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

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

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 …

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

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

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

Physics is a field of science that has traditionally used the scientific method to answer
questions about why natural phenomena occur and to make testable models that explain the …

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 …

This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …