arXiv subjects

Wenhan Gao

Publications and source records attributed to Wenhan Gao.

6 recordsLinked to original sources

arXiv2026

HP-JEPA: Hierarchical Partitioning for Multi-Resolution Graph Joint-Embedding Predictive Learning

Graph self-supervised learning aims to learn transferable representations from large-scale unlabeled graph data. Joint-embedding predictive architectures (JEPAs) avoid explicit negative-pair construction and raw-input reconstruction by predicting masked targets directly in latent space. However, existing graph JEPAs typically rely on a single predefined graph partition, biasing the learned representations toward one structural granularity and limiting their ability to capture complementary patterns at different graph scales. To address this limitation, we propose HP-JEPA, a hierarchical partitioning framework for multi-resolution graph joint-embedding prediction. HP-JEPA organizes each graph into an ordered bank of coarse-to-fine partition resolutions and performs context-target latent prediction separately at each resolution using an online encoder, an exponential-moving-average target encoder, and a latent predictor. The resulting resolution-specific graph representations are subsequently integrated through concatenation or task-specific resolution weighting, allowing downstream models to combine complementary local, regional, and global structural information. Experiments on seven graph classification benchmarks and one graph regression benchmark show that HP-JEPA outperforms the fixed-resolution Graph-JEPA baseline on 6 of 8 tasks, improving upon Graph-JEPA on most evaluated benchmarks. Size-stratified analyses further show that HP-JEPA achieves higher accuracy than Graph-JEPA in most evaluated graph-size quartiles on three representative datasets. These results highlight the effectiveness of hierarchical multi-resolution partitioning for transferable graph representation learning.

cs.LG↗

arXiv2026

GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generation

Gaussian Probability Path based Generative Models (GPPGMs) generate data by reversing a stochastic process that progressively corrupts samples with Gaussian noise. Despite state-of-the-art results in 3D molecular generation, their deployment is hindered by the high cost of long generative trajectories, often requiring hundreds to thousands of steps during training and sampling. In this work, we propose a principled method, named GAGA, to improve generation efficiency without sacrificing training granularity or inference fidelity of GPPGMs. Our key insight is that different data modalities obtain sufficient Gaussianity at markedly different steps during the forward process. Based on this observation, we analytically identify a characteristic step at which molecular data attains sufficient Gaussianity, after which the trajectory can be replaced by a closed-form Gaussian approximation. Unlike existing accelerators that coarsen or reformulate trajectories, our approach preserves full-resolution learning dynamics while avoiding redundant transport through truncated distributional states. Experiments on 3D molecular generation benchmarks demonstrate that our GAGA achieves substantial improvement on both generation quality and computational efficiency.

cs.LG↗

arXiv2025

Can Data-Driven Dynamics Reveal Hidden Physics? There Is A Need for Interpretable Neural Operators

Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms remains underexplored. In this work, we classify neural operators into two types: (1) Spatial domain models that learn on grids and (2) Functional domain models that learn with function bases. We present several viewpoints based on this classification and focus on learning data-driven dynamics adhering to physical principles. Specifically, we provide a way to explain the prediction-making process of neural operators and show that neural operator can learn hidden physical patterns from data. However, this explanation method is limited to specific situations, highlighting the urgent need for generalizable explanation methods. Next, we show that a simple dual-space multi-scale model can achieve SOTA performance and we believe that dual-space multi-spatio-scale models hold significant potential to learn complex physics and require further investigation. Lastly, we discuss the critical need for principled frameworks to incorporate known physics into neural operators, enabling better generalization and uncovering more hidden physical phenomena.

cs.LG↗

arXiv2025

Active Learning Based Sampling for High-Dimensional Nonlinear Partial Differential Equations

The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this approach, an active-learning-based sampling algorithm is proposed in this paper. This algorithm actively chooses the most informative training samples from a probability density function based on residual errors to facilitate error reduction. In particular, points with larger residual errors will have more chances of being selected for training. This algorithm imitates the human learning process: learners are likely to spend more time repeatedly studying mistakes than other tasks they have correctly finished. A series of numerical results are illustrated to demonstrate the effectiveness of our active-learning-based sampling in high dimensions to speed up the convergence of the deep-learning-based least squares method.

math.NA↗

arXiv2025

RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation

3D Geometric Graph Neural Networks (GNNs) have emerged as transformative tools for modeling molecular data. Despite their predictive power, these models often suffer from limited interpretability, raising concerns for scientific applications that require reliable and transparent insights. While existing methods have primarily focused on explaining molecular substructures in 2D GNNs, the transition to 3D GNNs introduces unique challenges, such as handling the implicit dense edge structures created by a cut-off radius. To tackle this, we introduce a novel explanation method specifically designed for 3D GNNs, which localizes the explanation to the immediate neighborhood of each node within the 3D space. Each node is assigned an radius of influence, defining the localized region within which message passing captures spatial and structural interactions crucial for the model's predictions. This method leverages the spatial and geometric characteristics inherent in 3D graphs. By constraining the subgraph to a localized radius of influence, the approach not only enhances interpretability but also aligns with the physical and structural dependencies typical of 3D graph applications, such as molecular learning.

cs.LG↗

arXiv2022

Differential Flatness of Lifting-Wing Quadcopters Subject to Drag and Lift for Accurate Tracking

In this paper, we propose an effective unified control law for accurately tracking agile trajectories for lifting-wing quadcopters with different installation angles, which have the capability of vertical takeoff and landing (VTOL) as well as high-speed cruise flight. First, we derive a differential flatness transform for the lifting-wing dynamics with a nonlinear model under coordinated turn condition. To increase the tracking performance on agile trajectories, the proposed controller incorporates the state and input variables calculated from differential flatness as feedforward. In particular, the jerk, the 3-order derivative of the trajectory, is converted into angular velocity as a feedforward item, which significantly improves the system bandwidth. At the same time, feedback and feedforward outputs are combined to deal with external disturbances and model mismatch. The control algorithm has been thoroughly evaluated in the outdoor flight tests, which show that it can achieve accurate trajectory tracking.

cs.RO↗