Large scale models of physical phenomena demand the development of new statistical and
computational tools in order to be effective. Many such models are “sloppy,” ie, exhibit …

Sparse model identification enables the discovery of nonlinear dynamical systems purely
from data; however, this approach is sensitive to noise, especially in the low-data limit. In this …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

All physical laws are described as mathematical relationships between state variables.
These variables give a complete and non-redundant description of the relevant system …

We put forth a deep learning approach for discovering nonlinear partial differential
equations from scattered and potentially noisy observations in space and time. Specifically …

While there is currently a lot of enthusiasm about “big data”, useful data is usually “small”
and expensive to acquire. In this paper, we present a new paradigm of learning partial …

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 …

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 …

Mathematical models of biological reactions at the system-level lead to a set of ordinary
differential equations with many unknown parameters that need to be inferred using …

We present a numerical framework for approximating unknown governing equations using
observation data and deep neural networks (DNN). In particular, we propose to use residual …