The elements of differentiable programming
Artificial intelligence has recently experienced remarkable advances, fueled by large
models, vast datasets, accelerated hardware, and, last but not least, the transformative …
models, vast datasets, accelerated hardware, and, last but not least, the transformative …
Automated derivation of the adjoint of high-level transient finite element programs
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 …
linear models of a finite element model. The technique is significantly more efficient and …
Getting Started with ADOL-C.
A Walther, A Griewank - Combinatorial scientific computing, 2009 - api.taylorfrancis.com
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 …
functions that are defined by computer programs written in C or C++ by means of …
An introduction to algorithmic differentiation
AH Gebremedhin, A Walther - Wiley Interdisciplinary Reviews …, 2020 - Wiley Online Library
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 …
accurate and efficient evaluation of derivatives of a function given as a computer model. The …
A memory-efficient neural ordinary differential equation framework based on high-level adjoint differentiation
H Zhang, W Zhao - IEEE Transactions on Artificial Intelligence, 2022 - ieeexplore.ieee.org
Neural ordinary differential equations (neural ODEs) have emerged as a novel network
architecture that bridges dynamical systems and deep learning. However, the gradient …
architecture that bridges dynamical systems and deep learning. However, the gradient …
PETSc TSAdjoint: a discrete adjoint ODE solver for first-order and second-order sensitivity analysis
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 …
adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative …
Algorithmic differentiation of numerical methods: Tangent and adjoint solvers for parameterized systems of nonlinear equations
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 …
automatic differentiation, of numerical simulation programs that contain calls to solvers for …
Multistage approaches for optimal offline checkpointing
P Stumm, A Walther - SIAM Journal on Scientific Computing, 2009 - SIAM
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 …
on the integration of the adjoint differential equation. For this purpose, the knowledge of the …
Asynchronous two-level checkpointing scheme for large-scale adjoints in the spectral-element solver Nek5000
Adjoints are an important computational tool for large-scale sensitivity evaluation,
uncertainty quantification, and derivative-based optimization. An essential component of …
uncertainty quantification, and derivative-based optimization. An essential component of …