Yifeng Xu

Qian Zhang, Long Chen, Yifeng Xu

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed convex set and is shown to be unconditionally energy stable. By the minimization approach, we also derive an variant of the first-order scheme for the Allen-Cahn equation, which has been constructed in the context of Invariant Energy Quadratization, and prove its unconditional energy stability.

Tianhao Hu, Guanglian Li, Fengru Wang et al.

The reliable and accurate numerical approximation of the $p$-Laplacian is particularly challenging in the extreme regimes $p \to 1^{+}$ and $p \gg 1$, where the operator becomes either highly singular or strongly degenerate, often causing severe instability in standard numerical methods. To address these difficulties, we propose a novel deep learning based framework, termed the dual variational neural network, for $p$-Laplace problems. The approach is based on a mixed formulation and an $L^q$-based Helmholtz decomposition, which decouples the original problem into two convex subproblems: a linear Poisson problem for the irrotational component and an unconstrained minimization problem over divergence-free fields for the solenoidal component. Following the decomposition, we employ two neural networks using a gradient--curl representation to approximate the flux, and further establish an error analysis of the neural approximation. The analysis relies on fundamental vector inequalities together with tools from statistical learning theory. Numerical experiments demonstrate robust convergence of the proposed method in challenging settings, including the extreme cases $p \to 1^{+}$ and $p \gg 1$, as well as the $p(x)$-Laplace equation.

Bangti Jin, Jing Li, Yifeng Xu et al.

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element space to approximate the phase field, and the nonconforming linear finite elements (Crouzeix-Raviart elements) and piecewise constants to approximate the velocity field and the pressure field, respectively. We establish the convergence of the adaptive method, i.e., the sequence of minimizers contains a subsequence that converges to a solution of the first-order optimality system, and the associated subsequence of discrete pressure fields also converges. The analysis relies crucially on a new discrete compactness result of nonconforming linear finite elements over a sequence of adaptively generated meshes. We present numerical results for several examples to illustrate the performance of the algorithm, including a comparison with the uniform refinement strategy.

Huilin Yin, Yangwenhui Xu, Jiaxiang Li et al.

Multi-agent trajectory prediction at signalized intersections is crucial for developing efficient intelligent transportation systems and safe autonomous driving systems. Due to the complexity of intersection scenarios and the limitations of single-vehicle perception, the performance of vehicle-centric prediction methods has reached a plateau. In this paper, we introduce an Infrastructure-to-Everything (I2X) collaborative prediction scheme. In this scheme, roadside units (RSUs) independently forecast the future trajectories of all vehicles and transmit these predictions unidirectionally to subscribing vehicles. Building on this scheme, we propose I2XTraj, a dedicated infrastructure-based trajectory prediction model. I2XTraj leverages real-time traffic signal states, prior maneuver strategy knowledge, and multi-agent interactions to generate accurate, joint multi-modal trajectory prediction. First, a continuous signal-informed mechanism is proposed to adaptively process real-time traffic signals to guide trajectory proposal generation under varied intersection configurations. Second, a driving strategy awareness mechanism estimates the joint distribution of maneuver strategies by integrating spatial priors of intersection areas with dynamic vehicle states, enabling coverage of the full set of feasible maneuvers. Third, a spatial-temporal-mode attention network models multi-agent interactions to refine and adjust joint trajectory outputs.Finally, I2XTraj is evaluated on two real-world datasets of signalized intersections, the V2X-Seq and the SinD drone dataset. In both single-infrastructure and online collaborative scenarios, our model outperforms state-of-the-art methods by over 30\% on V2X-Seq and 15\% on SinD, demonstrating strong generalizability and robustness.