Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition

The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a novel framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through Tensor Train (TT) decomposition. Our approach combines two complementary TT-based strategies: the algebraic TTOpt method, which utilizes maximum volume sampling, and the probabilistic PROTES method, which employs generative sampling. A key innovation is the development of physically-constrained encoding schemes that incorporate molecular constraints directly into the discretization process. We demonstrate the efficacy of our method by identifying global minima of Lennard-Jones clusters containing up to 45 atoms. Furthermore, we establish its practical applicability to real-world systems by optimizing 20-atom carbon clusters using a machine-learned Moment Tensor Potential, achieving geometries consistent with quantum-accurate simulations. This work establishes TT-decomposition as a powerful tool for molecular structure prediction and provides a general framework adaptable to a wide range of high-dimensional optimization problems in computational material science.

Enhanced Parking Perception by Multi-Task Fisheye Cross-view Transformers

Current parking area perception algorithms primarily focus on detecting vacant slots within a limited range, relying on error-prone homographic projection for both labeling and inference. However, recent advancements in Advanced Driver Assistance System (ADAS) require interaction with end-users through comprehensive and intelligent Human-Machine Interfaces (HMIs). These interfaces should present a complete perception of the parking area going from distinguishing vacant slots' entry lines to the orientation of other parked vehicles. This paper introduces Multi-Task Fisheye Cross View Transformers (MT F-CVT), which leverages features from a four-camera fisheye Surround-view Camera System (SVCS) with multihead attentions to create a detailed Bird-Eye View (BEV) grid feature map. Features are processed by both a segmentation decoder and a Polygon-Yolo based object detection decoder for parking slots and vehicles. Trained on data labeled using LiDAR, MT F-CVT positions objects within a 25m x 25m real open-road scenes with an average error of only 20 cm. Our larger model achieves an F-1 score of 0.89. Moreover the smaller model operates at 16 fps on an Nvidia Jetson Orin embedded board, with similar detection results to the larger one. MT F-CVT demonstrates robust generalization capability across different vehicles and camera rig configurations. A demo video from an unseen vehicle and camera rig is available at: https://streamable.com/jjw54x.