Sparse system identification is the data-driven process of obtaining parsimonious differential
equations that describe the evolution of a dynamical system, balancing model complexity …

We perform a principal component analysis (PCA) of two one-dimensional lattice models
belonging to distinct nonequilibrium universality classes—directed bond percolation and …

Species subject to predation and environmental threats commonly exhibit variable periods
of population boom and bust over long timescales. Understanding and predicting such …

We report a new method to tailor the entire two-dimensional (2D) dispersion relation based
on nonlocal phononic crystals, where beyond-nearest-neighbor (BNN) interactions are used …

Recent work in data-driven modeling has demonstrated that a weak formulation of model
equations enhances the noise robustness of a wide range of computational methods. In this …

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for
estimating model parameters for non-linear systems of ODEs. Without relying on any …

This paper presents Mechanistic Neural Networks, a neural network design for machine
learning applications in the sciences. It incorporates a new Mechanistic Block in standard …

The sparse identification of nonlinear dynamics (SINDy) has been established as an
effective technique to produce interpretable models of dynamical systems from time …

Non-stationary systems are found throughout the world, from climate patterns under the
influence of variation in carbon dioxide concentration to brain dynamics driven by ascending …

Reduced order models are becoming increasingly important for rendering complex and
multiscale spatio-temporal dynamics computationally tractable. The computational efficiency …