arXiv subjects

Qihong Yang

Publications and source records attributed to Qihong Yang.

10 recordsLinked to original sources

arXiv2026

A Novel Fourier Feature Network for Solving Partial Differential Equations

Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using $\cos$, $\sin$, or a combination of both. Similar to Extreme Learning Machines (ELMs), FENs employ a single-hidden-layer architecture to generate a set of basis functions. The target function is then approximated as a linear combination of these basis functions, with the coefficients determined using the least squares method. However, unlike ELMs, which often rely on affine transformations to improve representational power, FENs can achieve high-precision solutions without requiring such transformations on the input variables. To evaluate the representational capacity of these networks, we search for an optimal scaling factor within a predefined range for the randomly initialized and fixed weights and biases. By adjusting this scaling factor, we ensure a fair comparison between FENs and ELMs using various activation functions, such as $\text{sigmoid}$, $\tanh$, and $\text{swish}$. Our numerical experiments demonstrate that FENs consistently achieve higher accuracy than ELMs.

cs.LG↗

arXiv2026

Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Multi-Scale Separable Fourier Neural Network (MS-SFNN), a framework designed to overcome this limitation by explicitly encoding multi-scale Fourier features within a separable representation. The network factorizes the solution into $d$ single-coordinate subnetworks with fixed, randomly initialized weights; these subnetworks are combined via element-wise products to form a rich set of basis functions. This separable construction scales linearly with the problem dimension, thus inherently alleviating the curse of dimensionality. Crucially, each subnetwork is equipped with trainable scaling factors coupled with cosine activations, providing an adaptive mechanism for multi-scale frequency selection that endows the model with strong spectral approximation capability. The PDE solution is expressed as a linear combination of these learned basis functions, and the combination coefficients are determined by solving a large-scale least-squares system. To resolve the memory bottleneck in high-frequency or three-dimensional settings, we replace automatic differentiation (AD) with analytical derivatives of the basis functions and use a memory-efficient batched QR decomposition for solving the least-squares systems efficiently. Extensive numerical experiments demonstrate that MS-SFNN achieves superior accuracy and substantially outperforms state-of-the-art methods, including Physics-Informed Neural Network (PINN) and the Separated-Variable Spectral Neural Network (SV-SNN).

cs.LG↗

arXiv2026

A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear combination of basis functions integrated into the network, with coefficients determined by a direct least-squares solve, thereby bypassing traditional gradient-based training. The key methodological contribution include: (1) an efficient tensor-product scheme that generates multi-dimensional basis functions from combinations of two sets of subnetwork outputs, significantly reducing model complexity and parameter count while maintaining expressivity; (2) a block time-marching strategy to improve computational efficiency in long-time simulations; and (3) a linear reformulation strategy for handling nonlinear PDEs by treating known nonlinear terms as sources. TPNet achieves superior accuracy and shorter training times than conventional neural network solvers. This performance gain stems from its structured design and deterministic least-squares fitting, which contrast with the iterative, often computationally intensive optimization required by mainstream methods like Physics-Informed Neural Networks (PINNs).

cs.LG↗

arXiv2024

Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function

In the midst of the neural network's success in solving partial differential equations, tackling eigenvalue problems using neural networks remains a challenging task. However, the Physics Constrained-General Inverse Power Method Neural Network (PC-GIPMNN) approach was proposed and successfully applied to solve the single-group critical problems in reactor physics. This paper aims to solve critical problems in multi-group scenarios and in more complex geometries. Hence, inspired by the merits of traditional source iterative method, which can overcome the ill-condition of the right side of the equations effectively and solve the multi-group problem effectively, we propose two residual loss function called Decoupling Residual loss function and Direct Iterative loss function. Our loss function can deal with multi-group eigenvalue problem, and also single-group eigenvalue problem. Using the new residual loss functions, our study solves one-dimensional, two-dimensional, and three-dimensional multi-group problems in nuclear reactor physics without prior data. In numerical experiments, our approach demonstrates superior generalization capabilities compared to previous work.

math.NA↗

arXiv2024

Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE

In this work, we propose an end-to-end adaptive sampling neural network (MMPDE-Net) based on the moving mesh method, which can adaptively generate new sampling points by solving the moving mesh PDE. This model focuses on improving the quality of sampling points generation. Moreover, we develop an iterative algorithm based on MMPDE-Net, which makes the sampling points more precise and controllable. Since MMPDE-Net is a framework independent of the deep learning solver, we combine it with physics-informed neural networks (PINN) to propose moving sampling PINN (MS-PINN) and demonstrate its effectiveness by error analysis under some assumptions. Finally, we demonstrate the performance improvement of MS-PINN compared to PINN through numerical experiments of four typical examples, which numerically verify the effectiveness of our method.

