Junfeng Chen

Junfeng Chen

Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not determine a unique effective response, and a low-resolution observation may correspond to many plausible high-resolution fields. In such settings, deterministic surrogates may learn a well-defined mathematical object while still missing application-relevant uncertainty. This tutorial develops a self-contained module centered on the conditional-mean barrier: the point at which a squared-loss predictor has reached the conditional mean and the remaining error is irreducible aleatoric variance. We give two diagnostics for locating this barrier, residual-feature orthogonality and the coefficient of determination against its explained-variance ceiling, and prove that adding latent randomness to a squared-loss predictor collapses it back to the conditional mean. Crossing the barrier therefore requires a loss that scores distributions rather than point predictions. We briefly organize common distributional objectives, including negative log-likelihood, moment and observable matching, variational objectives, adversarial divergences, and score matching, by the feature of the conditional law each targets. The emphasis is the boundary itself and a finite-data procedure for recognizing it, rather than a survey of methods beyond it. CPU-based demonstrations on a two-branch law and a two-scale Lorenz-96 closure problem show how the diagnostics distinguish deterministic underfitting from residual distributional variability.

Junfeng Chen, Kailiang Wu

This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous flow map learning (FML) works [T. Qin, K. Wu, and D. Xiu, J. Comput. Phys., 395:620--635, 2019], [K. Wu and D. Xiu, J. Comput. Phys., 408:109307, 2020], and [Z. Chen, V. Churchill, K. Wu, and D. Xiu, J. Comput. Phys., 449:110782, 2022], which focused on learning single evolution operator with a fixed time step. This paper aims to learn a family of evolution operators with variable time steps, which constitute a semigroup for an autonomous system. The semigroup property is very crucial and links the system's evolutionary behaviors across varying time scales, but it was not considered in the previous works. We propose for the first time a framework of embedding the semigroup property into the data-driven learning process, through a novel neural network architecture and new loss functions. The framework is very feasible, can be combined with any suitable neural networks, and is applicable to learning general autonomous ODEs and PDEs. We present the rigorous error estimates and variance analysis to understand the prediction accuracy and robustness of our approach, showing the remarkable advantages of semigroup awareness in our model. Moreover, our approach allows one to arbitrarily choose the time steps for prediction and ensures that the predicted results are well self-matched and consistent. Extensive numerical experiments demonstrate that embedding the semigroup property notably reduces the data dependency of deep learning models and greatly improves the accuracy, robustness, and stability for long-time prediction.

Junfeng Chen, Kailiang Wu, Dongbin Xiu

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex systems remain unknown due to intricate underlying mechanisms. Recent advancements in machine learning and data science offer a new paradigm for modeling unknown equations from measurement or simulation data. This paradigm shift, known as data-driven discovery or modeling, stands at the forefront of AI for science, with significant progress made in recent years. In this paper, we introduce a systematic framework for data-driven modeling of unknown equations using deep learning. This versatile framework is capable of learning unknown ODEs, PDEs, DAEs, IDEs, SDEs, reduced or partially observed systems, and non-autonomous differential equations. Based on this framework, we have developed Deep Unknown Equations (DUE), an open-source software package designed to facilitate the data-driven modeling of unknown equations using modern deep learning techniques. DUE serves as an educational tool for classroom instruction, enabling students and newcomers to gain hands-on experience with differential equations, data-driven modeling, and contemporary deep learning approaches such as FNN, ResNet, generalized ResNet, operator semigroup networks (OSG-Net), and Transformers. Additionally, DUE is a versatile and accessible toolkit for researchers across various scientific and engineering fields. It is applicable not only for learning unknown equations from data but also for surrogate modeling of known, yet complex, equations that are costly to solve using traditional numerical methods. We provide detailed descriptions of DUE and demonstrate its capabilities through diverse examples, which serve as templates that can be easily adapted for other applications.

Junfeng Chen, Yuxiao Zhu, An Zhuo et al.

