Random walks and related spatial stochastic models have been used in a range of
application areas, including animal and plant ecology, infectious disease epidemiology …

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 …

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

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical
description of the behavior of an infinite number of interacting particles by imposing a …

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 …

Hysteresis phenomenon widely exists in various metamaterials and smart actuators.
Governing equations can describe and predict the static/dynamic behavior of the systems …

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

Weak form equation learning and surrogate modeling has proven to be computationally
efficient and robust to measurement noise in a wide range of applications including ODE …

Pattern-forming systems can exhibit a diverse array of complex behaviors as external
parameters are varied, enabling a variety of useful functions in biological and engineered …

Interacting particle system (IPS) models have proven to be highly successful for describing
the spatial movement of organisms. However, it is challenging to infer the interaction rules …