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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…

Machine Learning · Computer Science 2021-03-24 Philipp Andelfinger

Inverse design of complex flows is notoriously challenging because of the high cost of high dimensional optimization. Usually, optimization problems are either restricted to few control parameters, or adjoint-based approaches are used to…

Fluid Dynamics · Physics 2024-03-12 Mohammed Alhashim , Kaylie Hausknecht , Michael Brenner

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…

Computational Finance · Quantitative Finance 2017-06-08 Sébastien Geeraert , Charles-Albert Lehalle , Barak Pearlmutter , Olivier Pironneau , Adil Reghai

Algorithmic differentiation (AD) tools allow to obtain gradient information of a continuously differentiable objective function in a computationally cheap way using the so-called backward mode. It is common practice to use the same tools…

Optimization and Control · Mathematics 2024-12-02 Lukas Baumgärtner , Franz Bethke

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-08 Jan Hückelheim , Navjot Kukreja , Sri Hari Krishna Narayanan , Fabio Luporini , Gerard Gorman , Paul Hovland

Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives…

Numerical Analysis · Mathematics 2023-05-15 Jan Hückelheim , Harshitha Menon , William Moses , Bruce Christianson , Paul Hovland , Laurent Hascoët

Stochastic scientific models and machine learning optimization estimators have a large number of variables; hence computing large sparse Jacobians and Hessians is important. Algorithmic differentiation (AD) greatly reduces the programming…

Mathematical Software · Computer Science 2021-11-10 Bradley M. Bell , Kasper Kristensen

The Hessian-vector product computation appears in many scientific applications such as in optimization and finite element modeling. Often there is a need for computing Hessian-vector products at many data points concurrently. We propose an…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-31 Desh Ranjan , Mohammad Zubair

We implement a quantum optimal control algorithm based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and…

Quantum Physics · Physics 2017-04-19 Nelson Leung , Mohamed Abdelhafez , Jens Koch , David I. Schuster

We introduce Tritium, an automatic differentiation-based sensitivity analysis framework for differentially private (DP) machine learning (ML). Optimal noise calibration in this setting requires efficient Jacobian matrix computations and…

Machine Learning · Computer Science 2022-04-06 Dmitrii Usynin , Alexander Ziller , Moritz Knolle , Andrew Trask , Kritika Prakash , Daniel Rueckert , Georgios Kaissis

The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…

Optimization and Control · Mathematics 2020-06-09 Michel Schubiger , Goran Banjac , John Lygeros

The recent works on a deep learning (DL)-based joint design of preamble set for the transmitters and data-aided active user detection (AUD) in the receiver has demonstrated a significant performance improvement for grant-free sparse code…

Information Theory · Computer Science 2022-09-07 Minsig Han , Ameha Tsegaye Abebe , Chung G. Kang

We present JAX-PF, an open-source, GPU-accelerated, and differentiable Phase Field (PF) software package, supporting both explicit and implicit time stepping schemes. Leveraging the modern computing architecture JAX, JAX-PF achieves high…

Computational Physics · Physics 2026-01-13 Fanglei Hu , Jiachen Guo , Stephen Niezgoda , Wing Kam Liu , Jian Cao

Classical reverse-mode automatic differentiation (AD) imposes only a small constant-factor overhead in operation count over the original computation, but has storage requirements that grow, in the worst case, in proportion to the time…

Programming Languages · Computer Science 2018-07-18 Jeffrey Mark Siskind , Barak A. Pearlmutter

This paper presents reverse-mode algorithmic differentiation (AD) based on source code transformation, in particular of the Static Single Assignment (SSA) form used by modern compilers. The approach can support control flow, nesting,…

Programming Languages · Computer Science 2019-03-12 Michael Innes

Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid…

Numerical Analysis · Mathematics 2020-01-22 Andrea Vigliotti , Ferdinando Auricchio

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…

Numerical Analysis · Mathematics 2025-06-03 Julian Andrej , Tzanio Kolev , Boyan Lazarov

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…

Methodology · Statistics 2024-07-04 Kevin Tan , Giles Hooker , Edward L. Ionides

Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…

Mathematical Software · Computer Science 2018-03-13 Max Sagebaum , Nicolas R. Gauger

Online synaptic plasticity rules derived from gradient descent achieve high accuracy on a wide range of practical tasks. However, their software implementation often requires tediously hand-derived gradients or using gradient…

Neural and Evolutionary Computing · Computer Science 2025-01-22 Jamie Lohoff , Anil Kaya , Florian Assmuth , Emre Neftci