相关论文: A C++ implementation of the discrete adjoint sensi…

The Rust programming language is an attractive choice for robotics and related fields, offering highly efficient and memory-safe code. However, a key limitation preventing its broader adoption in these domains is the lack of high-quality,…

A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…

In this work we present useful techniques and possible enhancements when applying an Algorithmic Differentiation (AD) tool to the linear algebra library Eigen using our in-house AD by overloading (AD-O) tool dco/c++ as a case study. After…

Differential equations arise in mathematics, physics,medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to…

Algorithmic differentiation (AD) allows exact computation of derivatives given only an implementation of an objective function. Although many AD tools are available, a proper and efficient implementation of AD methods is not…

Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…

A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are 1) the adjoint code is obtained by letting the AD tool Tapenade…

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…

Modern deep learning algorithms use variations of gradient descent as their main learning methods. Gradient descent can be understood as the simplest Ordinary Differential Equation (ODE) solver; namely, the Euler method applied to the…

This paper contains an error analysis of two randomized explicit Runge-Kutta schemes for ordinary differential equations (ODEs) with time-irregular coefficient functions. In particular, the methods are applicable to ODEs of Carath\'eodory…

The task of integrating a large number of independent ODE systems arises in various scientific and engineering areas. For nonstiff systems, common explicit integration algorithms can be used on GPUs, where individual GPU threads…

In recent years, formal methods of privacy protection such as differential privacy (DP), capable of deployment to data-driven tasks such as machine learning (ML), have emerged. Reconciling large-scale ML with the closed-form reasoning…

Agent-based models (ABMs) simulate complex systems by capturing the bottom-up interactions of individual agents comprising the system. Many complex systems of interest, such as epidemics or financial markets, involve thousands or even…

Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…

In this paper, authors successfully construct a new algorithm for the new higher order scheme of weak approximation of SDEs. The algorithm presented here is based on [1][2]. Although this algorithm shares some features with the algorithm…

Quantization of the parameters of machine learning models, such as deep neural networks, requires solving constrained optimization problems, where the constraint set is formed by the Cartesian product of many simple discrete sets. For such…

This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding…

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form $G=\frac{1}{2}\sum_1^m (Ey_i-C_i)^2$, which often appear in the calibration of stochastic models. { We demonstrate that it allows a perfect…

A current trend in HPC systems is the utilization of architectures with SIMD or vector extensions to exploit data parallelism. There are several ways to take advantage of such modern vector architectures, each with a different impact on the…

In this paper, we compare the impact of iterated and direct approaches to sensitivity computation in fixed-step explicit singly diagonally-implicit Runge-Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We use the…