In the absence of governing equations, dimensional analysis is a robust technique for
extracting insights and finding symmetries in physical systems. Given measurement …

The discovery of governing equations from scientific data has the potential to transform data-
rich fields that lack well-characterized quantitative descriptions. Advances in sparse …

Dimensionless numbers and scaling laws provide elegant insights into the characteristic
properties of physical systems. Classical dimensional analysis and similitude theory fail to …

A major challenge in the study of dynamical systems is that of model discovery: turning data
into models that are not just predictive, but provide insight into the nature of the underlying …

While many phenomena in physics and engineering are formally high-dimensional, their
long-time dynamics often live on a lower-dimensional manifold. The present work introduces …

Automated data-driven modeling, the process of directly discovering the governing
equations of a system from data, is increasingly being used across the scientific community …

PySINDy is a Python package for the discovery of governing dynamical systems models
from data. In particular, PySINDy provides tools for applying the sparse identification of …

We design a physics-aware auto-encoder to specifically reduce the dimensionality of
solutions arising from convection-dominated nonlinear physical systems. Although existing …

Discovering nonlinear differential equations that describe system dynamics from empirical
data is a fundamental challenge in contemporary science. While current methods can …

We develop a data-driven model discovery and system identification technique for spatially-
dependent boundary value problems (BVPs). Specifically, we leverage the sparse …