Dapeng Lan

Yichen Luo, Peiyu Zhu, Dongxiao Hu et al.

While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology. The gradients from the PDE residuals and boundary constraints oppose each other, trapping the model in local minima. Current solutions, such as adaptive weighting or hard constraints, either fail to fundamentally resolve this ill-conditioning or are limited to simple geometries. In this study, we systematically analyze the possible causes of this gradient pathology from the perspectives of loss landscapes and optimization dynamics. Based on the obtained conclusion, we propose Constraint-Aligned loss with Manifold Lifting (CAML). By reformulating all zeroth-order terms into aligned constraints, our method effectively mitigates gradient conflicts. In addition, we introduce a delay factor to help the optimizer skip the high-curvature area. Experiments demonstrate that our CAML significantly enhances numerical stability and efficiency in highly complex PINN problems. Our code is open-sourced on https://github.com/YichenLuo-0/CAML.

Liang Cheng, Peiyuan Guan, Amir Taherkordi et al.

Variational Autoencoders (VAEs), as a form of deep generative model, have been widely used in recent years, and shown great great peformance in a number of different domains, including image generation and anomaly detection, etc.. This paper aims to explore neural network model compression method based on VAE. The experiment uses different neural network models for MNIST recognition as compression targets, including Feedforward Neural Network (FNN), Convolutional Neural Network (CNN), Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM). These models are the most basic models in deep learning, and other more complex and advanced models are based on them or inherit their features and evolve. In the experiment, the first step is to train the models mentioned above, each trained model will have different accuracy and number of total parameters. And then the variants of parameters for each model are processed as training data in VAEs separately, and the trained VAEs are tested by the true model parameters. The experimental results show that using the latent space as a representation of the model compression can improve the compression rate compared to some traditional methods such as pruning and quantization, meanwhile the accuracy is not greatly affected using the model parameters reconstructed based on the latent space. In the future, a variety of different large-scale deep learning models will be used more widely, so exploring different ways to save time and space on saving or transferring models will become necessary, and the use of VAE in this paper can provide a basis for these further explorations.

Yichen Luo, Jia Wang, Dapeng Lan et al.

Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale generalization capabilities, as well as high computational costs. This paper proposes the Multi-input and Multi-scale Efficient Transformer (MMET), a novel framework designed to address the above challenges. MMET decouples mesh and query points as two sequences and feeds them into the encoder and decoder, respectively, and uses a Gated Condition Embedding (GCE) layer to embed input variables or functions with varying dimensions, enabling effective solutions for multi-scale and multi-input problems. Additionally, a Hilbert curve-based reserialization and patch embedding mechanism decrease the input length. This significantly reduces the computational cost when dealing with large-scale geometric models. These innovations enable efficient representations and support multi-scale resolution queries for large-scale and multi-input PDE problems. Experimental evaluations on diverse benchmarks spanning different physical fields demonstrate that MMET outperforms SOTA methods in both accuracy and computational efficiency. This work highlights the potential of MMET as a robust and scalable solution for real-time PDE solving in engineering and physics-based applications, paving the way for future explorations into pre-trained large-scale models in specific domains. This work is open-sourced at https://github.com/YichenLuo-0/MMET.