Xueyu Zhu

Andrew Pensoneault, Xueyu Zhu

Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI) for high-dimensional inference tasks. We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost. These findings suggest that our proposed approach has great potential for uncertainty quantification in physics-informed machine learning for practical applications.

Jiayan Cao, Xueyu Zhu, Cheng Qian

Lane detection plays a critical role in the field of autonomous driving. Prevailing methods generally adopt basic concepts (anchors, key points, etc.) from object detection and segmentation tasks, while these approaches require manual adjustments for curved objects, involve exhaustive searches on predefined anchors, require complex post-processing steps, and may lack flexibility when applied to real-world scenarios.In this paper, we propose a novel approach, LanePtrNet, which treats lane detection as a process of point voting and grouping on ordered sets: Our method takes backbone features as input and predicts a curve-aware centerness, which represents each lane as a point and assigns the most probable center point to it. A novel point sampling method is proposed to generate a set of candidate points based on the votes received. By leveraging features from local neighborhoods, and cross-instance attention score, we design a grouping module that further performs lane-wise clustering between neighboring and seeding points. Furthermore, our method can accommodate a point-based framework, (PointNet++ series, etc.) as an alternative to the backbone. This flexibility enables effortless extension to 3D lane detection tasks. We conduct comprehensive experiments to validate the effectiveness of our proposed approach, demonstrating its superior performance.

Andrew Pensoneault, Xueyu Zhu

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and noisy data, accessing the uncertainty in DeepONet predictions becomes essential, especially in mission-critical or safety-critical applications. Existing methods, either computationally intensive or yielding unsatisfactory uncertainty quantification, leave room for developing efficient and informative uncertainty quantification (UQ) techniques tailored for DeepONets. In this work, we proposed a novel inference approach for efficient UQ for operator learning by harnessing the power of the Ensemble Kalman Inversion (EKI) approach. EKI, known for its derivative-free, noise-robust, and highly parallelizable feature, has demonstrated its advantages for UQ for physics-informed neural networks [28]. Our innovative application of EKI enables us to efficiently train ensembles of DeepONets while obtaining informative uncertainty estimates for the output of interest. We deploy a mini-batch variant of EKI to accommodate larger datasets, mitigating the computational demand due to large datasets during the training stage. Furthermore, we introduce a heuristic method to estimate the artificial dynamics covariance, thereby improving our uncertainty estimates. Finally, we demonstrate the effectiveness and versatility of our proposed methodology across various benchmark problems, showcasing its potential to address the pressing challenges of uncertainty quantification in DeepONets, especially for practical applications with limited and noisy data.