Point Cloud Registration (PCR) estimates the relative rigid transformation between two point clouds of the same scene. Despite significant progress with learning-based approaches, existing methods still face challenges when the overlapping region between the two point clouds is small. In this paper, we propose an adaptive multi-step refinement network that refines the registration quality at each step by leveraging the information from the preceding step. To achieve this, we introduce a training procedure and a refinement network. Firstly, to adapt the network to the current step, we utilize a generalized one-way attention mechanism, which prioritizes the last step's estimated overlapping region, and we condition the network on step indices. Secondly, instead of training the network to map either random transformations or a fixed pre-trained model's estimations to the ground truth, we train it on transformations with varying registration qualities, ranging from accurate to inaccurate, thereby enhancing the network's adaptiveness and robustness. Despite its conceptual simplicity, our method achieves state-of-the-art performance on both the 3DMatch/3DLoMatch and KITTI benchmarks. Notably, on 3DLoMatch, our method reaches 80.4% recall rate, with an absolute improvement of 1.2%.
Machine learning has long been considered as a black box for predicting combustion chemical kinetics due to the extremely large number of parameters and the lack of evaluation standards and reproducibility. The current work aims to understand two basic questions regarding the deep neural network (DNN) method: what data the DNN needs and how general the DNN method can be. Sampling and preprocessing determine the DNN training dataset, further affect DNN prediction ability. The current work proposes using Box-Cox transformation (BCT) to preprocess the combustion data. In addition, this work compares different sampling methods with or without preprocessing, including the Monte Carlo method, manifold sampling, generative neural network method (cycle-GAN), and newly-proposed multi-scale sampling. Our results reveal that the DNN trained by the manifold data can capture the chemical kinetics in limited configurations but cannot remain robust toward perturbation, which is inevitable for the DNN coupled with the flow field. The Monte Carlo and cycle-GAN samplings can cover a wider phase space but fail to capture small-scale intermediate species, producing poor prediction results. A three-hidden-layer DNN, based on the multi-scale method without specific flame simulation data, allows predicting chemical kinetics in various scenarios and being stable during the temporal evolutions. This single DNN is readily implemented with several CFD codes and validated in various combustors, including (1). zero-dimensional autoignition, (2). one-dimensional freely propagating flame, (3). two-dimensional jet flame with triple-flame structure, and (4). three-dimensional turbulent lifted flames. The results demonstrate the satisfying accuracy and generalization ability of the pre-trained DNN. The Fortran and Python versions of DNN and example code are attached in the supplementary for reproducibility.