As an indicator of urbanization, high-rise residential buildings, can meet the space requirements of an increasing population and improve land use efficiency. Such buildings are continuously built in the central areas of cities worldwide despite residential suburbanization. To predict high-rise residential building location, this study employs a geographic field model-based autologistic regression model (GFM-autologistic model). In line with this goal, a model is determined using both the value of the area under the receiver operating characteristic curve (ROC) and the Akaike information criterion (AIC) for GFM-autologistic, Euclidean distance (ED)-logistic and ED-autologistic models. The minimum AIC and the maximum ROC values of the GFM-autologistic model indicate that this model has the best fit. The GFM defines the external effect of ecological elements and locational factors, and it also quantifies distance decay through a linear intensity function with an influence threshold, thereby avoiding the bias caused by ED. Moreover, land prices are positive related to building height. High-rise residential development also considers open public spaces, such as rivers and city plazas. In summary, the spatial distribution of high-rise residential buildings displays a distance decay in the effect of ecological elements such as open spaces. Thus, this manuscript provides a theoretical basis for modern-city development planning and modern high-rise residential development.

Accurate estimate of long-term risk is critical for safe decision-making, but sampling from rare risk events and long-term trajectories can be prohibitively costly. Risk gradient can be used in many first-order techniques for learning and control methods, but gradient estimate is difficult to obtain using Monte Carlo (MC) methods because the infinitesimal divisor may significantly amplify sampling noise. Motivated by this gap, we propose an efficient method to evaluate long-term risk probabilities and their gradients using short-term samples without sufficient risk events. We first derive that four types of long-term risk probability are solutions of certain partial differential equations (PDEs). Then, we propose a physicsinformed learning technique that integrates data and physics information (aforementioned PDEs). The physics information helps propagate information beyond available data and obtain provable generalization beyond available data, which in turn enables long-term risk to be estimated using short-term samples of safe events. Finally, we demonstrate in simulation that the proposed technique has improved sample efficiency, generalizes well to unseen regions, and adapts to changing system parameters.

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