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Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
This paper addresses the problem of learning instantaneous occupancy levels of dynamic environments and predicting future occupancy levels. Due to the complexity of most real-world environments, such as urban streets or crowded areas, the…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduced model-form error into the system.…
Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on…
Machine learning approaches have been widely used for discovering the underlying physics of dynamical systems from measured data. Existing approaches, however, still lack robustness, especially when the measured data contain a large level…
As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically…
How to reproduce realistic motion in simulations has always been a fundamental problem for pedestrian dynamics, and a critical challenge for current studies is the natural correlation of the movement choices and the human behaviours. To…
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the…
Providing accurate/suitable information on behaviors in sma\-rt environments is a challenging and crucial task in pervasive computing where context-awareness and pro-activity are of fundamental importance. Behavioral identifications enable…
In a living system composed of interacting components such as molecules, cells, and tissues, each component often adaptively changes its internal states in response to interactions with its surrounding components. For example, individual…
Spatio-temporal graph learning is a fundamental problem in modern urban systems. Existing approaches tackle different tasks independently, tailoring their models to unique task characteristics. These methods, however, fall short of modeling…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
A grand challenge in modern neuroscience is to bridge the gap between the detailed mapping of microscale neural circuits and mechanistic understanding of cognitive functions. While extensive knowledge exists about neuronal connectivity and…
Multi-person motion prediction is a complex and emerging field with significant real-world applications. Current state-of-the-art methods typically adopt dual-path networks to separately modeling spatial features and temporal features.…
Over the past decades, improvements in data collection hardware coupled with novel artificial intelligence algorithms have made it possible for researchers to understand urban environments at an unprecedented scale. From local interactions…
Learning, inference, and emergence in biological and artificial systems are often studied within disparate theoretical frameworks, ranging from energy-based models to recurrent and attention-based architectures. Here we develop a unified…