Kernel-based parameter estimation of dynamical systems with unknown observation functions
arXiv:2009.04142 · doi:10.1063/5.0044529
Abstract
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems - the double pendulum and the Lorenz '63 model.
References in corpus (9)
- Kernel methods in machine learning
- Discovering Symbolic Models from Deep Learning with Inductive Biases
- Calibrate, Emulate, Sample
- Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems
- Poincaré Maps for Multiscale Physics Discovery and Nonlinear Floquet Theory
- Data-driven discovery of free-form governing differential equations
- Forecasting Sequential Data using Consistent Koopman Autoencoders
- Spectral Discovery of Jointly Smooth Features for Multimodal Data
- Discovery of Dynamics Using Linear Multistep Methods