arXiv subjects

Tianyi Shi

Publications and source records attributed to Tianyi Shi.

13 recordsLinked to original sources

arXiv2026

Distributed Trajectory Planning and Resource Allocation for Dynamic Multi-UAV Collaborative Computing

This paper investigates a multiple uncrewed aerial vehicles (UAVs)-enabled distributed mobile edge computing (MEC) framework, where the set of collaborative UAVs dynamically varies over time due to their energy states and service loads. The joint optimization of trajectory planning and resource allocation is formulated as a Stackelberg game, where UAVs and mobile terminals (MTs) are modeled as leaders and followers, respectively. UAVs aim to maximize their benefits by balancing executed workload, energy cost, and resource allocation revenue, while MTs seek to minimize their total overhead, composed of computing delay and resource costs, through offloading and resource-request decisions. A hierarchical joint optimization algorithm is developed within a multi-agent deep reinforcement learning (MADRL) framework to coordinate UAVs and MTs in a distributed manner. At the leader level, UAVs jointly determine their trajectories, task migration ratios, MT-UAV association, and unit computing resource pricing. Each UAV is modeled as an agent in a partially observable Markov decision process, and the agents are jointly trained via multi-agent proximal policy optimization (MAPPO) under the centralized-training-and-decentralized-execution paradigm. At the follower level, MTs determine their optimal task offloading ratios and requested computing resources using a two-stage iterative algorithm. Simulation results demonstrate stable convergence under dynamic UAV participation. Compared to the no-collaboration benchmark, the proposed algorithm improves UAV efficiency by 18.58% through inter-UAV task migration and reduces average MT overhead by 33.77% over the fully offloading scheme. It also outperforms other benchmarks under varying network scales and capabilities by jointly optimizing UAV operations and resource utilization.

cs.NI↗

arXiv2026

An Efficient and Robust Projection Enhanced Interpolation Based Tensor Train Decomposition

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low rank approximations. However, these methods might still suffer from accuracy degeneracy, nonrobustness, and high computation costs. In this paper, given existing skeletonized TT approximations, we propose a family of projection enhanced interpolation based algorithms to further improve approximation accuracy while keeping low computational complexity. We do this as a postprocessing step to existing interpolative decompositions, via oversampling data not in skeletons to include more information and selecting subsets of pivots for faster projections. We illustrate the performances of our proposed methods with extensive numerical experiments. These include up to 10D synthetic datasets such as tensors generated from kernel functions, and tensors constructed from Maxwellian distribution functions that arise in kinetic theory. Our results demonstrate significant accuracy improvement over original skeletonized TT approximations, while using limited amount of computational resources.

math.NA↗

arXiv2025

OLMA: One Loss for More Accurate Time Series Forecasting

Time series forecasting faces two important but often overlooked challenges. Firstly, the inherent random noise in the time series labels sets a theoretical lower bound for the forecasting error, which is positively correlated with the entropy of the labels. Secondly, neural networks exhibit a frequency bias when modeling the state-space of time series, that is, the model performs well in learning certain frequency bands but poorly in others, thus restricting the overall forecasting performance. To address the first challenge, we prove a theorem that there exists a unitary transformation that can reduce the marginal entropy of multiple correlated Gaussian processes, thereby providing guidance for reducing the lower bound of forecasting error. Furthermore, experiments confirm that Discrete Fourier Transform (DFT) can reduce the entropy in the majority of scenarios. Correspondingly, to alleviate the frequency bias, we jointly introduce supervision in the frequency domain along the temporal dimension through DFT and Discrete Wavelet Transform (DWT). This supervision-side strategy is highly general and can be seamlessly integrated into any supervised learning method. Moreover, we propose a novel loss function named OLMA, which utilizes the frequency domain transformation across both channel and temporal dimensions to enhance forecasting. Finally, the experimental results on multiple datasets demonstrate the effectiveness of OLMA in addressing the above two challenges and the resulting improvement in forecasting accuracy. The results also indicate that the perspectives of entropy and frequency bias provide a new and feasible research direction for time series forecasting. The code is available at: https://github.com/Yuyun1011/OLMA-One-Loss-for-More-Accurate-Time-Series-Forecasting.

cs.LG↗

arXiv2025

Joint Task Offloading and Channel Allocation in Spatial-Temporal Dynamic for MEC Networks

Computation offloading and resource allocation are critical in mobile edge computing (MEC) systems to handle the massive and complex requirements of applications restricted by limited resources. In a multi-user multi-server MEC network, the mobility of terminals causes computing requests to be dynamically distributed in space. At the same time, the non-negligible dependencies among tasks in some specific applications impose temporal correlation constraints on the solution as well, leading the time-adjacent tasks to experience varying resource availability and competition from parallel counterparts. To address such dynamic spatial-temporal characteristics as a challenge in the allocation of communication and computation resources, we formulate a long-term delay-energy trade-off cost minimization problem in the view of jointly optimizing task offloading and resource allocation. We begin by designing a priority evaluation scheme to decouple task dependencies and then develop a grouped Knapsack problem for channel allocation considering the current data load and channel status. Afterward, in order to meet the rapid response needs of MEC systems, we exploit the double duel deep Q network (D3QN) to make offloading decisions and integrate channel allocation results into the reward as part of the dynamic environment feedback in D3QN, constituting the joint optimization of task offloading and channel allocation. Finally, comprehensive simulations demonstrate the performance of the proposed algorithm in the delay-energy trade-off cost and its adaptability for various applications.

cs.NI↗

arXiv2024

A Linear-complexity Tensor Butterfly Algorithm for Compressing High-dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels, and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a $d$-dimensional integral operator discretized into a $2d$-mode tensor with $n^{2d}$ entries, the overall CPU time and memory requirement scale as $O(n^d)$, in stark contrast to the $O(n^d\log n)$ requirement of existing matrix algorithms such as matrix butterfly algorithm and fast Fourier transforms (FFT), where $n$ is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents over $512\times$ larger problem sizes than existing butterfly algorithms. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and $30\times$ memory reduction comparing with existing ones. Moreover, the tensor butterfly algorithm also permits $O(n^d)$-complexity FFTs and Radon transforms up to $d=6$ dimensions.

math.NA↗

arXiv2024

Distributed memory parallel adaptive tensor-train cross approximation

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have been proposed for different tensor inputs and assumptions. In this paper, we propose subtensor parallel adaptive TT cross, which partitions a tensor onto distributed memory machines with multidimensional process grids, and constructs an TT approximation iteratively with tensor elements. We derive two iterative formulations for pivot selection and TT core construction under the distributed memory setting, conduct communication and scaling analysis of the algorithm, and illustrate its performance with multiple test experiments. These include up to 6D Hilbert tensors and tensors constructed from Maxwellian distribution functions that arise in kinetic theory. Our results demonstrate significant accuracy with greatly reduced storage requirements via the TT cross approximation. Furthermore, we demonstrate good to optimal strong and weak scaling performance for the proposed parallel algorithm.

math.NA↗

arXiv2023

FreeCOS: Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation

Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method that learns robust and distinctive features from fractals and unlabeled images (FreeCOS). The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS.

cs.CV↗

arXiv2023

Affinity Feature Strengthening for Accurate, Complete and Robust Vessel Segmentation

Vessel segmentation is crucial in many medical image applications, such as detecting coronary stenoses, retinal vessel diseases and brain aneurysms. However, achieving high pixel-wise accuracy, complete topology structure and robustness to various contrast variations are critical and challenging, and most existing methods focus only on achieving one or two of these aspects. In this paper, we present a novel approach, the affinity feature strengthening network (AFN), which jointly models geometry and refines pixel-wise segmentation features using a contrast-insensitive, multiscale affinity approach. Specifically, we compute a multiscale affinity field for each pixel, capturing its semantic relationships with neighboring pixels in the predicted mask image. This field represents the local geometry of vessel segments of different sizes, allowing us to learn spatial- and scale-aware adaptive weights to strengthen vessel features. We evaluate our AFN on four different types of vascular datasets: X-ray angiography coronary vessel dataset (XCAD), portal vein dataset (PV), digital subtraction angiography cerebrovascular vessel dataset (DSA) and retinal vessel dataset (DRIVE). Extensive experimental results demonstrate that our AFN outperforms the state-of-the-art methods in terms of both higher accuracy and topological metrics, while also being more robust to various contrast changes. The source code of this work is available at https://github.com/TY-Shi/AFN.

cs.CV↗

arXiv2023

OpenDriver: An Open-Road Driver State Detection Dataset

Among numerous studies for driver state detection, wearable physiological measurements offer a practical method for real-time monitoring. However, there are few driver physiological datasets in open-road scenarios, and the existing datasets suffer from issues such as poor signal quality, small sample sizes, and short data collection periods. Therefore, in this paper, a large-scale multimodal driving dataset, OpenDriver, for driver state detection is developed. The OpenDriver encompasses a total of 3,278 driving trips, with a signal collection duration spanning approximately 4,600 hours. Two modalities of driving signals are enrolled in OpenDriver: electrocardiogram (ECG) signals and six-axis motion data of the steering wheel from a motion measurement unit (IMU), which were recorded from 81 drivers and their vehicles. Furthermore, three challenging tasks are involved in our work, namely ECG signal quality assessment, individual biometric identification based on ECG signals, and physiological signal analysis in complex driving environments. To facilitate research in these tasks, corresponding benchmarks have also been introduced. First, a noisy augmentation strategy is applied to generate a larger-scale ECG signal dataset with realistic noise simulation for quality assessment. Second, an end-to-end contrastive learning framework is employed for individual biometric identification. Finally, a comprehensive analysis of drivers' HRV features under different driving conditions is conducted. Each benchmark provides evaluation metrics and reference results. The OpenDriver dataset will be publicly available at https://github.com/bdne/OpenDriver.

