Lijun Yang

Hongkun Dou, Zike Chen, Zeyu Li et al.

Diffusion models have gained prominence as powerful generative tools for solving inverse problems due to their ability to model complex data distributions. However, existing methods typically rely on complete knowledge of the forward observation process to compute gradients for guided sampling, limiting their applicability in scenarios where such information is unavailable. In this work, we introduce \textbf{\emph{Constrained Particle Seeking (CPS)}}, a novel gradient-free approach that leverages all candidate particle information to actively search for the optimal particle while incorporating constraints aligned with high-density regions of the unconditional prior. Unlike previous methods that passively select promising candidates, CPS reformulates the inverse problem as a constrained optimization task, enabling more flexible and efficient particle seeking. We demonstrate that CPS can effectively solve both image and scientific inverse problems, achieving results comparable to gradient-based methods while significantly outperforming gradient-free alternatives. Code is available at https://github.com/deng-ai-lab/CPS.

Jiawei Wu, Teng Wang, Jiaqi Nan et al.

Traditional numerical simulation methods require substantial computational resources to accurately determine the complete nonlinear thermoacoustic response of flames to various perturbation frequencies and amplitudes. In this paper, we have developed deep learning algorithms that can construct a comprehensive flame nonlinear response from limited numerical simulation data. To achieve this, we propose using a frequency-sweeping data type as the training dataset, which incorporates a rich array of learnable information within a constrained dataset. To enhance the precision in learning flame nonlinear response patterns from the training data, we introduce a Dual-Path neural network. This network consists of a Chronological Feature Path and a Temporal Detail Feature Path. The Dual-Path network is specifically designed to focus intensively on the temporal characteristics of velocity perturbation sequences, yielding more accurate flame response patterns and enhanced generalization capabilities. Validations confirm that our approach can accurately model flame nonlinear responses, even under conditions of significant nonlinearity, and exhibits robust generalization capabilities across various test scenarios.

Hongkun Dou, Zeyu Li, Xingyu Jiang et al.

Diffusion models (DMs) have recently demonstrated remarkable success in modeling large-scale data distributions. However, many downstream tasks require guiding the generated content based on specific differentiable metrics, typically necessitating backpropagation during the generation process. This approach is computationally expensive, as generating with DMs often demands tens to hundreds of recursive network calls, resulting in high memory usage and significant time consumption. In this paper, we propose a more efficient alternative that approaches the problem from the perspective of parallel denoising. We show that full backpropagation throughout the entire generation process is unnecessary. The downstream metrics can be optimized by retaining the computational graph of only one step during generation, thus providing a shortcut for gradient propagation. The resulting method, which we call Shortcut Diffusion Optimization (SDO), is generic, high-performance, and computationally lightweight, capable of optimizing all parameter types in diffusion sampling. We demonstrate the effectiveness of SDO on several real-world tasks, including controlling generation by optimizing latent and aligning the DMs by fine-tuning network parameters. Compared to full backpropagation, our approach reduces computational costs by $\sim 90\%$ while maintaining superior performance. Code is available at https://github.com/deng-ai-lab/SDO.

Zeyu Li, Hongkun Dou, Shen Fang et al.

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schrödinger Bridge (PalSB). This framework leverages a diffusion Schrödinger bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques.

Xiaohui Yang, Wenming Wu, Yunmei Chen et al.

Microarray gene expression data-based tumor classification is an active and challenging issue. In this paper, an integrated tumor classification framework is presented, which aims to exploit information in existing available samples, and focuses on the small sample problem and unbalanced classification problem. Firstly, an inverse space sparse representation based classification (ISSRC) model is proposed by considering the characteristics of gene-based tumor data, such as sparsity and a small number of training samples. A decision information factors (DIF)-based gene selection method is constructed to enhance the representation ability of the ISSRC. It is worth noting that the DIF is established from reducing clinical misdiagnosis rate and dimension of small sample data. For further improving the representation ability and classification stability of the ISSRC, feature learning is conducted on the selected gene subset. The feature learning method is constructed by complementing the advantages of non-negative matrix factorization (NMF) and deep learning. Without confusion, the ISSRC combined with gene selection and feature learning is called the integrated ISSRC, whose stability, optimization and the corresponding convergence are analyzed. Extensive experiments on six public microarray gene expression datasets show the integrated ISSRC-based tumor classification framework is superior to classical and state-of-the-art methods. There are significant improvements in classification accuracy, specificity and sensitivity, whether there is a tumor in the early diagnosis, what kind of tumor, or whether metastasis occurs after tumor surgery.

Ji Feng, Qingsheng Zhu, Jinlong Huang et al.

Various kinds of k-nearest neighbor (KNN) based classification methods are the bases of many well-established and high-performance pattern-recognition techniques, but both of them are vulnerable to their parameter choice. Essentially, the challenge is to detect the neighborhood of various data sets, while utterly ignorant of the data characteristic. This article introduces a new supervised classification method: the extend natural neighbor (ENaN) method, and shows that it provides a better classification result without choosing the neighborhood parameter artificially. Unlike the original KNN based method which needs a prior k, the ENaNE method predicts different k in different stages. Therefore, the ENaNE method is able to learn more from flexible neighbor information both in training stage and testing stage, and provide a better classification result.