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Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence of cracks that take the form of one or many pieces of surface (with boundary). When the background medium can be considered as homogeneous, boundary integral equations appear as a method of choice for the numerical solution to fractures problems. With such an approach, the problem is reformulated as a fully non-local equation posed at the surface of cracks. Discretization of boundary integral resulting in the so-called Boundary Element Method (BEM) leads to densely populated matrices due to the full non-locality of the operators under consideration. After the discretization process, geologists are faced with a system of equations that turns out difficult to solve numerically. Many empirical algorithms have been proposed by geologists to solve this system of equations. Unfortunately, none of them is guaranteed to converge in theory (in particular when faults (fractures) intersect each other forming a geometrically highly irregular structure). In practice, none of them appears to be either robust or efficient. We investigate another approach, referred to as interior point methods, for which convergence can be ensured (even if faults are too close). Interior point methods have proved their efficiency in a wide variety of domains, most notably for linear programming. Here, even though we do not have any optimization problem, we can adapt ideas from interior point methods for the numerical resolution of the system considered. The numerical results obtained demonstrate computational efficiency and accuracy, highlighting the robustness and effectiveness of the implemented methods.

This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods can suffer from order reduction when applied to linearized problems involving unbounded and non-commuting operators. In this work, we consider a fourth-stage third-order Runge--Kutta method, which successfully achieves the expected order of accuracy and avoids order reduction, as long as all required order conditions are satisfied. The convergence analysis is carried out under the assumption of higher regularity for the initial data. Numerical experiments are provided to validate the theoretical results., Comment: 16 pages, 2 figures

Test-time adaptation (TTA) has emerged as a promising solution to tackle the continual domain shift in machine learning by allowing model parameters to change at test time, via self-supervised learning on unlabeled testing data. At the same time, it unfortunately opens the door to unforeseen vulnerabilities for degradation over time. Through a simple theoretical continual TTA model, we successfully identify a risk in the sampling process of testing data that could easily degrade the performance of a continual TTA model. We name this risk as Reusing of Incorrect Prediction (RIP) that TTA attackers can employ or as a result of the unintended query from general TTA users. The risk posed by RIP is also highly realistic, as it does not require prior knowledge of model parameters or modification of testing samples. This simple requirement makes RIP as the first black-box TTA attack algorithm that stands out from existing white-box attempts. We extensively benchmark the performance of the most recent continual TTA approaches when facing the RIP attack, providing insights on its success, and laying out potential roadmaps that could enhance the resilience of future continual TTA systems.

In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context, we compare Leja and Krylov based methods to compute the action of exponential and related matrix functions. We set up a performance model by counting the different operations needed to implement the considered algorithms. This model assumes that the evaluation of the right-hand side is memory bound and allows us to evaluate performance in a hardware independent way. We find that exponential integrators perform comparably to explicit Runge-Kutta schemes for problems that are advection dominated in the entire domain. Moreover, they are able to outperform explicit methods in situations where small parts of the domain are diffusion dominated. We generally observe that Leja based methods outperform Krylov iterations in the problems considered. This is in particular true if computing inner products is expensive.

Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently gained attention for handling stiff differential equations. This paper explores exponential Runge--Kutta methods for solving such equations, focusing on the simplified form $u^{\prime}(t)+A u(t)=B u(t)$, where $A$ generates an analytic semigroup and $B$ is relatively bounded with respect to $A$. By treating $A$ exactly and $B$ explicitly, we derive error bounds for exponential Runge--Kutta methods up to third order. Our analysis shows that these methods maintain their order under mild regularity conditions on the initial data $u_0$, while also addressing the phenomenon of order reduction in higher-order methods. Through a careful convergence analysis and numerical investigations, this study provides a comprehensive understanding of the applicability and limitations of exponential Runge--Kutta methods in solving linear parabolic equations involving two unbounded and non-commuting operators., Comment: 25 pages, 4 figures

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function evaluations (NFE) to transform Gaussian noise samples into images, resulting in higher computational costs compared to single-step generative models such as GANs or VAEs. Therefore, reducing the number of NFEs while preserving generation quality is crucial. To address this, we propose LD3, a lightweight framework designed to learn the optimal time discretization for sampling. LD3 can be combined with various samplers and consistently improves generation quality without having to retrain resource-intensive neural networks. We demonstrate analytically and empirically that LD3 improves sampling efficiency with much less computational overhead. We evaluate our method with extensive experiments on 7 pre-trained models, covering unconditional and conditional sampling in both pixel-space and latent-space DPMs. We achieve FIDs of 2.38 (10 NFE), and 2.27 (10 NFE) on unconditional CIFAR10 and AFHQv2 in 5-10 minutes of training. LD3 offers an efficient approach to sampling from pre-trained diffusion models. Code is available at https://github.com/vinhsuhi/LD3/tree/main.

Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach., Comment: 14 pages, 6 figures

This paper considers a class of noncoercive nonlinear elliptic problems with coefficients defined in Marcinkiewicz and Lorentz spaces. We prove the existence of a solution for the corresponding Dirichlet problem and investigate the higher integrability properties of the solution., Comment: 13 pages

Work related musculoskeletal disorders (WMSDs) are often caused by repetitive lifting, making them a significant concern in occupational health. Although wearable assist devices have become the norm for mitigating the risk of back pain, most spinal assist devices still possess a partially rigid structure that impacts the user comfort and flexibility. This paper addresses this issue by presenting a smart textile actuated spine assistance robotic exosuit (SARE), which can conform to the back seamlessly without impeding the user movement and is incredibly lightweight. The SARE can assist the human erector spinae to complete any action with virtually infinite degrees of freedom. To detect the strain on the spine and to control the smart textile automatically, a soft knitting sensor which utilizes fluid pressure as sensing element is used. The new device is validated experimentally with human subjects where it reduces peak electromyography (EMG) signals of lumbar erector spinae by around 32 percent in loaded and around 22 percent in unloaded conditions. Moreover, the integrated EMG decreased by around 24.2 percent under loaded condition and around 23.6 percent under unloaded condition. In summary, the artificial muscle wearable device represents an anatomical solution to reduce the risk of muscle strain, metabolic energy cost and back pain associated with repetitive lifting tasks., Comment: 6 pages, 7 figures

Facilitating large-scale, cross-institutional collaboration in biomedical machine learning projects requires a trustworthy and resilient federated learning (FL) environment to ensure that sensitive information such as protected health information is kept confidential. In this work, we introduce APPFLx, a low-code FL framework that enables the easy setup, configuration, and running of FL experiments across organizational and administrative boundaries while providing secure end-to-end communication, privacy-preserving functionality, and identity management. APPFLx is completely agnostic to the underlying computational infrastructure of participating clients. We demonstrate the capability of APPFLx as an easy-to-use framework for accelerating biomedical studies across institutions and healthcare systems while maintaining the protection of private medical data in two case studies: (1) predicting participant age from electrocardiogram (ECG) waveforms, and (2) detecting COVID-19 disease from chest radiographs. These experiments were performed securely across heterogeneous compute resources, including a mixture of on-premise high-performance computing and cloud computing, and highlight the role of federated learning in improving model generalizability and performance when aggregating data from multiple healthcare systems. Finally, we demonstrate that APPFLx serves as a convenient and easy-to-use framework for accelerating biomedical studies across institutions and healthcare system while maintaining the protection of private medical data.

Despite the promising performance of current 3D human pose estimation techniques, understanding and enhancing their generalization on challenging in-the-wild videos remain an open problem. In this work, we focus on the robustness of 2D-to-3D pose lifters. To this end, we develop two benchmark datasets, namely Human3.6M-C and HumanEva-I-C, to examine the robustness of video-based 3D pose lifters to a wide range of common video corruptions including temporary occlusion, motion blur, and pixel-level noise. We observe the poor generalization of state-of-the-art 3D pose lifters in the presence of corruption and establish two techniques to tackle this issue. First, we introduce Temporal Additive Gaussian Noise (TAGN) as a simple yet effective 2D input pose data augmentation. Additionally, to incorporate the confidence scores output by the 2D pose detectors, we design a confidence-aware convolution (CA-Conv) block. Extensively tested on corrupted videos, the proposed strategies consistently boost the robustness of 3D pose lifters and serve as new baselines for future research.

Current test-time adaptation (TTA) approaches aim to adapt a machine learning model to environments that change continuously. Yet, it is unclear whether TTA methods can maintain their adaptability over prolonged periods. To answer this question, we introduce a diagnostic setting - recurring TTA where environments not only change but also recur over time, creating an extensive data stream. This setting allows us to examine the error accumulation of TTA models, in the most basic scenario, when they are regularly exposed to previous testing environments. Furthermore, we simulate a TTA process on a simple yet representative $\epsilon$-perturbed Gaussian Mixture Model Classifier, deriving theoretical insights into the dataset- and algorithm-dependent factors contributing to gradual performance degradation. Our investigation leads us to propose persistent TTA (PeTTA), which senses when the model is diverging towards collapse and adjusts the adaptation strategy, striking a balance between the dual objectives of adaptation and model collapse prevention. The supreme stability of PeTTA over existing approaches, in the face of lifelong TTA scenarios, has been demonstrated over comprehensive experiments on various benchmarks. Our project page is available at https://hthieu166.github.io/petta., Comment: Accepted to the 38th Conference on Neural Information Processing Systems (NeurIPS 2024)

This paper presents a knowledge graph construction method for legal case documents and related laws, aiming to organize legal information efficiently and enhance various downstream tasks. Our approach consists of three main steps: data crawling, information extraction, and knowledge graph deployment. First, the data crawler collects a large corpus of legal case documents and related laws from various sources, providing a rich database for further processing. Next, the information extraction step employs natural language processing techniques to extract entities such as courts, cases, domains, and laws, as well as their relationships from the unstructured text. Finally, the knowledge graph is deployed, connecting these entities based on their extracted relationships, creating a heterogeneous graph that effectively represents legal information and caters to users such as lawyers, judges, and scholars. The established baseline model leverages unsupervised learning methods, and by incorporating the knowledge graph, it demonstrates the ability to identify relevant laws for a given legal case. This approach opens up opportunities for various applications in the legal domain, such as legal case analysis, legal recommendation, and decision support., Comment: ISAILD@KSE 2023

