-- Human activity intensity prediction is crucial to many location - based services. Despite tremendous p rogress in modeling d ynamics of human activity, most existing methods overlook physical constraints of spatial interaction, leading to uninterpretable spatial correlations and over - smoothing phenomenon . To address these limitations, this work proposes a physics - informed deep learning framework, namely Gravity - informed Spatiotemporal Transformer (Gravityformer) by integrat ing the universal law of gravitation to refin e transformer attention. Specifically, it (1) estimates two spatially explicit mass parameters based on spatiotemporal embedding feature, (2) models the spatial interaction in end - to - end neural network using proposed adaptive gravity model to learn the physic al constrain t, and (3) utilizes the learned spatial interaction to guide and mitigate the over - smoothing phenomenon in transformer attention. Moreover, a parallel spatiotemporal graph convolution transformer is proposed for achieving a balance between coupled spatial and temporal learning. Systematic experiments on six real - world large - scale activity datasets demonstrate the quantitative and qualitative superiority of our model over state - of - the - art benchmarks. Additionally, the learned gravity attention matrix can be not only disentangled and interpreted based on geographical laws, but also improved the generalization in zero - shot cross - region inference . This work provides a novel insight into integrating physical laws with deep learning for spatiotemporal prediction . Index Terms -- Human activity intensity prediction; Gravity model; Spatial interaction; Physics - informed machine learning; Over - smoothing phenomenon; Spatiotemporal graph neural network . This work is supported by the National Natural Science Foundation of China ( Grant # 42430106, 42371468, 424B2013) . Y i Wang, Zhenghong Wang, Fan Zhang, Chengling Tang, Weiyu Zhang and Yu Liu are with Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China. Chaogui Kang is with National Engineering Research Center of Geographic Information System, China University of Geosciences (Wuhan) 430074, China. Sijie Ruan is with School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China . Di Zhu and Zhongfu Ma are with Department of Geography, Environment and Society, University of Minnesota, Twin Cities, Minneapolis, MN 55455, USA . Y u Zheng is with JD iCity, JD Technology, Beijing 100176, China . P hilip S. Yu is with Department of Computer Science, University of Illinois Chicago, Chicago 60607, USA .

Accurate prediction of trips between zones is critical for transportation planning, as it supports resource allocation and infrastructure development across various modes of transport. Although the gravity model has been widely used due to its simplicity, it often inadequately represents the complex factors influencing modern travel behavior. This study introduces a data-driven approach to enhance the gravity model by integrating geographical, economic, social, and travel data from the counties in Tennessee and New York state. Using machine learning techniques, we extend the capabilities of the traditional model to handle more complex interactions between variables. Our experiments demonstrate that machine learning-enhanced models significantly outperform the traditional model. Our results show a 51.48% improvement in R-squared, indicating a substantial enhancement in the model's explanatory power. Also, a 63.59% reduction in Mean Absolute Error (MAE) reflects a significant increase in prediction accuracy. Furthermore, a 44.32% increase in Common Part of Commuters (CPC) demonstrates improved prediction reliability. These findings highlight the substantial benefits of integrating diverse datasets and advanced algorithms into transportation models. They provide urban planners and policymakers with more reliable forecasting and decision-making tools.

The mobility patterns of people in cities evolve alongside changes in land use and population. This makes it crucial for urban planners to simulate and analyze human mobility patterns for purposes such as transportation optimization and sustainable urban development. Existing generative models borrowed from machine learning rely heavily on historical trajectories and often overlook evolving factors like changes in population density and land use. Mechanistic approaches incorporate population density and facility distribution but assume static scenarios, limiting their utility for future projections where historical data for calibration is unavailable. This study introduces a novel, data-driven approach for generating origin-destination mobility flows tailored to simulated urban scenarios. Our method leverages adaptive factors such as dynamic region sizes and land use archetypes, and it utilizes conditional generative adversarial networks (cGANs) to blend historical data with these adaptive parameters. The approach facilitates rapid mobility flow generation with adjustable spatial granularity based on regions of interest, without requiring extensive calibration data or complex behavior modeling. The promising performance of our approach is demonstrated by its application to mobile phone data from Singapore, and by its comparison with existing methods.