cs.AI↗

arXiv2022

Learning Green's functions associated with time-dependent partial differential equations

Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with partial differential equations (PDEs) from pairs of forcing functions and solutions when numerical solvers are not available or the underlying physics is poorly understood. In this work, we attempt to provide theoretical foundations to understand the amount of training data needed to learn time-dependent PDEs. Given input-output pairs from a parabolic PDE in any spatial dimension $n\geq 1$, we derive the first theoretically rigorous scheme for learning the associated solution operator, which takes the form of a convolution with a Green's function $G$. Until now, rigorously learning Green's functions associated with time-dependent PDEs has been a major challenge in the field of scientific machine learning because $G$ may not be square-integrable when $n>1$, and time-dependent PDEs have transient dynamics. By combining the hierarchical low-rank structure of $G$ together with randomized numerical linear algebra, we construct an approximant to $G$ that achieves a relative error of $\smash{\mathcal{O}(Γ_ε^{-1/2}ε)}$ in the $L^1$-norm with high probability by using at most $\smash{\mathcal{O}(ε^{-\frac{n+2}{2}}\log(1/ε))}$ input-output training pairs, where $Γ_ε$ is a measure of the quality of the training dataset for learning $G$, and $ε>0$ is sufficiently small.

math.NA↗

arXiv2022

Local Intensity Order Transformation for Robust Curvilinear Object Segmentation

Segmentation of curvilinear structures is important in many applications, such as retinal blood vessel segmentation for early detection of vessel diseases and pavement crack segmentation for road condition evaluation and maintenance. Currently, deep learning-based methods have achieved impressive performance on these tasks. Yet, most of them mainly focus on finding powerful deep architectures but ignore capturing the inherent curvilinear structure feature (e.g., the curvilinear structure is darker than the context) for a more robust representation. In consequence, the performance usually drops a lot on cross-datasets, which poses great challenges in practice. In this paper, we aim to improve the generalizability by introducing a novel local intensity order transformation (LIOT). Specifically, we transfer a gray-scale image into a contrast-invariant four-channel image based on the intensity order between each pixel and its nearby pixels along with the four (horizontal and vertical) directions. This results in a representation that preserves the inherent characteristic of the curvilinear structure while being robust to contrast changes. Cross-dataset evaluation on three retinal blood vessel segmentation datasets demonstrates that LIOT improves the generalizability of some state-of-the-art methods. Additionally, the cross-dataset evaluation between retinal blood vessel segmentation and pavement crack segmentation shows that LIOT is able to preserve the inherent characteristic of curvilinear structure with large appearance gaps. An implementation of the proposed method is available at https://github.com/TY-Shi/LIOT.

eess.IV↗

arXiv2021

Parallel algorithms for computing the tensor-train decomposition

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT format from various tensor inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT and its variants for streaming data, (3) Tucker2TT for Tucker format, and (4) TT-fADI for solutions of Sylvester tensor equations. We provide theoretical guarantees of accuracy, parallelization methods, scaling analysis, and numerical results. For example, for a $d$-dimension tensor in $\mathbb{R}^{n\times\dots\times n}$, a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of $\mathcal{O}(n^{\lfloor d/2 \rfloor})$, improving upon $\mathcal{O}(n^{d-1})$ from previous algorithms.

math.NA↗

arXiv2020

On the compressibility of tensors

Tensors are often compressed by expressing them in low rank tensor formats. In this paper, we develop three methodologies that bound the compressibility of a tensor: (1) Algebraic structure, (2) Smoothness, and (3) Displacement structure. For each methodology, we derive bounds on storage costs that partially explain the abundance of compressible tensors in applied mathematics. For example, we show that the solution tensor $\mathcal{X} \in \mathbb{C}^{n \times n \times n}$ of a discretized Poisson equation $-\nabla^2 u =1$ on $[-1,1]^3$ with zero Dirichlet conditions can be approximated to a relative accuracy of $0<ε<1$ in the Frobenius norm by a tensor in tensor-train format with $\mathcal{O}(n (\log n)^2 (\log(1/ε))^2)$ degrees of freedom. As this bound is constructive, we are also able to solve this equation spectrally with $\mathcal{O}(n (\log n)^3 (\log(1/ε))^3)$ complexity.

math.NA↗