In recent years, natural language processing has gained significant popularity in various sectors, including the legal domain. This paper presents NeCo Team's solutions to the Vietnamese text processing tasks provided in the Automated Legal Question Answering Competition 2023 (ALQAC 2023), focusing on legal domain knowledge acquisition for low-resource languages through data enrichment. Our methods for the legal document retrieval task employ a combination of similarity ranking and deep learning models, while for the second task, which requires extracting an answer from a relevant legal article in response to a question, we propose a range of adaptive techniques to handle different question types. Our approaches achieve outstanding results on both tasks of the competition, demonstrating the potential benefits and effectiveness of question answering systems in the legal field, particularly for low-resource languages., Comment: ISAILD@KSE 2023

Cross-silo privacy-preserving federated learning (PPFL) is a powerful tool to collaboratively train robust and generalized machine learning (ML) models without sharing sensitive (e.g., healthcare of financial) local data. To ease and accelerate the adoption of PPFL, we introduce APPFLx, a ready-to-use platform that provides privacy-preserving cross-silo federated learning as a service. APPFLx employs Globus authentication to allow users to easily and securely invite trustworthy collaborators for PPFL, implements several synchronous and asynchronous FL algorithms, streamlines the FL experiment launch process, and enables tracking and visualizing the life cycle of FL experiments, allowing domain experts and ML practitioners to easily orchestrate and evaluate cross-silo FL under one platform. APPFLx is available online at https://appflx.link

This paper presents the NOWJ team's approach to the COLIEE 2023 Competition, which focuses on advancing legal information processing techniques and applying them to real-world legal scenarios. Our team tackles the four tasks in the competition, which involve legal case retrieval, legal case entailment, statute law retrieval, and legal textual entailment. We employ state-of-the-art machine learning models and innovative approaches, such as BERT, Longformer, BM25-ranking algorithm, and multi-task learning models. Although our team did not achieve state-of-the-art results, our findings provide valuable insights and pave the way for future improvements in legal information processing., Comment: COLIEE 2023

Multi-document summarization is challenging because the summaries should not only describe the most important information from all documents but also provide a coherent interpretation of the documents. This paper proposes a method for multi-document summarization based on cluster similarity. In the extractive method we use hybrid model based on a modified version of the PageRank algorithm and a text correlation considerations mechanism. After generating summaries by selecting the most important sentences from each cluster, we apply BARTpho and ViT5 to construct the abstractive models. Both extractive and abstractive approaches were considered in this study. The proposed method achieves competitive results in VLSP 2022 competition., Comment: In Proceedings of the 9th International Workshop on Vietnamese Language and Speech Processing (VLSP 2022)

The ability to use digitally recorded and quantified neurological exam information is important to help healthcare systems deliver better care, in-person and via telehealth, as they compensate for a growing shortage of neurologists. Current neurological digital biomarker pipelines, however, are narrowed down to a specific neurological exam component or applied for assessing specific conditions. In this paper, we propose an accessible vision-based exam and documentation solution called Digitized Neurological Examination (DNE) to expand exam biomarker recording options and clinical applications using a smartphone/tablet. Through our DNE software, healthcare providers in clinical settings and people at home are enabled to video capture an examination while performing instructed neurological tests, including finger tapping, finger to finger, forearm roll, and stand-up and walk. Our modular design of the DNE software supports integrations of additional tests. The DNE extracts from the recorded examinations the 2D/3D human-body pose and quantifies kinematic and spatio-temporal features. The features are clinically relevant and allow clinicians to document and observe the quantified movements and the changes of these metrics over time. A web server and a user interface for recordings viewing and feature visualizations are available. DNE was evaluated on a collected dataset of 21 subjects containing normal and simulated-impaired movements. The overall accuracy of DNE is demonstrated by classifying the recorded movements using various machine learning models. Our tests show an accuracy beyond 90% for upper-limb tests and 80% for the stand-up and walk tests.

A new control approach is proposed for the grid insertion of Power Park Modules (PPMs). It allows full participation of these modules to ancillary services. This means that, not only their control have some positive impact on the grid frequency and voltage dynamics, but they can effectively participate to existing primary and secondary control loops together with the classic thermal/inertia synchronous generators and fulfill the same specifications both from the control and contractual points of view. To achieve such level of performances, a system approach based on an innovatory control model is proposed. The latter control model drops classic hypothesis for separation of voltage and frequency dynamics used till now in order to gather these dynamics into a small size model. From the system point of view, dynamics are grouped by time-scales of phenomena in the proposed control model. This results in more performant controls in comparison to classic approaches which orient controls to physical actuators (control of grid side converter and of generator side converter). Also, this allows coordination between control of converters and generator or, in case of multimachines specifications, among several PPMs. From the control synthesis point of view, classic robust approaches are used (like, e.g., H-infinity synthesis). Implementation and validation tests are presented for wind PPMs but the approach holds for any other type of PPM. These results will be further used to control the units of the new concept of Dynamic Virtual Power Plant introduced in the H2020 POSYTYF project.