Proximity operations to small bodies, such as asteroids and comets, demand high levels of autonomy to achieve cost-effective, safe, and reliable Guidance, Navigation and Control (GNC) solutions. Enabling autonomous GNC capabilities in the vicinity of these targets is thus vital for future space applications. However, the highly non-linear and uncertain environment characterizing their vicinity poses unique challenges that need to be assessed to grant robustness against unknown shapes and gravity fields. In this paper, a pipeline designed to generate variable density gravity field models is proposed, allowing the generation of a coherent set of scenarios that can be used for design, validation, and testing of GNC algorithms. The proposed approach consists in processing a polyhedral shape model of the body with a given density distribution to compute the coefficients of the spherical harmonics expansion associated with the gravity field. To validate the approach, several comparison are conducted against analytical solutions, literature results, and higher fidelity models, across a diverse set of targets with varying morphological and physical properties. Simulation results demonstrate the effectiveness of the methodology, showing good performances in terms of modeling accuracy and computational efficiency. This research presents a faster and more robust framework for generating environmental models to be used in simulation and hardware-in-the-loop testing of onboard GNC algorithms.

Invasive species in water bodies pose a major threat to the environment and biodiversity globally. Due to increased transportation and trade, non-native species have been introduced to new environments, causing damage to ecosystems and leading to economic losses in agriculture, forestry, and fisheries. Therefore, there is a pressing need for risk assessment and management techniques to mitigate the impact of these invasions. This study aims to develop a new physics-inspired model to forecast maritime shipping traffic and thus inform risk assessment of invasive species spread through global transportation networks. Inspired by the gravity model for international trades, our model considers various factors that influence the likelihood and impact of vessel activities, such as shipping flux density, distance between ports, trade flow, and centrality measures of transportation hubs. Additionally, by analyzing the risk network of invasive species, we provide a comprehensive framework for assessing the invasion threat level given a pair of origin and destination. Accordingly, this paper introduces transformers to gravity models to rebuild the short- and long-term dependencies that make the risk analysis feasible. Thus, we introduce a physics-inspired framework that achieves an 89% segmentation accuracy for existing and non-existing trajectories and an 84.8% accuracy for the number of vessels flowing between key port areas, representing more than 10% improvement over the traditional deep-gravity model. Along these lines, this research contributes to a better understanding of invasive species risk assessment. It allows policymakers, conservationists, and stakeholders to prioritize management actions by identifying high-risk invasion pathways. Besides, our model is versatile and can include new data sources, making it suitable for assessing species invasion risks in a changing global landscape.

Modeling of human mobility is critical to address questions in urban planning and transportation, as well as global challenges in sustainability, public health, and economic development. However, our understanding and ability to model mobility flows within and between urban areas are still incomplete. At one end of the modeling spectrum we have simple so-called gravity models, which are easy to interpret and provide modestly accurate predictions of mobility flows. At the other end, we have complex machine learning and deep learning models, with tens of features and thousands of parameters, which predict mobility more accurately than gravity models at the cost of not being interpretable and not providing insight on human behavior. Here, we show that simple machine-learned, closed-form models of mobility are able to predict mobility flows more accurately, overall, than either gravity or complex machine and deep learning models. At the same time, these models are simple and gravity-like, and can be interpreted in terms similar to standard gravity models. Furthermore, these models work for different datasets and at different scales, suggesting that they may capture the fundamental universal features of human mobility.

