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In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted $L^p(0,T)$ norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions., Comment: 27 pages

The CGI (CGI) has the potential of low cost, low dose, and high resolution, which is very attractive for the development of radiation imaging field. However, many sub-coding plates must be used in the modulation process, which greatly affects the development of CGI technology. In order to reduce the coding plates, we refer to the rotation method of computed tomography (CT), then propose a novel CGI method based on rotational modulation method of a single-column striped coding plate. This method utilizes the spatial variation of a single sub-coding plate (rotation) to realize multiple modulation of the ray field and improves the utilization rate of a single sub-coding plate. However, for this rotation scheme of CGI, the traditional binary modulation matrix is no longer applicable. To obtain the system matrix of the rotated striped coding plate, an area model based on beam boundaries is established. Subsequently, numerical and Monte Carlo simulations were conducted. The results reveal that our scheme enables high-quality imaging of N*N resolution objects using only N sub-coding plates, under both full-sampling and under-sampling scenarios. Moreover, our scheme demonstrates superiority over the Hadamard scheme in both imaging quality and the number of required sub-coding plates, whether in scenarios of full-sampling or under-sampling. Finally, an {\alpha} ray imaging platform was established to further demonstrate the feasibility of the rotational modulation method. By employing our scheme, a mere 8 sub-coding plates were employed to achieve CGI of the radiation source intensity distribution, achieving a resolution of 8*8. Therefore, the novel ray CGI based on rotational modulation method can achieve high-quality imaging effect with fewer sub-coding plates, which has important practical value and research significance for promoting single-pixel radiation imaging technology.

In this study, we present several improvements of the non-relativistic Friedrichs-Lee model with multiple discrete and continuous states and still retain its solvability. Our findings establish a solid theoretical basis for the exploration of resonance phenomena in scenarios involving the presence of multiple interfering states across various channels. The scattering amplitudes associated with the continuous states naturally adhere to coupled-channel unitarity, rendering this framework particularly valuable for investigating hadronic resonant states appearing in multiple coupled channels. Moreover, this generalized framework exhibits a wide-range applicability, enabling investigations into resonance phenomena across diverse physical domains, including hadron physics, nuclear physics, optics, and cold atom physics, among others., Comment: 25 pages, 2 figures

Federated Learning (FL) is a distributed learning paradigm that can coordinate heterogeneous edge devices to perform model training without sharing private data. While prior works have focused on analyzing FL convergence with respect to hyperparameters like batch size and aggregation frequency, the joint effects of adjusting these parameters on model performance, training time, and resource consumption have been overlooked, especially when facing dynamic data streams and network characteristics. This paper introduces novel analytical models and optimization algorithms that leverage the interplay between batch size and aggregation frequency to navigate the trade-offs among convergence, cost, and completion time for dynamic FL training. We establish a new convergence bound for training error considering heterogeneous datasets across devices and derive closed-form solutions for co-optimized batch size and aggregation frequency that are consistent across all devices. Additionally, we design an efficient algorithm for assigning different batch configurations across devices, improving model accuracy and addressing the heterogeneity of both data and system characteristics. Further, we propose an adaptive control algorithm that dynamically estimates network states, efficiently samples appropriate data batches, and effectively adjusts batch sizes and aggregation frequency on the fly. Extensive experiments demonstrate the superiority of our offline optimal solutions and online adaptive algorithm., Comment: 20 pages, 12 figures

In open multi-agent environments, the agents may encounter unexpected teammates. Classical multi-agent learning approaches train agents that can only coordinate with seen teammates. Recent studies attempted to generate diverse teammates to enhance the generalizable coordination ability, but were restricted by pre-defined teammates. In this work, our aim is to train agents with strong coordination ability by generating teammates that fully cover the teammate policy space, so that agents can coordinate with any teammates. Since the teammate policy space is too huge to be enumerated, we find only dissimilar teammates that are incompatible with controllable agents, which highly reduces the number of teammates that need to be trained with. However, it is hard to determine the number of such incompatible teammates beforehand. We therefore introduce a continual multi-agent learning process, in which the agent learns to coordinate with different teammates until no more incompatible teammates can be found. The above idea is implemented in the proposed Macop (Multi-agent compatible policy learning) algorithm. We conduct experiments in 8 scenarios from 4 environments that have distinct coordination patterns. Experiments show that Macop generates training teammates with much lower compatibility than previous methods. As a result, in all scenarios Macop achieves the best overall coordination ability while never significantly worse than the baselines, showing strong generalization ability.

The fine-tuning paradigm in addressing long-tail learning tasks has sparked significant interest since the emergence of foundation models. Nonetheless, how fine-tuning impacts performance in long-tail learning was not explicitly quantified. In this paper, we disclose that heavy fine-tuning may even lead to non-negligible performance deterioration on tail classes, and lightweight fine-tuning is more effective. The reason is attributed to inconsistent class conditions caused by heavy fine-tuning. With the observation above, we develop a low-complexity and accurate long-tail learning algorithms LIFT with the goal of facilitating fast prediction and compact models by adaptive lightweight fine-tuning. Experiments clearly verify that both the training time and the learned parameters are significantly reduced with more accurate predictive performance compared with state-of-the-art approaches. The implementation code is available at https://github.com/shijxcs/LIFT., Comment: Accepted by ICML 2024

Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To optimize them, a two-layer online ensemble is usually deployed due to the inherent uncertainty of the non-stationarity, in which a group of base-learners are maintained and a meta-algorithm is employed to track the best one on the fly. However, the two-layer structure raises the concern about the computational complexity -- those methods typically maintain $\mathcal{O}(\log T)$ base-learners simultaneously for a $T$-round online game and thus perform multiple projections onto the feasible domain per round, which becomes the computational bottleneck when the domain is complicated. In this paper, we present efficient methods for optimizing dynamic regret and adaptive regret, which reduce the number of projections per round from $\mathcal{O}(\log T)$ to $1$. Moreover, our obtained algorithms require only one gradient query and one function evaluation at each round. Our technique hinges on the reduction mechanism developed in parameter-free online learning and requires non-trivial twists on non-stationary online methods. Empirical studies verify our theoretical findings., Comment: preliminary conference version appeared at NeurIPS 2022; this extended version improves the paper presentation, further investigates the interval dynamic regret, and adds two applications (online non-stochastic control and online PCA)

Serverless computing has gained popularity in edge computing due to its flexible features, including the pay-per-use pricing model, auto-scaling capabilities, and multi-tenancy support. Complex Serverless-based applications typically rely on Serverless workflows (also known as Serverless function orchestration) to express task execution logic, and numerous application- and system-level optimization techniques have been developed for Serverless workflow scheduling. However, there has been limited exploration of optimizing Serverless workflow scheduling in edge computing systems, particularly in high-density, resource-constrained environments such as system-on-chip clusters and single-board-computer clusters. In this work, we discover that existing Serverless workflow scheduling techniques typically assume models with limited expressiveness and cause significant resource contention. To address these issues, we propose modeling Serverless workflows using behavior trees, a novel and fundamentally different approach from existing directed-acyclic-graph- and state machine-based models. Behavior tree-based modeling allows for easy analysis without compromising workflow expressiveness. We further present observations derived from the inherent tree structure of behavior trees for contention-free function collections and awareness of exact and empirical concurrent function invocations. Based on these observations, we introduce BeeFlow, a behavior tree-based Serverless workflow system tailored for resource-constrained edge clusters. Experimental results demonstrate that BeeFlow achieves up to 3.2X speedup in a high-density, resource-constrained edge testbed and 2.5X speedup in a high-profile cloud testbed, compared with the state-of-the-art., Comment: Accepted by Journal of Systems Architecture

