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In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…
Traffic simulators act as an essential component in the operating and planning of transportation systems. Conventional traffic simulators usually employ a calibrated physical car-following model to describe vehicles' behaviors and their…
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
Transport across heterogeneous, patchy environments is a ubiquitous phenomenon spanning fields of study including ecological movement, intracellular transport and regions of specialised function in a cell. These regions or patches may be…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
Context plays a significant role in the generation of motion for dynamic agents in interactive environments. This work proposes a modular method that utilises a learned model of the environment for motion prediction. This modularity…
In autonomous driving, an accurate understanding of environment, e.g., the vehicle-to-vehicle and vehicle-to-lane interactions, plays a critical role in many driving tasks such as trajectory prediction and motion planning. Environment…
Mean field games (MFGs) model the limit of large populations of strategically interacting agents, yet both forward and inverse problems remain challenging. For the forward problem, a difficulty is to design numerical methods with global…
Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to anyarbitrary region, and the fluxes between any two regions. The considered description offers a general and unified…
Generative posterior sampling using diffusion models has emerged as a dominant paradigm for solving inverse problems in imaging, which usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG)…
Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and long-time non-Gaussian diffusive motion, unless interrupted. Despite its relevance to numerous…
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…
Range migrations in response to climate change, invasive species and the emergence of novel ecosystems highlight the importance of temporal turnover in community composition as a fundamental part of global change in the Anthropocene.…
The basic conceptual picture and theoretical basis for development of transport equations in porous media are examined. The general form of the governing equations is derived for conservative chemical transport in heterogeneous geological…
Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing…
Perceiving the surrounding environment in terms of objects is useful for any general purpose intelligent agent. In this paper, we investigate a fundamental mechanism making object perception possible, namely the identification of…
Understanding the dynamics of an environment, such as the movement of humans and vehicles, is crucial for agents to achieve long-term autonomy in urban environments. This requires the development of methods to capture the multi-modal and…