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

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 …

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 …

Algorithmic differentiation (AD), also known as automatic differentiation, is a technology for
accurate and efficient evaluation of derivatives of a function given as a computer model. The …

Combinatorial techniques have become essential tools across the landscape of
computational science, and some of the combinatorial ideas undergirding these tools are …

Neural ordinary differential equations (neural ODEs) have emerged as a novel network
architecture that bridges dynamical systems and deep learning. However, the gradient …

We present a new software system, PETSc TSAdjoint, for first-order and second-order
adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative …

We discuss software tool support for the algorithmic differentiation (AD), also known as
automatic differentiation, of numerical simulation programs that contain calls to solvers for …

The computation of derivatives for optimizing time-dependent flow problems is often based
on the integration of the adjoint differential equation. For this purpose, the knowledge of the …

Adjoints are an important computational tool for large-scale sensitivity evaluation,
uncertainty quantification, and derivative-based optimization. An essential component of …