arXiv subjects

Junqing Chen

Publications and source records attributed to Junqing Chen.

25 records · Page 2Linked to original sources

arXiv2021

BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs, BINet learns to solve, as a proxy, associated boundary integral equations using neural networks. The benefits are three-fold. Firstly, only the boundary conditions need to be fitted since the PDE can be automatically satisfied with single or double layer representations according to the potential theory. Secondly, the dimension of the boundary integral equations is typically smaller, and as such, the sample complexity can be reduced significantly. Lastly, in the proposed method, all differential operators of the original PDEs have been removed, hence the numerical efficiency and stability are improved. Adopting neural tangent kernel (NTK) techniques, we provide proof of the convergence of BINets in the limit that the width of the neural network goes to infinity. Extensive numerical experiments show that, without calculating high-order derivatives, BINet is much easier to train and usually gives more accurate solutions, especially in the cases that the boundary conditions are not smooth enough. Further, BINet outperforms strong baselines for both one single PDE and parameterized PDEs in the bounded and unbounded domains.

math.NA↗

arXiv2020

DialogXL: All-in-One XLNet for Multi-Party Conversation Emotion Recognition

This paper presents our pioneering effort for emotion recognition in conversation (ERC) with pre-trained language models. Unlike regular documents, conversational utterances appear alternately from different parties and are usually organized as hierarchical structures in previous work. Such structures are not conducive to the application of pre-trained language models such as XLNet. To address this issue, we propose an all-in-one XLNet model, namely DialogXL, with enhanced memory to store longer historical context and dialog-aware self-attention to deal with the multi-party structures. Specifically, we first modify the recurrence mechanism of XLNet from segment-level to utterance-level in order to better model the conversational data. Second, we introduce dialog-aware self-attention in replacement of the vanilla self-attention in XLNet to capture useful intra- and inter-speaker dependencies. Extensive experiments are conducted on four ERC benchmarks with mainstream models presented for comparison. The experimental results show that the proposed model outperforms the baselines on all the datasets. Several other experiments such as ablation study and error analysis are also conducted and the results confirm the role of the critical modules of DialogXL.

cs.CL↗

arXiv2019

Mathematical and numerical study of a three-dimensional inverse eddy current problem

We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the recovery process. Then by virtue of non-radiating source conceptions, we establish a regularity result for the tangential trace of the true solution on the boundary, which is necessary to justify our subsequent mathematical formulation. After that, we formulate the inverse problem as a constrained optimization problem with an appropriate regularization and prove the existence and stability of the regularized minimizers. To facilitate the numerical solution of the nonlinear non-convex constrained optimization, we introduce a feasible Lagrangian and its discrete variant. Then the gradient of the objective functional is derived using the adjoint technique. By means of the gradient, a nonlinear conjugate gradient method is formulated for solving the optimization system, and a Sobolev gradient is incorporated to accelerate the iterative process. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm.

math.AP↗

arXiv2014

Detection and classification from electromagnetic induction data

In this paper we introduce an efficient algorithm for identifying conductive objects using induction data derived from eddy currents. Our method consists of first extracting geometric features from the induction data and then matching them to precomputed data for known objects from a given dictionary. The matching step relies on fundamental properties of conductive polarization tensors and new invariants introduced in this paper. A new shape identification scheme is introduced and studied. We test it numerically in the presence of measurement noise. Stability and resolution capabilities of the proposed identification algorithm are quantified in numerical simulations.

math.AP↗

arXiv2014

Reverse Time Migration for Extended Obstacles: Acoustic Waves

We consider the resolution of the single frequency reverse time migration (RTM) method for extended targets without the assumption of the validation of geometric optics approximation. The resolution analysis, which applies in both penetrable and non-penetrable obstacles with sound soft or impedance boundary condition on the boundary of the obstacle, implies that the imaginary part of the cross-correlation imaging functional is always positive and thus may have better stability properties. Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.

math-ph↗

arXiv2013

Target Detection and Characterization from Electromagnetic Induction Data

The goal of this paper is to contribute to the field of nondestructive testing by eddy currents. We provide a mathematical analysis and a numerical framework for simulating the imaging of arbitrarily shaped small volume conductive inclusions from electromagnetic induction data. We derive, with proof, a small-volume expansion of the eddy current data measured away from the conductive inclusion. The formula involves two polarization tensors: one associated with the magnetic contrast and the second with the conductivity of the inclusion. Based on this new formula, we design a location search algorithm. We include in this paper a discussion on data sampling, noise reduction, and on probability of detection. We provide numerical examples that support our findings.

math.AP↗

arXiv2010

A Calculus of Consistent Component-based Software Updates

It is important to enable reasoning about the meaning and possible effects of updates to ensure that the updated system operates correctly. A formal, mathematical model of dynamic update should be developed, in order to understand by both users and implementors of update technology what design choices can be considered. In this paper, we define a formal calculus $updateπ$, a variant extension of higher-order $π$ calculus, to model dynamic updates of component-based software, which is language and technology independent. The calculus focuses on following main concepts: proper granularity of update, timing of dynamic update, state transformation between versions, update failure check and recovery. We describe a series of rule on safe component updates to model some general processes of dynamic update and discuss its reduction semantics coincides with a labelled transition system semantics that illustrate the expressive power of these calculi.

cs.LO↗