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) show considerable potential in their capacity to identify solutions to complex differential equations. Over the past two years, much work has gone into the development of PINNs capable of solving the gravity field modeling problem -- i.e.\ learning a differentiable form of the gravitational potential from position and acceleration estimates. While the past PINN gravity models (PINN-GMs) have demonstrated advantages in model compactness, robustness to noise, and sample efficiency; there remain key modeling challenges which this paper aims to address. Specifically, this paper introduces the third generation of the Physics-Informed Neural Network Gravity Model (PINN-GM-III) which solves the problems of extrapolation error, bias towards low-altitude samples, numerical instability at high-altitudes, and compliant boundary conditions through numerous modifications to the model's design. The PINN-GM-III is tested by modeling a known heterogeneous density asteroid, and its performance is evaluated using seven core metrics which showcases its strengths against its predecessors and other analytic and numerical gravity models.

Human migration and mobility drives major societal phenomena including epidemics, economies, innovation, and the diffusion of ideas. Although human mobility and migration have been heavily constrained by geographic distance throughout the history, advances and globalization are making other factors such as language and culture increasingly more important. Advances in neural embedding models, originally designed for natural language, provide an opportunity to tame this complexity and open new avenues for the study of migration. Here, we demonstrate the ability of the model word2vec to encode nuanced relationships between discrete locations from migration trajectories, producing an accurate, dense, continuous, and meaningful vector-space representation. The resulting representation provides a functional distance between locations, as well as a digital double that can be distributed, re-used, and itself interrogated to understand the many dimensions of migration. We show that the unique power of word2vec to encode migration patterns stems from its mathematical equivalence with the gravity model of mobility. Focusing on the case of scientific migration, we apply word2vec to a database of three million migration trajectories of scientists derived from the affiliations listed on their publication records. Using techniques that leverage its semantic structure, we demonstrate that embeddings can learn the rich structure that underpins scientific migration, such as cultural, linguistic, and prestige relationships at multiple levels of granularity. Our results provide a theoretical foundation and methodological framework for using neural embeddings to represent and understand migration both within and beyond science.

As a result, KR is critical to offering a simple strategy for defining relevant and contextual information within a finite number of facts from a specific domain of interest; these facts are referred to as a knowledge base (KB). In the past years, Knowledge Graph (KG), as a form of KR, has gained attention because it provides a contextual, natural, and human-like form of representing knowledge in specific domains and common sense. KG is formed in statements called triples on the T = (h, r, t) form, where h (head) and t (tail) represent objects in real life, and r, the relation is the connection between those entities. Internet companies like Google, Wikipedia, and Facebook have found a simple but powerful unified tool in the KG field to describe their multi-structured and multi-dimensional knowledge base, capturing user data to transform it into vast KBs [3]. The KG approach is particularly relevant to studying international trade, a significant cornerstone of economic and social development in the globalized economy [4, 5]. International trade is complex and interconnected, with multiple entities (commodities, companies, and countries) interacting in multiple ways [6]. This method helps to understand those complex interactions in a structured and intuitive way. In international economics, the gravity model, a fundamental part of the current method, is widely used to predict trade relations between entities based on factors like size (GDP, population) and distance or other factors [7, 8, 9].

The presence of a high number of zero flow trades continues to provide a challenge in identifying gravity parameters to explain international trade using the gravity model. Linear regression with a logarithmic linear equation encounters an indefinite value on the logarithmic trade. Although several approaches to solving this problem have been proposed, the majority of them are no longer based on linear regression, making the process of finding solutions more complex. In this work, we suggest a two-step technique for determining the gravity parameters: first, perform linear regression locally to establish a dummy value to substitute trade flow zero, and then estimating the gravity parameters. Iterative techniques are used to determine the optimum parameters. Machine learning is used to test the estimated parameters by analyzing their position in the cluster. We calculated international trade figures for 2004, 2009, 2014, and 2019. We just examine the classic gravity equation and discover that the powers of GDP and distance are in the same cluster and are both worth roughly one. The strategy presented here can be used to solve other problems involving log-linear regression.