Thermodynamic activity coefficients play an essential role in the description of phase equilibria, which are fundamental to the simulation and optimization of all separation processes. Although it is known that multiplicities with respect to binary interaction parameters can occur, no systematic study of these multiplicities has been undertaken yet. In this contribution, their rigorous pointwise classification is presented, valid for the entire range of binary compositions. Furthermore, implications not only for the non‐random two‐lqiuid (NRTL)‐parameterization to capture temperature‐dependence are discussed, but also for extrapolation and regression tasks. The findings are illustrated for vapor‐liquid equilibria of different binary mixtures.

Wind comfort is an important factor when new buildings in existing urban areas are planned. It is common practice to use computational fluid dynamics (CFD) simulations to model wind comfort. These simulations are usually time-consuming, making it impossible to explore a high number of different design choices for a new urban development with wind simulations. Data-driven approaches based on simulations have shown great promise, and have recently been used to predict wind comfort in urban areas. These surrogate models could be used in generative design software and would enable the planner to explore a large number of options for a new design. In this paper, we propose a novel machine learning workflow (MLW) for direct wind comfort prediction. The MLW incorporates a regression and a classification U-Net, trained based on CFD simulations. Furthermore, we present an augmentation strategy focusing on generating more training data independent of the underlying wind statistics needed to calculate the wind comfort criterion. We train the models based on different sets of training data and compare the results. All trained models (regression and classification) yield an $F_1$-score greater than 80% and can be combined with any wind rose statistic.

Accurate prediction of urban wind flow is essential for urban planning and environmental assessment. Classical computational fluid dynamics (CFD) methods are computationally expensive, while machine learning approaches often lack explainability and generalizability. To address the limitations of both approaches, we propose Diff-KNN, a hybrid method that combines Coarse-Scale CFD simulations with a K-Nearest Neighbors (KNN) model trained on the residuals between coarse- and fine-scale CFD results. Diff-KNN reduces velocity prediction errors by up to 83.5% compared to Pure-KNN and 56.6% compared to coarse CFD alone. Tested on the AIJE urban dataset, Diff-KNN effectively corrects flow inaccuracies near buildings and within narrow street canyons, where traditional methods struggle. This study demonstrates how residual learning can bridge physics-based and data-driven modeling for accurate and interpretable fine-scale urban wind prediction.

For the location optimization of several ambulance stations, we outline a multi-criteria integer program to maximize the reached population within different time bounds. This technique is based on a realistic driving time estimation for ambulances on a detailed road network. The results show that, depending on which time bound is more valued, ambulance stations are more likely to be located in urban areas or evenly distributed across the study region. We used this model for real-world studies in Southwest Germany, where several ambulance station locations were optimized simultaneously.