Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has
served as a primary prototype for investigating the transition to turbulence in wall-bounded …

We discuss the emerging advances and opportunities at the intersection of machine
learning (ML) and climate physics, highlighting the use of ML techniques, including …

Modern generative machine learning models are able to create realistic outputs far beyond
their training data, such as photorealistic artwork, accurate protein structures or …

The notion of an evolutional deep neural network (EDNN) is introduced for the solution of
partial differential equations (PDE). The parameters of the network are trained to represent …

Transfer learning (TL), which enables neural networks (NNs) to generalize out-of-distribution
via targeted re-training, is becoming a powerful tool in scientific machine learning (ML) …

Chaotic systems are notoriously challenging to predict because of their sensitivity to
perturbations and errors due to time step**. Despite this unpredictable behavior, for many …

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to
attractors that exist on finite-dimensional manifolds. We present a data-driven reduced-order …

A dynamical systems approach to turbulence envisions the flow as a trajectory through a
high-dimensional state space [Hopf, Commun. Appl. Maths 1, 303 (1948)]. The chaotic …

Because the Navier–Stokes equations are dissipative, the long-time dynamics of a flow in
state space are expected to collapse onto a manifold whose dimension may be much lower …

Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing
computational costs for simulation as well as for model-based control approaches. This work …