Weak form equation learning and surrogate modeling has proven to be computationally
efficient and robust to measurement noise in a wide range of applications including ODE …

Time-reversal symmetry arises naturally as a structural property in many dynamical systems
of interest. While the importance of hard-wiring symmetry is increasingly recognized in …

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 …

We present an approach to construct structure-preserving emulators for Hamiltonian flow
maps and Poincaré maps based directly on orbit data. Intended applications are in …

Incorporating prior knowledge of physics laws and structural properties of dynamical
systems into the design of deep learning architectures has proven to be a powerful …

Advection-dominated dynamical systems, characterized by partial differential equations, are
found in applications ranging from weather forecasting to engineering design where …

Reconstructing the Kolmogorov-Arnold-Moser (KAM) dynamics diagram of Hamiltonian
system from the time series of a limited number of parameters is an outstanding question in …

A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories
are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic …

An accurate data-based prediction of the long-term evolution of Hamiltonian systems
requires a network that preserves the appropriate structure under each time step. Every …

In this work, we develop a method for learning interpretable, thermodynamically stable and
Galilean invariant partial differential equations (PDEs) based on the conservation …