This paper presents a new Bayesian approach to equation discovery–combined structure
detection and parameter estimation–for system identification (SI) in nonlinear structural …

Data-driven discovery of governing laws for complex nonlinear structural dynamic systems
remains a challenging issue of paramount importance. This work addresses the above issue …

This paper presents the use of spike-and-slab (SS) priors for discovering governing
differential equations of motion of nonlinear structural dynamic systems. The problem of …

Extracting governing physics from data is a key challenge in many areas of science and
technology. The existing techniques for equation discovery are mostly applicable to …

Abstract Machine learning methods have revolutionized studies in several areas of
knowledge, helping to understand and extract information from experimental data. Recently …

The problem of identifying single degree-of-freedom (SDOF) nonlinear mechanical
oscillators with piecewise-linear (PWL) restoring forces is considered. PWL nonlinear …

Extracting governing equations from data is a central challenge in many diverse areas of
science and engineering. Data are abundant whereas models often remain elusive, as in …

Stochastic differential equations (SDEs) are mathematical models that are widely used to
describe complex processes or phenomena perturbed by random noise from different …

We propose a sparse regression method capable of discovering the governing partial
differential equation (s) of a given system by time series measurements in the spatial …

Discovering governing equations of complex dynamical systems directly from data is a
central problem in scientific machine learning. In recent years, the sparse identification of …