Related papers: Neural Integration of Continuous Dynamics
Dynamical systems are capable of performing computation in a reservoir computing paradigm. This paper presents a general representation of these systems as an artificial neural network (ANN). Initially, we implement the simplest dynamical…
Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…
In this paper, we study symmetric integrators for solving second-order ordinary differential equations on the basis of the notion of continuous-stage Runge-Kutta-Nystrom methods. The construction of such methods heavily relies on the…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…
Data-driven modeling of nonlinear dynamical systems is often hampered by measurement noise. We propose a denoising framework, called Runge-Kutta and Total Variation Based Implicit Neural Representation (RKTV-INR), that represents the state…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…
Motivated by the Hodgkin-Huxley model of neuronal dynamics, we study explicit numerical integrators for "conditionally linear" systems of ordinary differential equations. We show that splitting and composition methods, when applied to the…
In order to drastically reduce the heavy computational burden associated with time-domain simulations, this paper introduces a Physics-Informed Neural Network (PINN) to directly learn the solutions of power system dynamics. In contrast to…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not…
We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined by multiple time stepping algorithms. Similar to the…
The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…