Introduced more than a half-century ago, Granger causality has become a popular tool for
analyzing time series data in many application domains, from economics and finance to …

An overview of the recent developments of time-series neural network modeling is
presented along with its use in model predictive control (MPC). A tutorial on the construction …

It is widely known that neural networks (NNs) are universal approximators of continuous
functions. However, a less known but powerful result is that a NN with a single hidden layer …

The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Interpretability in machine learning (ML) is crucial for high stakes decisions and
troubleshooting. In this work, we provide fundamental principles for interpretable ML, and …

In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …

While it is widely known that neural networks are universal approximators of continuous
functions, a less known and perhaps more powerful result is that a neural network with a …

We introduce a new family of deep neural network models. Instead of specifying a discrete
sequence of hidden layers, we parameterize the derivative of the hidden state using a …

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

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 …