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

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

Brain disorders represent an ever-increasing health challenge worldwide. While
conventional drug therapies are less effective due to the presence of the blood-brain barrier …

Sparse system identification is the data-driven process of obtaining parsimonious differential
equations that describe the evolution of a dynamical system, balancing model complexity …

Units equivariance (or units covariance) is the exact symmetry that follows from the
requirement that relationships among measured quantities of physics relevance must obey …

This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML)
modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high …

Electrochemical systems with increasing complexity are gaining importance in catalytic
energy conversion applications. Due to the interplay between transport phenomena and …

Equation discovery, also known as symbolic regression, is a machine learning task of
inducing closed-form equations from data and background knowledge. The latter takes …

Any representation of data involves arbitrary investigator choices. Because those choices
are external to the data-generating process, each choice leads to an exact symmetry …

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside
the range of training data. This is achieved when machine-learning models can …