arXiv subjects

Jiayu Han

Publications and source records attributed to Jiayu Han.

At least 19 recordsLinked to original sources

arXiv2026

An extended Lagrange FEM for the Maxwell eigenvalue problem

We construct an extended Lagrange FE space to solve the Maxwell equation and its eigenvalue problem in $\mathbb R^d$ $(d=2,3)$, which is the sum of the vectorial $p-$order Lagrange FE space ($p\ge1$) and the gradient of the $p+1-$order Lagrange FE space. The two lowest-order methods in 3D adopt slightly less degrees of freedom than the second family of the same order edge element methods in 3D. We construct a Clément interpolant operator to prove the discrete compactness of the FE space and the convergence of the new methods for both Maxwell equation and its eigenvalue problem. For the extended linear Lagrange element method, an average-type curl recovery approach is designed to obtain numerical solution of super-convergence. In the numerical part, we verify the optimal convergence order for the two lowest-order methods, discuss the upper bound property of numerical eigenvalues and investigate the lower bound property by the average-type curl recovery approach.

math.NA↗

arXiv2025

A finite element method for Maxwell's transmission eigenvalue problem in anisotropic media

In this paper, we introduce a finite element method employing the Nedéléc element space for solving the Maxwell's transmission eigenvalue problem in anisotropic media. The well-posedness of the source problems are derived using $\mathbb T$-coercivity approach. We discuss the discrete compactness property of the finite element space under the case of anisotropic coefficients and conduct a finite element error analysis for the proposed approach. Additionally, we present some numerical examples to support the theoretical result.

math.NA↗

arXiv2022

Probing for Understanding of English Verb Classes and Alternations in Large Pre-trained Language Models

We investigate the extent to which verb alternation classes, as described by Levin (1993), are encoded in the embeddings of Large Pre-trained Language Models (PLMs) such as BERT, RoBERTa, ELECTRA, and DeBERTa using selectively constructed diagnostic classifiers for word and sentence-level prediction tasks. We follow and expand upon the experiments of Kann et al. (2019), which aim to probe whether static embeddings encode frame-selectional properties of verbs. At both the word and sentence level, we find that contextual embeddings from PLMs not only outperform non-contextual embeddings, but achieve astonishingly high accuracies on tasks across most alternation classes. Additionally, we find evidence that the middle-to-upper layers of PLMs achieve better performance on average than the lower layers across all probing tasks.

cs.CL↗

arXiv2022

An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem

An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the numerical scheme for the quad-curl equation and then derive an error estimate in a mesh-dependent norm, which is optimal with respect to h but has different p-version error bounds under conforming and nonconforming tetrahedron meshes. The hp-version discrete compactness of the DG space is established for the convergence proof. The performance of the method is demonstrated by numerical experiments using conforming/nonconforming meshes and h-version/p-version refinement. The optimal h-version convergence rate and the exponential p-version convergence rate are observed.

math.NA↗

arXiv2022

$\bf H(\mathrm{curl}^2)$ conforming element for Maxwell's transmission eigenvalue problem using fixed-point approach

Using newly developed ${\bf H}(\mathrm{curl}^2)$ conforming elements, we solve the Maxwell's transmission eigenvalue problem. Both real and complex eigenvalues are considered. Based on the fixed-point weak formulation with reasonable assumptions, the optimal error estimates for numerical eigenvalues and eigenfunctions (in the ${\bf H}(\mathrm{curl}^2)$-norm and ${\bf H}(\mathrm{curl})$-semi-norm) are established.

math.NA↗

arXiv2022

Distantly Supervised Relation Extraction via Recursive Hierarchy-Interactive Attention and Entity-Order Perception

Wrong-labeling problem and long-tail relations severely affect the performance of distantly supervised relation extraction task. Many studies mitigate the effect of wrong-labeling through selective attention mechanism and handle long-tail relations by introducing relation hierarchies to share knowledge. However, almost all existing studies ignore the fact that, in a sentence, the appearance order of two entities contributes to the understanding of its semantics. Furthermore, they only utilize each relation level of relation hierarchies separately, but do not exploit the heuristic effect between relation levels, i.e., higher-level relations can give useful information to the lower ones. Based on the above, in this paper, we design a novel Recursive Hierarchy-Interactive Attention network (RHIA) to further handle long-tail relations, which models the heuristic effect between relation levels. From the top down, it passes relation-related information layer by layer, which is the most significant difference from existing models, and generates relation-augmented sentence representations for each relation level in a recursive structure. Besides, we introduce a newfangled training objective, called Entity-Order Perception (EOP), to make the sentence encoder retain more entity appearance information. Substantial experiments on the popular (NYT) dataset are conducted. Compared to prior baselines, our RHIA-EOP achieves state-of-the-art performance in terms of precision-recall (P-R) curves, AUC, Top-N precision and other evaluation metrics. Insightful analysis also demonstrates the necessity and effectiveness of each component of RHIA-EOP.

cs.CL↗

arXiv2021

Spurious solutions for high order curl problems

We investigate numerical solutions of high order curl problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spurious solutions, while mixed formulations with finite elements in complexes solve the problems correctly. To explain the numerical results, we clarify the cohomological structures in high order curl problems by relating the partial differential equations to the Hodge-Laplacian boundary problems of the gradcurl-complexes.

math.NA↗

arXiv2021

Event-driven Two-stage Solution to Non-intrusive Load Monitoring

Existing methods of non-intrusive load monitoring (NILM) in literatures generally suffer from high computational complexity and/or low accuracy in identifying working household appliances. This paper proposes an event-driven Factorial Hidden Markov model (eFHMM) for multiple appliances with multiple states in a household, aiming for low computational complexity and high load disaggregation accuracy. The proposed eFHMM decreases the computational complexity to be linear to the event number, which ensures online load disaggregation. Furthermore, the eFHMM is solved in two stages, where the first stage identifies state-changing appliance using transient signatures and the second stage confirms the inferred states using steady-state signatures. The combination of transient and steady-state signatures, which are extracted from transient and steady periods segmented by detected events, enhances the uniqueness of each state transition and associated appliances, which ensures accurate load disaggregation. The event-driven two-stage NILM solution, termed as eFHMM-TS, is naturally fit into an edge-cloud framework, which makes possible the real-world application of NILM. The proposed eFHMM-TS method is validated on the LIFTED and synD datasets. Results demonstrate that the eFHMM-TS method outperforms other methods and can be applied in practice.

eess.SP↗

arXiv2021

Adaptive Event Detection for Representative Load Signature Extraction

Event detection is the first step in event-based non-intrusive load monitoring (NILM) and it can provide useful transient information to identify appliances. However, existing event detection methods with fixed parameters may fail in case of unpredictable and complicated residential load changes such as high fluctuation, long transition, and near simultaneity. This paper proposes a dynamic time-window approach to deal with these highly complex load variations. Specifically, a window with adaptive margins, multi-timescale window screening, and adaptive threshold (WAMMA) method is proposed to detect events in aggregated home appliance load data with high sampling rate (>1Hz). The proposed method accurately captures the transient process by adaptively tuning parameters including window width, margin width, and change threshold. Furthermore, representative transient and steady-state load signatures are extracted and, for the first time, quantified from transient and steady periods segmented by detected events. Case studies on a 20Hz dataset, the 50Hz LIFTED dataset, and the 60Hz BLUED dataset show that the proposed method can robustly outperform other state-of-art event detection methods. This paper also shows that the extracted load signatures can improve NILM accuracy and help develop other applications such as load reconstruction to generate realistic load data for NILM research.

eess.SP↗

arXiv2020

LfEdNet: A Task-based Day-ahead Load Forecasting Model for Stochastic Economic Dispatch

Load forecasting is one of the most important and studied topics in modern power systems. Most of the existing researches on day-ahead load forecasting try to build a good model to improve the forecasting accuracy. The forecasted load is then used as the input to generation scheduling with the ultimate goal of minimizing the cost of generation schedules. However, existing day-ahead load forecasting models do not consider this ultimate goal at the training/forecasting stage. This paper proposes a task-based day-ahead load forecasting model labeled as LfEdNet that combines two individual layers in one model, including a load forecasting layer based on deep neural network (Lf layer) and a day-ahead stochastic economic dispatch (SED) layer (Ed layer). The training of LfEdNet aims to minimize the cost of the day-ahead SED in the Ed layer by updating the parameters of the Lf layer. Sequential quadratic programming (SQP) is used to solve the day-ahead SED in the Ed layer. The test results demonstrate that the forecasted results produced by LfEdNet can lead to lower cost of day-ahead SED while maintaining a relatively high forecasting accuracy.

eess.SY↗

arXiv2019

A Multi-timescale Two-stage Robust Grid-friendly Dispatch Model for Microgrid Operation

Uncertainty in renewable energy generation and load consumption is a great challenge for microgrid operation, especially in islanded mode as the microgrid may be small in size and has limited flexible resources. In this paper, a multi-timescale, two-stage robust unit commitment and economic dispatch model is proposed to optimize the microgrid operation. The first stage is a combination of day-ahead hourly and real-time sub-hourly model, which means the day-ahead dispatch result must also satisfy the real-time condition at the same time. The second stage is to verify the feasibility of the day-ahead dispatch result in worst-case condition considering high-level uncertainty in renewable energy dispatch and load consumptions. In the proposed model, battery energy storage system (BESS) and solar PV units are integrated as a combined solar-storage system. The BESS plays an essential role to balance the variable output of solar PV units, which keeps the combined solar-storage system output unchanged on an hourly basis. In this way, it largely neutralizes the impact of solar uncertainty and makes the microgrid operation grid friendly. Furthermore, in order to enhance the flexibility and resilience of the microgrid, both BESS and thermal units provide regulating reserve to manage solar and load uncertainty. The model has been tested in a controlled hardware in loop (CHIL) environment for the Bronzeville Community Microgrid system in Chicago. The simulation results show that the proposed model works effectively in managing the uncertainty in solar PV and load and can provide a flexible dispatch in both grid-connected and islanded modes.

eess.SY↗

arXiv2019

LIFTED: Household Appliance-level Load Dataset and Data Compression with Lossless Coding considering Precision

The issue of estimating the detailed appliance level load consumption has received considerable attention. This paper first presents a Labelled hIgh-Frequency daTaset for Electricity Disaggregation (LIFTED), which can be used for research on nonintrusive load monitoring (NILM). This dataset consists of one-week detailed appliance-level electricity usage information including voltage, current, active power, and reactive power for a single apartment in the United States, down-sampled at 50Hz. This paper also proposes an efficient Lossless Coding considering Precision (LCP) algorithm on data compression. This algorithm considers both the precision requirements of practical applications on load datasets and the unique characteristics of household appliance-level load datasets. The LCP algorithm is tested on the LIFTED dataset and the results demonstrate that LCP can achieve a higher compression ratio compared to several existing algorithms.

eess.SP↗

arXiv2019

JSCN: Joint Spectral Convolutional Network for Cross Domain Recommendation

Cross-domain recommendation can alleviate the data sparsity problem in recommender systems. To transfer the knowledge from one domain to another, one can either utilize the neighborhood information or learn a direct mapping function. However, all existing methods ignore the high-order connectivity information in cross-domain recommendation area and suffer from the domain-incompatibility problem. In this paper, we propose a \textbf{J}oint \textbf{S}pectral \textbf{C}onvolutional \textbf{N}etwork (JSCN) for cross-domain recommendation. JSCN will simultaneously operate multi-layer spectral convolutions on different graphs, and jointly learn a domain-invariant user representation with a domain adaptive user mapping module. As a result, the high-order comprehensive connectivity information can be extracted by the spectral convolutions and the information can be transferred across domains with the domain-invariant user mapping. The domain adaptive user mapping module can help the incompatible domains to transfer the knowledge across each other. Extensive experiments on $24$ Amazon rating datasets show the effectiveness of JSCN in the cross-domain recommendation, with $9.2\%$ improvement on recall and $36.4\%$ improvement on MAP compared with state-of-the-art methods. Our code is available online ~\footnote{https://github.com/JimLiu96/JSCN}.

cs.LG↗

arXiv2017

Multigrid methods based on shifted inverse iteration for the Maxwell eigenvalue problem

In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and electric permittivity. With the aid of the mixed form of source problem associated with the eigenvalue problem, we prove the uniform convergence of the discrete solution operator to the solution operator in $L^2(\Omega)$ using discrete compactness of edge element space. Then we prove the asymptotically optimal error estimates for both multigrid methods. Numerical experiments confirm our theoretical analysis.

math.NA↗

arXiv2016

A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems

Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need to solve a series of primal and dual eigenvalue problems on a coarse mesh and the associated boundary value problems on the finer and finer meshes. Theoretical analysis and numerical results show that our method is simple and easy to implement and is efficient for computing real and complex transmission eigenvalues.

math.NA↗

arXiv2016

Non-conforming finite element methods for transmission eigenvalue problem

The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem.

math.NA↗

arXiv2015

An $H^m$-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues

In this paper we develop an $H^m$-conforming ($m\ge1$) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval $[-1,1]$ that is made up of the generalized Jacobi polynomials (GJPs) and the nodal basis functions. So the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval $[-1,1]$. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally we apply the $H^2$-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot topic in the field engineering and mathematics.

math.NA↗

arXiv2015

Error estimates and a two grid scheme for approximating transmission eigenvalues

In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand side term is a selfadjoint, continuous and coercive sesquilinear form. To solve the resulting nonselfadjoint eigenvalue problem, we give an $H^{2}$ conforming finite element discretization and establish a two grid discretization scheme. We present a complete error analysis for both discretization schemes, and theoretical analysis and numerical experiments show that the methods presented in this paper can efficiently compute real and complex transmission eigenvalues.

math.NA↗