Machine Learning for Initial Value Problems of Parameter-Dependent Dynamical Systems

by   Roland Pulch, et al.

We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many time points. We examine the mapping from the set of parameters to the discrete values of the trajectories. An evaluation of this mapping requires to solve an initial value problem. Alternatively, we determine an approximation, where the evaluation requires low computation work, using a concept of machine learning. We employ feedforward neural networks, which are fitted to data from samples of the trajectories. Results of numerical computations are presented for a test example modelling an electric circuit.


page 1

page 2

page 3

page 4


Hamiltonian Neural Networks for solving differential equations

There has been a wave of interest in applying machine learning to study ...

Safely Learning Dynamical Systems

A fundamental challenge in learning an unknown dynamical system is to re...

Long-time predictive modeling of nonlinear dynamical systems using neural networks

We study the use of feedforward neural networks (FNN) to develop models ...

Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators

We introduce the mean inverse integrator (MII), a novel approach to incr...

On Topologically Controlled Model Reduction for Discrete-Time Systems

In this document the author proves that several problems in data-driven ...

Variational integration of learned dynamical systems

The principle of least action is one of the most fundamental physical pr...

Machine Learning assisted Chimera and Solitary states in Networks

Chimera and Solitary states have captivated scientists and engineers due...

Please sign up or login with your details

Forgot password? Click here to reset