Inspired by the Keplerian Map and the Flyby Map, a Gravity Assist Mapping using Gaussian Process Regression for the fully spatial Circular Restricted Three-Body Problem is developed. A mapping function for quantifying the flyby effects over one orbital period is defined. The Gaussian Process Regression model is established by proper mean and covariance functions. The model learns the dynamics of flyby's from training samples, which are generated by numerical propagation. To improve the efficiency of this method, a new criterion is proposed to determine the optimal size of the training dataset. We discuss its robustness to show the quality of practical usage. The influence of different input elements on the flyby effects is studied. The accuracy and efficiency of the proposed model have been investigated for different energy levels, ranging from representative high- to low-energy cases. It shows improvements over the Kick Map, an independent semi-analytical method available in literature. The accuracy and efficiency of predicting the variation of the semi-major axis are improved by factors of 3.3, and 1.27×10⁴, respectively.

We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

Low-thrust trajectories can benefit the search for propellant-optimal trajectories, but increases in modeling complexity and computational load remain a challenge for efficient mission design and optimization. In this paper, an approach for developing models utilizing Gaussian Process (GP) regression and classification is proposed to perform computationally efficient optimization while obtaining acceptable accuracies for trajectories based on exponential sinusoid shaping. The goal of this work is to predict a combination of values of input variables which corresponds to a shape-based trajectory with the smallest total velocity increment (ΔV) or propellant mass fraction (J _m). A GP classification model is constructed to assess whether a given combination of values of input variables corresponds to a feasible trajectory. GP regression models are developed to predict the total ΔV and J _m corresponding to a combination of shape parameters, which can replace the required integration along the shape. In addition, advanced regression models are developed to predict the target values while requiring only three input parameters, thereby replacing the entire shape computation. In order to develop a GP model that fits the problem at hand, the underlying functions and parameters should be selected rationally. In this work, a novel model development approach is proposed to ensure that the mean function, covariance function, likelihood function, inference method, and hyperparameters, which dominate the performance of the models, are chosen rationally in terms of mean absolute percentage error (MAPE) and prediction time. Using this approach, GP models are developed and tested on transfer trajectories from Earth to Mars and Ceres, and from Mars to Earth, and their performance, in terms of MAPE and prediction time, is compared to that of more common optimization techniques in combination with the exponential sinusoid and other shape-based methods. The results demonstrate that the computation time can significantly be reduced while achieving promising MAPE’s, especially when the goal is to locate regions of feasible or near-optimal trajectories. The proposed model development procedure is tested for robustness, which provides confidence in the proposed approach. Furthermore, it is found that the models which map three input variables directly to a ΔV or J _m value perform better than the ones trained with shape information, which demonstrates the strength of GP models as applied to low-thrust trajectory optimization.

Metal-organic frameworks (MOFs) represent a fascinating class of solid crystalline materials which can be self-assembled in a straightforward manner by the coordination of metal ions or clusters with organic ligands. Owing to their intrinsic porous characteristics, unique chemical versatility and abundant functionalities, MOFs have received substantial attention for diverse industrial applications, including membrane separation. Exciting research activities ranging from fabrication strategies to separation applications of MOF-based membranes have appeared. Inspired by the marvelous achievements of MOF-based membranes in gas separations, liquid separations are also being explored for the purpose of constructing continuous MOFs membranes or MOF-based mixed matrix membranes. Although these are in an emerging stage of vigorous development, most efforts are directed towards improving the liquid separation efficiency with well-designed MOF-based membranes. Therefore, as an increasing trend in membrane separation, the field of MOF-based membranes for liquid separation is highlighted in this review. The criteria for judicious selection of MOFs in fabricating MOF-based membranes are given. Special attention is paid to rational design strategies for MOF-based membranes, along with the latest application progress in the area of liquid separations, such as pervaporation, water treatment, and organic solvent nanofiltration. Moreover, some attractive dual-function applications of MOF-based membranes in the removal of micropollutants, degradation, and antibacterial activity are also reviewed. Finally, we define the remaining challenges and future opportunities in this field. This Tutorial Review provides an overview and outlook for MOF-based membranes for liquid separations. Further development of MOF-based membranes for liquid separation must consider the demands of strict separation standards and environmental safety for industrial application.