Related papers: Constants of motion network
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Wide-spread adoption of unmanned vehicle technologies requires the ability to predict the motion of the combined vehicle operation from observations. While the general prediction of such motion for an arbitrary control mechanism is…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
While generic object detection has achieved large improvements with rich feature hierarchies from deep nets, detecting small objects with poor visual cues remains challenging. Motion cues from multiple frames may be more informative for…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and…
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…