Qiaolin He

Qihong Yang, Qiaolin He

We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional input, it employs $d$ independent subnetworks -- each acting on a single coordinate -- and constructs basis functions via element-wise multiplication of their outputs. The PDE solution is approximated as a linear combination of these basis functions, with coefficients determined by least squares. Critically, all network weights and biases are randomly initialized once, from a uniform distribution with unit variance, and remain fixed thereafter. To enhance expressivity, a tunable scaling factor is introduced in each subnetwork to modulate the frequency content of the resulting basis functions. Fourier features are explicitly embedded through cosine activations, endowing the method with strong spectral approximation capabilities. To mitigate the memory bottleneck associated with dense collocation in high-frequency or three-dimensional problems, we replace automatic differentiation with analytically derived basis function derivatives and develop a memory-efficient batched QR decomposition algorithm for solving large-scale least-squares systems. Numerical experiments demonstrate that MS-SFNN achieves unprecedented accuracy across a range of challenging PDEs, significantly outperforming state-of-the-art methods such as Physics-Informed Neural Networks (PINN) and Separated-Variable Spectral Neural Networks (SV-SNN).

Qihong Yang, Yangtao Deng, Qiaolin He et al.

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).

Yu Yang, Helin Gong, Qihong Yang et al.

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.

Qihong Yang, Yangtao Deng, Yu Yang et al.

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.

Yu Yang, Qihong Yang, Yangtao Deng et al.

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.

Ronghao Lin, Shuai Shen, Weipeng Hu et al.

Multimodal Empathetic Response Generation (MERG) is crucial for building emotionally intelligent human-computer interactions. Although large language models (LLMs) have improved text-based ERG, challenges remain in handling multimodal emotional content and maintaining identity consistency. Thus, we propose E3RG, an Explicit Emotion-driven Empathetic Response Generation System based on multimodal LLMs which decomposes MERG task into three parts: multimodal empathy understanding, empathy memory retrieval, and multimodal response generation. By integrating advanced expressive speech and video generative models, E3RG delivers natural, emotionally rich, and identity-consistent responses without extra training. Experiments validate the superiority of our system on both zero-shot and few-shot settings, securing Top-1 position in the Avatar-based Multimodal Empathy Challenge on ACM MM 25. Our code is available at https://github.com/RH-Lin/E3RG.

Ronghao Lin, Sijie Mai, Ying Zeng et al.

This paper presents the winning approach for the 1st MultiModal Deception Detection (MMDD) Challenge at the 1st Workshop on Subtle Visual Computing (SVC). Aiming at the domain shift issue across source and target domains, we propose a Multi-source Multimodal Progressive Domain Adaptation (MMPDA) framework that transfers the audio-visual knowledge from diverse source domains to the target domain. By gradually aligning source and the target domain at both feature and decision levels, our method bridges domain shifts across diverse multimodal datasets. Extensive experiments demonstrate the effectiveness of our approach securing Top-2 place. Our approach reaches 60.43% on accuracy and 56.99\% on F1-score on competition stage 2, surpassing the 1st place team by 5.59% on F1-score and the 3rd place teams by 6.75% on accuracy. Our code is available at https://github.com/RH-Lin/MMPDA.

Ronghao Lin, Qiaolin He, Sijie Mai et al.

Multimodal machine learning, mimicking the human brain's ability to integrate various modalities has seen rapid growth. Most previous multimodal models are trained on perfectly paired multimodal input to reach optimal performance. In real-world deployments, however, the presence of modality is highly variable and unpredictable, causing the pre-trained models in suffering significant performance drops and fail to remain robust with dynamic missing modalities circumstances. In this paper, we present a novel Cyclic INformative Learning framework (CyIN) to bridge the gap between complete and incomplete multimodal learning. Specifically, we firstly build an informative latent space by adopting token- and label-level Information Bottleneck (IB) cyclically among various modalities. Capturing task-related features with variational approximation, the informative bottleneck latents are purified for more efficient cross-modal interaction and multimodal fusion. Moreover, to supplement the missing information caused by incomplete multimodal input, we propose cross-modal cyclic translation by reconstruct the missing modalities with the remained ones through forward and reverse propagation process. With the help of the extracted and reconstructed informative latents, CyIN succeeds in jointly optimizing complete and incomplete multimodal learning in one unified model. Extensive experiments on 4 multimodal datasets demonstrate the superior performance of our method in both complete and diverse incomplete scenarios.

Pancheng Niu, Jun Guo, Qiaolin He et al.

Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is often hindered by limited representational capacity and optimization difficulties caused by competing physical constraints and conflicting gradients. In this work, we study PINN training from a unified architecture-optimization perspective. We first propose a layer-wise dynamic attention mechanism to enhance representational flexibility, resulting in the Layer-wise Dynamic Attention PINN (LDA-PINN). We then reformulate PINN training as a multi-task learning problem and introduce a conflict-resolved gradient update strategy to alleviate gradient interference, leading to the Gradient-Conflict-Resolved PINN (GC-PINN). By integrating these two components, we develop the Architecture-Conflict-Resolved PINN (ACR-PINN), which combines attentive representations with conflict-aware optimization while preserving the standard PINN loss formulation. Extensive experiments on benchmark PDEs, including the Burgers, Helmholtz, Klein-Gordon, and lid-driven cavity flow problems, demonstrate that ACR-PINN achieves faster convergence and significantly lower relative $L_2$ and $L_\infty$ errors than standard PINNs. These results highlight the effectiveness of architecture-optimization co-design for improving the robustness and accuracy of PINN-based solvers.