Related papers: A C++ implementation of the discrete adjoint sensi…
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and nonlinear solvers. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years,…
A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material…
The application of operator overloading algorithmic differentiation (AD) to computer programs in order to compute the derivative is quite common. But, the replacement of the underlying computational floating point type with the specialized…
This document, as the title stated, is meant to provide a vectorized implementation of adjoint dynamics calculation for Graph Convolutional Neural Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the gradient…
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a…
Automatic Differentiation (AD) is instrumental for science and industry. It is a tool to evaluate the derivative of a function specified through a computer program. The range of AD application domain spans from Machine Learning to Robotics…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
The efficient method for computing the sensitivities is the adjoint method. The cost of solving an adjoint equation is comparable to the cost of solving the governing equation. Once the adjoint solution is obtained, the sensitivities to any…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…
Neural ordinary differential equations (NODEs) have recently attracted increasing attention; however, their empirical performance on benchmark tasks (e.g. image classification) are significantly inferior to discrete-layer models. We…
The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…
Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…
Automatic differentiation is a set of techniques to efficiently and accurately compute the derivative of a function represented by a computer program. Existing C++ libraries for automatic differentiation (e.g. Adept, Stan Math Library),…
The existing variants of the Differential Evolution (DE) algorithm come with certain limitations, such as poor local search and susceptibility to premature convergence. This study introduces Adaptive Differential Evolution with…
This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…
This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta algorithm for solving Ordinary Differential Equations. This algorithm can be used for studying many different problems and in particular it can be applied for…