We present AlphaNet, a local frame-based equivariant model designed to achieve both accurate and efficient simulations for atomistic systems. Recently, machine learning force fields (MLFFs) have gained prominence in molecular dynamics simulations due to their advantageous efficiency-accuracy balance compared to classical force fields and quantum mechanical calculations, alongside their transferability across various systems. Despite the advancements in improving model accuracy, the efficiency and scalability of MLFFs remain significant obstacles in practical applications. AlphaNet enhances computational efficiency and accuracy by leveraging the local geometric structures of atomic environments through the construction of equivariant local frames and learnable frame transitions. We substantiate the efficacy of AlphaNet across diverse datasets, including defected graphene, formate decomposition, zeolites, and surface reactions. AlphaNet consistently surpasses well-established models, such as NequIP and DeepPot, in terms of both energy and force prediction accuracy. Notably, AlphaNet offers one of the best trade-offs between computational efficiency and accuracy among existing models. Moreover, AlphaNet exhibits scalability across a broad spectrum of system and dataset sizes, affirming its versatility.

Sampling critical testing scenarios is an essential step in intelligence testing for Automated Vehicles (AVs). However, due to the lack of prior knowledge on the distribution of critical scenarios in sampling space, we can hardly efficiently find the critical scenarios or accurately evaluate the intelligence of AVs. To solve this problem, we formulate the testing as a continuous optimization process which iteratively generates potential critical scenarios and meanwhile evaluates these scenarios. A bi-level loop is proposed for such life-long learning and testing. In the outer loop, we iteratively learn space knowledge by evaluating AV in the already sampled scenarios and then sample new scenarios based on the retained knowledge. Outer loop stops when all generated samples cover the whole space. While to maximize the coverage of the space in each outer loop, we set an inner loop which receives newly generated samples in outer loop and outputs the updated positions of these samples. We assume that points in a small sphere-like subspace can be covered (or represented) by the point in the center of this sphere. Therefore, we can apply a multi-rounds heuristic strategy to move and pack these spheres in space to find the best covering solution. The simulation results show that faster and more accurate evaluation of AVs can be achieved with more critical scenarios.