Related papers: Constants of motion network
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…
Human motion modelling is a classical problem at the intersection of graphics and computer vision, with applications spanning human-computer interaction, motion synthesis, and motion prediction for virtual and augmented reality. Following…
Fast and accurate structural dynamics analysis is important for structural design and damage assessment. Structural dynamics analysis leveraging machine learning techniques has become a popular research focus in recent years. Although the…
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…
We identify a conserved quantity in continuous-time optimization dynamics, termed computational inertia. Defined as the sum of kinetic energy (parameter velocity) and potential energy (loss), this scalar remains invariant under idealized,…
Human motion prediction is an essential component for enabling closer human-robot collaboration. The task of accurately predicting human motion is non-trivial. It is compounded by the variability of human motion, both at a skeletal level…
We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…