math.NA↗

arXiv2023

Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems

In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented by optimizing the specially defined loss function. The largest positive eigenvalue, smallest eigenvalue and interior eigenvalues with the given prior knowledge can be solved efficiently. We examine the applicability and accuracy of our methods in the numerical experiments in one dimension, two dimensions and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.

math.NA↗

arXiv2023

On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem

In practical engineering experiments, the data obtained through detectors are inevitably noisy. For the already proposed data-enabled physics-informed neural network (DEPINN) \citep{DEPINN}, we investigate the performance of DEPINN in calculating the neutron diffusion eigenvalue problem from several perspectives when the prior data contain different scales of noise. Further, in order to reduce the effect of noise and improve the utilization of the noisy prior data, we propose innovative interval loss functions and give some rigorous mathematical proofs. The robustness of DEPINN is examined on two typical benchmark problems through a large number of numerical results, and the effectiveness of the proposed interval loss function is demonstrated by comparison. This paper confirms the feasibility of the improved DEPINN for practical engineering applications in nuclear reactor physics.

cs.LG↗

arXiv2022

A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems

We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for complex engineering problems, a very small amount of prior data from physical experiments are suggested to be used, to improve the accuracy and efficiency of training. We design an adaptive optimization procedure with Adam and LBFGS to accelerate the convergence in the training stage. We discuss the effect of different physical parameters, sampling techniques, loss function allocation and the generalization performance of the proposed DEPINN model for solving complex problem. The feasibility of proposed DEPINN model is tested on three typical benchmark problems, from simple geometry to complex geometry, and from mono-energetic equation to two-group equations. Numerous numerical results show that DEPINN can efficiently solve NDEPs with an appropriate optimization procedure. The proposed DEPINN can be generalized for other input parameter settings once its structure been trained. This work confirms the possibility of DEPINN for practical engineering applications in nuclear reactor physics.

physics.comp-ph↗

arXiv2021

Denoising User-aware Memory Network for Recommendation

For better user satisfaction and business effectiveness, more and more attention has been paid to the sequence-based recommendation system, which is used to infer the evolution of users' dynamic preferences, and recent studies have noticed that the evolution of users' preferences can be better understood from the implicit and explicit feedback sequences. However, most of the existing recommendation techniques do not consider the noise contained in implicit feedback, which will lead to the biased representation of user interest and a suboptimal recommendation performance. Meanwhile, the existing methods utilize item sequence for capturing the evolution of user interest. The performance of these methods is limited by the length of the sequence, and can not effectively model the long-term interest in a long period of time. Based on this observation, we propose a novel CTR model named denoising user-aware memory network (DUMN). Specifically, the framework: (i) proposes a feature purification module based on orthogonal mapping, which use the representation of explicit feedback to purify the representation of implicit feedback, and effectively denoise the implicit feedback; (ii) designs a user memory network to model the long-term interests in a fine-grained way by improving the memory network, which is ignored by the existing methods; and (iii) develops a preference-aware interactive representation component to fuse the long-term and short-term interests of users based on gating to understand the evolution of unbiased preferences of users. Extensive experiments on two real e-commerce user behavior datasets show that DUMN has a significant improvement over the state-of-the-art baselines. The code of DUMN model has been uploaded as an additional material.

cs.IR↗

arXiv2020

LRC-BERT: Latent-representation Contrastive Knowledge Distillation for Natural Language Understanding

The pre-training models such as BERT have achieved great results in various natural language processing problems. However, a large number of parameters need significant amounts of memory and the consumption of inference time, which makes it difficult to deploy them on edge devices. In this work, we propose a knowledge distillation method LRC-BERT based on contrastive learning to fit the output of the intermediate layer from the angular distance aspect, which is not considered by the existing distillation methods. Furthermore, we introduce a gradient perturbation-based training architecture in the training phase to increase the robustness of LRC-BERT, which is the first attempt in knowledge distillation. Additionally, in order to better capture the distribution characteristics of the intermediate layer, we design a two-stage training method for the total distillation loss. Finally, by verifying 8 datasets on the General Language Understanding Evaluation (GLUE) benchmark, the performance of the proposed LRC-BERT exceeds the existing state-of-the-art methods, which proves the effectiveness of our method.

cs.CL↗