Hongxu Liu

Hongxu Liu, Xiangmin Jiao

ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.

Hang Chen, Jiaying Zhu, Hongyang Chen et al.

The "Locate-then-Update" paradigm has become a predominant approach in the post-training of large language models (LLMs), identifying critical components via mechanistic interpretability for targeted parameter updates. However, this paradigm rests on a fundamental yet unverified assumption: can mechanisms derived from current static parameters reliably guide future dynamic parameter updates? To investigate this, we systematically track the structural evolution of Transformer circuits throughout the supervised fine-tuning (SFT) process, revealing the underlying dynamics of task mechanisms. We introduce three novel metrics-Circuit Distance, Circuit Stability, and Circuit Conflict-to analyze circuit evolution across three dimensions: neural migration, semantic stability, and cross-task interference. Our empirical results reveal that circuits inherently exhibit "Free Evolution" during parameter updates. Consequently, static mechanisms extracted from current states inevitably suffer from temporal latency, making them fundamentally inadequate for guiding future states. Moreover, by deconstructing the "illusion of effectiveness" in existing methods, this work underscores the necessity of "foresight" in mechanistic localization and proposes a predictive framework for future research.

Hongxu Liu, Xinyu Chen, Haoyang Zheng et al.

Recovering a continuous colormap from a single 2D scalar field visualization can be quite challenging, especially in the absence of a corresponding color legend. In this paper, we propose a novel colormap recovery approach that extracts the colormap from a color-encoded 2D scalar field visualization by simultaneously predicting the colormap and underlying data using a decoupling-and-reconstruction strategy. Our approach first separates the input visualization into colormap and data using a decoupling module, then reconstructs the visualization with a differentiable color-mapping module. To guide this process, we design a reconstruction loss between the input and reconstructed visualizations, which serves both as a constraint to ensure strong correlation between colormap and data during training, and as a self-supervised optimizer for fine-tuning the predicted colormap of unseen visualizations during inferencing. To ensure smoothness and correct color ordering in the extracted colormap, we introduce a compact colormap representation using cubic B-spline curves and an associated color order loss. We evaluate our method quantitatively and qualitatively on a synthetic dataset and a collection of real-world visualizations from the VIS30K dataset. Additionally, we demonstrate its utility in two prototype applications -- colormap adjustment and colormap transfer -- and explore its generalization to visualizations with color legends and ones encoded using discrete color palettes.

Yunlei Shi, Zhaopeng Chen, Yansong Wu et al.

Collaborative robots are expected to be able to work alongside humans and in some cases directly replace existing human workers, thus effectively responding to rapid assembly line changes. Current methods for programming contact-rich tasks, especially in heavily constrained space, tend to be fairly inefficient. Therefore, faster and more intuitive approaches to robot teaching are urgently required. This work focuses on combining visual servoing based learning from demonstration (LfD) and force-based learning by exploration (LbE), to enable fast and intuitive programming of contact-rich tasks with minimal user effort required. Two learning approaches were developed and integrated into a framework, and one relying on human to robot motion mapping (the visual servoing approach) and one on force-based reinforcement learning. The developed framework implements the non-contact demonstration teaching method based on visual servoing approach and optimizes the demonstrated robot target positions according to the detected contact state. The framework has been compared with two most commonly used baseline techniques, pendant-based teaching and hand-guiding teaching. The efficiency and reliability of the framework have been validated through comparison experiments involving the teaching and execution of contact-rich tasks. The framework proposed in this paper has performed the best in terms of teaching time, execution success rate, risk of damage, and ease of use.

Yunlei Shi, Zhaopeng Chen, Hongxu Liu et al.

Contact-rich manipulation tasks are commonly found in modern manufacturing settings. However, manually designing a robot controller is considered hard for traditional control methods as the controller requires an effective combination of modalities and vastly different characteristics. In this paper, we firstly consider incorporating operational space visual and haptic information into reinforcement learning(RL) methods to solve the target uncertainty problem in unstructured environments. Moreover, we propose a novel idea of introducing a proactive action to solve the partially observable Markov decision process problem. Together with these two ideas, our method can either adapt to reasonable variations in unstructured environments and improve the sample efficiency of policy learning. We evaluated our method on a task that involved inserting a random-access memory using a torque-controlled robot, and we tested the success rates of the different baselines used in the traditional methods. We proved that our method is robust and can tolerate environmental variations very well.