Related papers: Rheo-SINDy: Finding a Constitutive Model from Rheo…
Fluid-like materials are ubiquitous, spanning from living biological tissues to geological formations, and across scales ranging from micrometers to kilometers. Inferring their rheological properties remains a major challenge, particularly…
Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential…
The growing integration of renewable energy sources has significantly reduced grid inertia, making modern power systems more vulnerable to instabilities. Accurate estimation of dynamic parameters such as inertia constants and damping…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives…
We draw on the latest advancements in the physics community to propose a novel method for discovering the governing non-linear dynamics of physical systems in reinforcement learning (RL). We establish that this method is capable of…
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…
Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…
We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…
We propose a probabilistic model discovery method for identifying ordinary differential equations (ODEs) governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy)…
Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…
Choosing a suitable model and determining its associated parameters from fitting to experimental data is fundamental for many problems in biomechanics. Models of shear-thinning complex fluids, dating from the work of Bird, Carreau, Cross…
We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of polymer solutions. In this…
The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…
Phase mixing is a fundamental kinetic process that governs dissipation and stability in collisionless plasmas, but its inherent filamentation in velocity space creates major challenges for both high-fidelity simulations and reduced-order…
Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a…
The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…