-time semantic mapping, and online sensor calibration performed on edge computing units. Although boundary detection and semantic segmentation are complementary tasks, most studies focus on lightweight models for semantic segmentation but overlook the critical role of boundary detection. In this work, we introduce Mobile-Seed, a lightweight, dual-task framework tailored for simultaneous semantic segmentation and boundary detection. Our framework features a two-stream encoder, an active fusion decoder (AFD) and a dual-task regularization approach. The encoder is divided into two pathways: one captures category-aware semantic information, while the other discerns boundaries from multi-scale features. The AFD module dynamically adapts the fusion of semantic and boundary information by learning channel-wise relationships, allowing for precise weight assignment of each channel. Furthermore, we introduce a regularization loss to mitigate the conflicts in dual-task learning and deep diversity supervision. Compared to existing methods, the proposed Mobile-Seed offers a lightweight framework to simultaneously improve semantic segmentation performance and accurately locate object boundaries. Experiments on the Cityscapes dataset have shown that Mobile-Seed achieves notable improvement over the state-of-the-art (SOTA) baseline by 2.2 percentage points (pp) in mIoU and 4.2 pp in mF-score, while maintaining an online inference speed of 23.9 frames-per-second (FPS) with 1024x2048 resolution input on an RTX 2080 Ti GPU. Additional experiments on CamVid and PASCAL Context datasets confirm our method's generalizability. Code and additional results are publicly available at \url{https://martin-liao.github.io/Mobile-Seed/}.

Neural Approximate Dynamic Programming for the Ultra-fast Order Dispatching Problem

Same-Day Delivery (SDD) services aim to maximize the fulfillment of online orders while minimizing delivery delays but are beset by operational uncertainties such as those in order volumes and courier planning. Our work aims to enhance the operational efficiency of SDD by focusing on the ultra-fast Order Dispatching Problem (ODP), which involves matching and dispatching orders to couriers within a centralized warehouse setting, and completing the delivery within a strict timeline (e.g., within minutes). We introduce important extensions to ultra-fast ODP such as order batching and explicit courier assignments to provide a more realistic representation of dispatching operations and improve delivery efficiency. As a solution method, we primarily focus on NeurADP, a methodology that combines Approximate Dynamic Programming (ADP) and Deep Reinforcement Learning (DRL), and our work constitutes the first application of NeurADP outside of the ride-pool matching problem. NeurADP is particularly suitable for ultra-fast ODP as it addresses complex one-to-many matching and routing intricacies through a neural network-based VFA that captures high-dimensional problem dynamics without requiring manual feature engineering as in generic ADP methods. We test our proposed approach using four distinct realistic datasets tailored for ODP and compare the performance of NeurADP against myopic and DRL baselines by also making use of non-trivial bounds to assess the quality of the policies. Our numerical results indicate that the inclusion of order batching and courier queues enhances the efficiency of delivery operations and that NeurADP significantly outperforms other methods. Detailed sensitivity analysis with important parameters confirms the robustness of NeurADP under different scenarios, including variations in courier numbers, spatial setup, vehicle capacity, and permitted delay time.

Neural Structure Learning with Stochastic Differential Equations

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.