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their effectiveness is somewhat diminished when addressing issues involving singularities, such as point sources or geometric irregularities, where the approximations they provide often suffer from reduced accuracy due to the limited regularity of the exact solution. In this work, we investigate PINNs for solving Poisson equations in polygonal domains with geometric singularities and mixed boundary conditions. We propose a novel singularity enriched PINN (SEPINN), by explicitly incorporating the singularity behavior of the analytic solution, e.g., corner singularity, mixed boundary condition and edge singularities, into the ansatz space, and present a convergence analysis of the scheme. We present extensive numerical simulations in two and three-dimensions to illustrate the efficiency of the method, and also a comparative study with several existing neural network based approaches., Comment: 32 pages, to appear at SIAM Journal on Scientific Computing

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order optimality system of the optimal control problem, and employs deep neural networks to represent the solutions to the reduced system. We present an error analysis of the scheme, and provide $L^2(\Omega)$ error bounds on the state, control and adjoint in terms of neural network parameters (e.g., depth, width, and parameter bounds) and the numbers of sampling points. The main tools in the analysis include offset Rademacher complexity and boundedness and Lipschitz continuity of neural network functions. We present several numerical examples to illustrate the method and compare it with two existing ones., Comment: 26 pages

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is constructed to sequentially recover these two parameters. In the first step, we implement a straightforward reformulation that results in a standard problem of identifying the diffusion coefficient. This coefficient is then numerically recovered, with no requirement for knowledge of the potential, by utilizing an output least-square method coupled with finite element discretization. In the second step, the previously recovered diffusion coefficient is employed to reconstruct the potential coefficient, applying a method similar to the first step. Our approach is stimulated by a constructive conditional stability, and we provide rigorous a priori error estimates in $L^2(\Omega)$ for the recovered diffusion and potential coefficients. Our approach is stimulated by a constructive conditional stability, and we provide rigorous a priori error estimates in $L^2(\Omega)$ for the recovered diffusion and potential coefficients. To derive these estimates, we develop a weighted energy argument and suitable positivity conditions. These estimates offer a beneficial guide for choosing regularization parameters and discretization mesh sizes, in accordance with the noise level. Some numerical experiments are presented to demonstrate the accuracy of the numerical scheme and support our theoretical results., Comment: 28 pages

We study the $J/\psi \pi$ and $D\bar{D}^*$ coupled-channel system within a covariant framework. The $J/\psi \pi$ and $D\bar{D}^*$ invariant-mass distributions measured at 4.23~GeV and 4.26~GeV by BESIII and the finite-volume energy levels from recent lattice QCD simulations are simultaneously fitted. Phase shifts and inelasticities of the $J/\psi \pi$ and $D\bar{D}^*$ scattering are predicted using the resulting amplitudes. Poles corresponding to the $Z_c(3900)$ state are found in the complex energy plane and their couplings with $J/\psi \pi$ and $D\bar{D}^*$ are determined. Our results indicate that the current lattice data do not preclude the existence of a physical $Z_c(3900)$ state., Comment: 22 pages, 4 figures

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it can exploit the unknown niceness of the environments and attain problem-dependent guarantees. Specifically, we obtain $\mathcal{O}(\log V_T)$, $\mathcal{O}(d \log V_T)$ and $\hat{\mathcal{O}}(\sqrt{V_T})$ regret bounds for strongly convex, exp-concave and convex loss functions, respectively, where $d$ is the dimension, $V_T$ denotes problem-dependent gradient variations and the $\hat{\mathcal{O}}(\cdot)$-notation omits $\log V_T$ factors. Our result not only safeguards the worst-case guarantees but also directly implies the small-loss bounds in analysis. Moreover, when applied to adversarial/stochastic convex optimization and game theory problems, our result enhances the existing universal guarantees. Our approach is based on a multi-layer online ensemble framework incorporating novel ingredients, including a carefully designed optimism for unifying diverse function types and cascaded corrections for algorithmic stability. Notably, despite its multi-layer structure, our algorithm necessitates only one gradient query per round, making it favorable when the gradient evaluation is time-consuming. This is facilitated by a novel regret decomposition equipped with carefully designed surrogate losses., Comment: NeurIPS 2023

