Over the past several decades, computational fluid dynamics has been increasingly used in
the aerospace industry for the design and study of new and derivative aircraft. In this review …

Artificial intelligence has recently experienced remarkable advances, fueled by large
models, vast datasets, accelerated hardware, and, last but not least, the transformative …

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph
neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs …

This paper presents a review of all existing discrete methods for computing the derivatives of
computational models within a unified mathematical framework. This framework hinges on a …

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent
linear models of a finite element model. The technique is significantly more efficient and …

Computing derivatives is key to many algorithms in scientific computing and machine
learning such as optimization, uncertainty quantification, and stability analysis. Enzyme is a …

This article focuses on the formulation, validation and application of the continuous adjoint
method for turbulent flows in aero/hydrodynamic optimization. Though discrete adjoint has …

The C++ package ADOL-C facilitates the evaluation of first and higher derivatives of vector
functions that are defined by computer programs written in C or C++ by means of …

Residual neural networks (ResNets) are a promising class of deep neural networks that
have shown excellent performance for a number of learning tasks, eg, image classification …

The adjoint method has long been considered as the tool of choice for gradient-based
optimisation in computational fluid dynamics (CFD). It is the independence of the …