Robot swarms promise scalable assistance in complex and hazardous environments. Task planning lies at the core of human-swarm collaboration, translating the operator's intent into coordinated swarm actions and helping determine when validation or intervention is required during execution. In long-horizon missions under dynamic scenarios, however, reliable task planning becomes difficult to maintain: emerging events and changing conditions demand continual adaptation, and sustained operator oversight imposes substantial cognitive burden. Existing LLM-based planning tools can support plan generation, yet they remain susceptible to invalid task orderings and infeasible robot actions, resulting in frequent manual adjustment. Here we introduce a neuro-symbolic framework for long-horizon human-swarm collaboration that tightly melds verifiable task planning with context-grounded LLM reasoning. We formalize mission goals and operational rules as temporal logic formulas and admissible task orderings as task automata. Conditioned on these formal constraints and live perceptual context, LLMs generate executable subtask sequences that satisfy mission rules and remain grounded in the current scene. An uncertainty-aware scheduler then assigns subtasks across the heterogeneous swarm to maximize parallelisms while remaining resilient to disruptions. An event-triggered interaction protocol further limits operator involvement to sparse, high-level confirmation and guidance. Deployment on a heterogeneous robotic fleet yields similar results while remaining robust to hardware-specific actuation and communication uncertainties. Together, these results support a formal and scalable paradigm for reliable and low-overhead human-swarm collaboration in dynamic environments

Junfeng Chen, Kailiang Wu

Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems. Transformers with the self-attention mechanism$\unicode{x2013}$a powerful tool originally designed for natural language processing$\unicode{x2013}$have recently been adapted for operator learning. However, they confront challenges, including high computational demands and limited interpretability. This raises a critical question: Is there a more efficient attention mechanism for Transformer-based operator learning? This paper proposes the Position-induced Transformer (PiT), built on an innovative position-attention mechanism, which demonstrates significant advantages over the classical self-attention in operator learning. Position-attention draws inspiration from numerical methods for PDEs. Different from self-attention, position-attention is induced by only the spatial interrelations of sampling positions for input functions of the operators, and does not rely on the input function values themselves, thereby greatly boosting efficiency. PiT exhibits superior performance over current state-of-the-art neural operators in a variety of complex operator learning tasks across diverse PDE benchmarks. Additionally, PiT possesses an enhanced discretization convergence feature, compared to the widely-used Fourier neural operator.

Jin Lian, Zhongyu Wan, Ming Gao et al.

Cross-layer feature pyramid networks (CFPNs) have achieved notable progress in multi-scale feature fusion and boundary detail preservation for salient object detection. However, traditional CFPNs still suffer from two core limitations: (1) a computational bottleneck caused by complex feature weighting operations, and (2) degraded boundary accuracy due to feature blurring in the upsampling process. To address these challenges, we propose CFMD, a novel cross-layer feature pyramid network that introduces two key innovations. First, we design a context-aware feature aggregation module (CFLMA), which incorporates the state-of-the-art Mamba architecture to construct a dynamic weight distribution mechanism. This module adaptively adjusts feature importance based on image context, significantly improving both representation efficiency and generalization. Second, we introduce an adaptive dynamic upsampling unit (CFLMD) that preserves spatial details during resolution recovery. By adjusting the upsampling range dynamically and initializing with a bilinear strategy, the module effectively reduces feature overlap and maintains fine-grained boundary structures. Extensive experiments on three standard benchmarks using three mainstream backbone networks demonstrate that CFMD achieves substantial improvements in pixel-level accuracy and boundary segmentation quality, especially in complex scenes. The results validate the effectiveness of CFMD in jointly enhancing computational efficiency and segmentation performance, highlighting its strong potential in salient object detection tasks.

Fuqin Deng, Hua Feng, Mingjian Liang et al.

The occupancy grid map is a critical component of autonomous positioning and navigation in the mobile robotic system, as many other systems' performance depends heavily on it. To guarantee the quality of the occupancy grid maps, researchers previously had to perform tedious manual recognition for a long time. This work focuses on automatic abnormal occupancy grid map recognition using the residual neural networks and a novel attention mechanism module. We propose an effective channel and spatial Residual SE(csRSE) attention module, which contains a residual block for producing hierarchical features, followed by both channel SE (cSE) block and spatial SE (sSE) block for the sufficient information extraction along the channel and spatial pathways. To further summarize the occupancy grid map characteristics and experiment with our csRSE attention modules, we constructed a dataset called occupancy grid map dataset (OGMD) for our experiments. On this OGMD test dataset, we tested few variants of our proposed structure and compared them with other attention mechanisms. Our experimental results show that the proposed attention network can infer the abnormal map with state-of-the-art (SOTA) accuracy of 96.23% for abnormal occupancy grid map recognition.

Fuqin Deng, Hua Feng, Mingjian Liang et al.

The RGB-Thermal (RGB-T) information for semantic segmentation has been extensively explored in recent years. However, most existing RGB-T semantic segmentation usually compromises spatial resolution to achieve real-time inference speed, which leads to poor performance. To better extract detail spatial information, we propose a two-stage Feature-Enhanced Attention Network (FEANet) for the RGB-T semantic segmentation task. Specifically, we introduce a Feature-Enhanced Attention Module (FEAM) to excavate and enhance multi-level features from both the channel and spatial views. Benefited from the proposed FEAM module, our FEANet can preserve the spatial information and shift more attention to high-resolution features from the fused RGB-T images. Extensive experiments on the urban scene dataset demonstrate that our FEANet outperforms other state-of-the-art (SOTA) RGB-T methods in terms of objective metrics and subjective visual comparison (+2.6% in global mAcc and +0.8% in global mIoU). For the 480 x 640 RGB-T test images, our FEANet can run with a real-time speed on an NVIDIA GeForce RTX 2080 Ti card.

Junfeng Chen, Yuan Gao, Junjie Hu et al.

We study a novel problem that tackles learning based sensor scanning in 3D and uncertain environments with heterogeneous multi-robot systems. Our motivation is two-fold: first, 3D environments are complex, the use of heterogeneous multi-robot systems intuitively can facilitate sensor scanning by fully taking advantage of sensors with different capabilities. Second, in uncertain environments (e.g. rescue), time is of great significance. Since the learning process normally takes time to train and adapt to a new environment, we need to find an effective way to explore and adapt quickly. To this end, in this paper, we present a meta-learning approach to improve the exploration and adaptation capabilities. The experimental results demonstrate our method can outperform other methods by approximately 15%-27% on success rate and 70%-75% on adaptation speed.

Tianwei Zhang, Huayan Zhang, Xiaofei Li et al.

Dynamic objects in the environment, such as people and other agents, lead to challenges for existing simultaneous localization and mapping (SLAM) approaches. To deal with dynamic environments, computer vision researchers usually apply some learning-based object detectors to remove these dynamic objects. However, these object detectors are computationally too expensive for mobile robot on-board processing. In practical applications, these objects output noisy sounds that can be effectively detected by on-board sound source localization. The directional information of the sound source object can be efficiently obtained by direction of sound arrival (DoA) estimation, but depth estimation is difficult. Therefore, in this paper, we propose a novel audio-visual fusion approach that fuses sound source direction into the RGB-D image and thus removes the effect of dynamic obstacles on the multi-robot SLAM system. Experimental results of multi-robot SLAM in different dynamic environments show that the proposed method uses very small computational resources to obtain very stable self-localization results.

Junjie Hu, Xiyue Guo, Junfeng Chen et al.

As vision based perception methods are usually built on the normal light assumption, there will be a serious safety issue when deploying them into low light environments. Recently, deep learning based methods have been proposed to enhance low light images by penalizing the pixel-wise loss of low light and normal light images. However, most of them suffer from the following problems: 1) the need of pairs of low light and normal light images for training, 2) the poor performance for dark images, 3) the amplification of noise. To alleviate these problems, in this paper, we propose a two-stage unsupervised method that decomposes the low light image enhancement into a pre-enhancement and a post-refinement problem. In the first stage, we pre-enhance a low light image with a conventional Retinex based method. In the second stage, we use a refinement network learned with adversarial training for further improvement of the image quality. The experimental results show that our method outperforms previous methods on four benchmark datasets. In addition, we show that our method can significantly improve feature points matching and simultaneous localization and mapping in low light conditions.

Xiyue Guo, Junjie Hu, Junfeng Chen et al.

The core problem of visual multi-robot simultaneous localization and mapping (MR-SLAM) is how to efficiently and accurately perform multi-robot global localization (MR-GL). The difficulties are two-fold. The first is the difficulty of global localization for significant viewpoint difference. Appearance-based localization methods tend to fail under large viewpoint changes. Recently, semantic graphs have been utilized to overcome the viewpoint variation problem. However, the methods are highly time-consuming, especially in large-scale environments. This leads to the second difficulty, which is how to perform real-time global localization. In this paper, we propose a semantic histogram-based graph matching method that is robust to viewpoint variation and can achieve real-time global localization. Based on that, we develop a system that can accurately and efficiently perform MR-GL for both homogeneous and heterogeneous robots. The experimental results show that our approach is about 30 times faster than Random Walk based semantic descriptors. Moreover, it achieves an accuracy of 95% for global localization, while the accuracy of the state-of-the-art method is 85%.