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Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations,…
Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work…
Recently, diffusion-based recommendation methods have achieved impressive results. However, existing approaches predominantly treat each user's historical interactions as independent training samples, overlooking the potential of…
Accurate and high-resolution precipitation nowcasting from radar echo sequences is crucial for disaster mitigation and economic planning, yet it remains a significant challenge. Key difficulties include modeling complex multi-scale…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
Global Climate Models (GCMs) are crucial for predicting future climate changes by simulating the Earth systems. However, the GCM Outputs exhibit systematic biases due to model uncertainties, parameterization simplifications, and inadequate…
Most modern approaches to quadruped locomotion focus on using Deep Reinforcement Learning (DRL) to learn policies from scratch, in an end-to-end manner. Such methods often fail to scale, as every new problem or application requires…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural…
Many manipulation tasks require the robot to control the contact between a grasped compliant tool and the environment, e.g. scraping a frying pan with a spatula. However, modeling tool-environment interaction is difficult, especially when…
Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the…
Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and…
Mapping people dynamics is a crucial skill for robots, because it enables them to coexist in human-inhabited environments. However, learning a model of people dynamics is a time consuming process which requires observation of large amount…
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center…
Optical flow, or the estimation of motion fields from image sequences, is one of the fundamental problems in computer vision. Unlike most pixel-wise tasks that aim at achieving consistent representations of the same category, optical flow…
Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of…