Abstract Machine learning is rapidly becoming a core technology for scientific computing,
with numerous opportunities to advance the field of computational fluid dynamics. Here we …

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

Recent work in scientific machine learning has developed so-called physics-informed neural
network (PINN) models. The typical approach is to incorporate physical domain knowledge …

Data scarcity is a major challenge when training deep learning (DL) models. DL demands a
large amount of data to achieve exceptional performance. Unfortunately, many applications …

We present the application of a class of deep learning, known as Physics Informed Neural
Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how …

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 …

In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

In the last 50 years there has been a tremendous progress in solving numerically the Navier-
Stokes equations using finite differences, finite elements, spectral, and even meshless …

Progress in combustion science and engineering has led to the generation of large amounts
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …

The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …