Related papers: Automatically identifying ordinary differential eq…

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically…

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…

We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the…

Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability…

Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…

Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…

In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates physical principles with black-box basis functions to compensate for…

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is…

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…