Kun Cai

Kun Cai, David Y. Gao, Qing H. Qin

Post buckling problem of a large deformed beam is analyzed using canonical dual finite element method (CD-FEM). The feature of this method is to choose correctly the canonical dual stress so that the original non-convex potential energy functional is reformulated in a mixed complementary energy form with both displacement and stress fields, and a pure complementary energy is explicitly formulated in finite dimensional space. Based on the canonical duality theory and the associated triality theorem, a primal-dual algorithm is proposed, which can be used to find all possible solutions of this nonconvex post-buckling problem. Numerical results show that the global maximum of the pure-complementary energy leads to a stable buckled configuration of the beam. While the local extrema of the pure-complementary energy present unstable deformation states, especially. We discovered that the unstable buckled state is very sensitive to the number of total elements and the external loads. Theoretical results are verified through numerical examples and some interesting phenomena in post-bifurcation of this large deformed beam are observed.

Junyuan Zhang, Jing Cao, Abdullah Dawar et al.

In continuum topology optimization (TO), two essential procedures are involved: structural analysis through the solution of partial differential equations (PDEs) and the subsequent update of design variables. Both procedures can be addressed by training neural networks using the corresponding physical information. Accordingly, Physics-Informed Neural Network (PINN)-based algorithms have been developed for TO. However, PINN-based methods suffer from several notable limitations, including high computational cost, spectral bias, and limited adaptability in solving PDEs.To overcome these challenges, this study proposes a novel algorithm that incorporates two Higher-Order ReLU-based Kolmogorov-Arnold Networks (HRKANs). Specifically, a displacement-informed HRKAN (d-HRKAN) is designed to predict PDE solutions, while a sensitivity-informed HRKAN (s-HRKAN) is developed to perform sensitivity analysis for updating design variables. For convenience, the proposed approach is referred to as the Dual Physics-Informed Kolmogorov-Arnold Networks-based Topology Optimization (DPIKAN-TO) method. By leveraging learnable activation functions, the proposed neural networks can accurately approximate the responses of complex structural systems. Moreover, compared with conventional PINN-based methods, DPIKAN-TO demonstrates significantly improved computational efficiency and reduced computational cost. Numerical examples show that DPIKAN-TO can successfully identify optimal material layouts for linear structures, compliant mechanisms, and fluid-solid coupled systems. Furthermore, owing to the use of learnable activation functions, the proposed framework can be readily extended to structural optimization problems governed by new types of PDEs.

Xinquan Chen, Zhenyun Yin, Shan He et al.

As large models evolve from conversational assistants into autonomous agents, challenges increasingly arise from long-horizon decision making, tool use, and real environment interaction. Existing agenticinfrastructure remain fragmented across evaluation, data management, and agent evolution, making it difficult to discover risks systematically and improve models in a continuous closed loop. In this report, we present \textbf{Safactory}, a scalable agent factory for trustworthy autonomous intelligence. Safactory integrates three tightly coupled platforms: a \textbf{Parallel Simulation Platform} for trajectory generation, a \textbf{Trustworthy Data Platform} for trajectory storage and experience extraction, and an \textbf{Autonomous Evolution Platform} for asynchronous reinforcement learning and on-policy distillation. As far as we know, Safactory is the first framework to propose a unified evolutionary pipeline for next-generation trustworthy autonomous intelligence.