Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

Signal propagation in complex networks drives epidemics, is responsible for information
going viral, promotes trust and facilitates moral behavior in social groups, enables the …

Abstract Recurrent Neural Networks (RNNs) offer fast inference on long sequences but are
hard to optimize and slow to train. Deep state-space models (SSMs) have recently been …

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

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

Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …

Digital twin can be defined as a virtual representation of a physical asset enabled through
data and simulators for real-time prediction, optimization, monitoring, controlling, and …

The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

SIMPLE aerodynamic configurations under even modest conditions can exhibit complex
flows with a wide range of temporal and spatial features. It has become common practice in …

Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …