Yixiao Chen

Ruining Yang, Yi Xu, Yixiao Chen et al.

Accurate trajectory prediction is fundamental to autonomous driving, as it underpins safe motion planning and collision avoidance in complex environments. However, existing benchmark datasets suffer from a pronounced long-tail distribution problem, with most samples drawn from low-density scenarios and simple straight-driving behaviors. This underrepresentation of high-density scenarios and safety critical maneuvers such as lane changes, overtaking and turning is an obstacle to model generalization and leads to overly optimistic evaluations. To address these challenges, we propose a novel trajectory generation framework that simultaneously enhances scenarios density and enriches behavioral diversity. Specifically, our approach converts continuous road environments into a structured grid representation that supports fine-grained path planning, explicit conflict detection, and multi-agent coordination. Built upon this representation, we introduce behavior-aware generation mechanisms that combine rule-based decision triggers with Frenet-based trajectory smoothing and dynamic feasibility constraints. This design allows us to synthesize realistic high-density scenarios and rare behaviors with complex interactions that are often missing in real data. Extensive experiments on the large-scale Argoverse 1 and Argoverse 2 datasets demonstrate that our method significantly improves both agent density and behavior diversity, while preserving motion realism and scenario-level safety. Our synthetic data also benefits downstream trajectory prediction models and enhances performance in challenging high-density scenarios.

Pengyu Lai, Yixiao Chen, Hui Xu

A primary challenge in using neural networks to approximate nonlinear dynamical systems governed by partial differential equations (PDEs) is transforming these systems into a suitable format, especially when dealing with non-linearizable dynamics or the need for infinite-dimensional spaces for linearization. This paper introduces DyMixOp, a novel neural operator framework for PDEs that integrates insights from complex dynamical systems to address this challenge. Grounded in inertial manifold theory, DyMixOp transforms infinite-dimensional nonlinear PDE dynamics into a finite-dimensional latent space, establishing a structured foundation that maintains essential nonlinear interactions and enhances physical interpretability. A key innovation is the Local-Global-Mixing (LGM) transformation, inspired by convection dynamics in turbulence. This transformation effectively captures both fine-scale details and nonlinear interactions, while mitigating spectral bias commonly found in existing neural operators. The framework is further strengthened by a dynamics-informed architecture that connects multiple LGM layers to approximate linear and nonlinear dynamics, reflecting the temporal evolution of dynamical systems. Experimental results across diverse PDE benchmarks demonstrate that DyMixOp achieves state-of-the-art performance, significantly reducing prediction errors, particularly in convection-dominated scenarios reaching up to 86.7\%, while maintaining computational efficiency and scalability.