In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally cannot expect high-order accuracy in space in solving the subdiffusion equation with nonsmooth initial data. In this paper, a new splitting of the solution is constructed for high-order finite element approximations to the subdiffusion equation with nonsmooth initial data. The method is constructed by splitting the solution into two parts, i.e., a time-dependent smooth part and a time-independent nonsmooth part, and then approximating the two parts via different strategies. The time-dependent smooth part is approximated by using high-order finite element method in space and convolution quadrature in time, while the steady nonsmooth part could be approximated by using smaller mesh size or other methods that could yield high-order accuracy. Several examples are presented to show how to accurately approximate the steady nonsmooth part, including piecewise smooth initial data, Dirac--Delta point initial data, and Dirac measure concentrated on an interface. The argument could be directly extended to subdiffusion equations with nonsmooth source data. Extensive numerical experiments are presented to support the theoretical analysis and to illustrate the performance of the proposed high-order splitting finite element methods., Comment: 25 pages

This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary measurement corresponding to a fairly general boundary excitation uniquely determines the order of the fractional derivative and the polygonal support of the diffusion coefficient, without knowing either the initial condition or the source. The uniqueness analysis further inspires the development of a robust numerical algorithm for recovering the fractional order and diffusion coefficient. The proposed algorithm combines small-time asymptotic expansion, analytic continuation of the solution and the level set method. We present extensive numerical experiments to illustrate the feasibility of the simultaneous recovery. In addition, we discuss the uniqueness of recovering general diffusion and potential coefficients from one single partial boundary measurement, when the boundary excitation is more specialized., Comment: 28 pages

Graph Neural Networks (GNNs) have gained growing interest in miscellaneous applications owing to their outstanding ability in extracting latent representation on graph structures. To render GNN-based service for IoT-driven smart applications, traditional model serving paradigms usually resort to the cloud by fully uploading geo-distributed input data to remote datacenters. However, our empirical measurements reveal the significant communication overhead of such cloud-based serving and highlight the profound potential in applying the emerging fog computing. To maximize the architectural benefits brought by fog computing, in this paper, we present Fograph, a novel distributed real-time GNN inference framework that leverages diverse and dynamic resources of multiple fog nodes in proximity to IoT data sources. By introducing heterogeneity-aware execution planning and GNN-specific compression techniques, Fograph tailors its design to well accommodate the unique characteristics of GNN serving in fog environments. Prototype-based evaluation and case study demonstrate that Fograph significantly outperforms the state-of-the-art cloud serving and fog deployment by up to 5.39x execution speedup and 6.84x throughput improvement., Comment: Accepted by IEEE/ACM Transactions on Networking

Since acquiring perfect supervision is usually difficult, real-world machine learning tasks often confront inaccurate, incomplete, or inexact supervision, collectively referred to as weak supervision. In this work, we present WSAUC, a unified framework for weakly supervised AUC optimization problems, which covers noisy label learning, positive-unlabeled learning, multi-instance learning, and semi-supervised learning scenarios. Within the WSAUC framework, we first frame the AUC optimization problems in various weakly supervised scenarios as a common formulation of minimizing the AUC risk on contaminated sets, and demonstrate that the empirical risk minimization problems are consistent with the true AUC. Then, we introduce a new type of partial AUC, specifically, the reversed partial AUC (rpAUC), which serves as a robust training objective for AUC maximization in the presence of contaminated labels. WSAUC offers a universal solution for AUC optimization in various weakly supervised scenarios by maximizing the empirical rpAUC. Theoretical and experimental results under multiple settings support the effectiveness of WSAUC on a range of weakly supervised AUC optimization tasks., Comment: Accepted by IEEE TPAMI

Converting the medium infrared field to the visible band is an effective image detection method. We propose a comprehensive theory of image up-conversion under continuous optical pumping, and discuss the relationship between the experimental parameters and imaging field of view, resolution, quantum efficiency, and conversion bandwidth. Theoretical predictions of upconversion imaging results are given based on numerical simulations, which show good agreement with experimental results. In particular, coherent and incoherent light illumination are studied separately and the advantages and disadvantages of their imaging performance are compared and analysed. This work provides a study of the upconversion image detection performance of the system, which is of great value in guiding the design of the detection system and bringing it to practical applications., Comment: 12 pages, 8 figures