Related papers: Higher-Order Automatic Differentiation Using Symbo…

Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield…

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 algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…

This document presents a new C++ Automatic Differentiation (AD) tool, AD-HOC (Automatic Differentiation for High-Order Calculations). This tool aims to have the following features: -Calculation of user specified derivatives of arbitrary…

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…

In this paper, we propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples in a weighted…

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a…

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…

In this paper, we present a machine learning method for the discovery of analytic solutions to differential equations. The method utilizes an inherently interpretable algorithm, genetic programming based symbolic regression. Unlike…

This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…

Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

The development of computing has made credit scoring approaches possible, with various machine learning (ML) and deep learning (DL) techniques becoming more and more valuable. While complex models yield more accurate predictions, their…

We demonstrate that automatic differentiation (AD), which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and…

To each directed acyclic graph (this includes some D-dimensional lattices) one can associate some abelian algebras that we call directed abelian algebras (DAA). On each site of the graph one attaches a generator of the algebra. These…

Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…

Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our…

The Catani--Seymour dipole subtraction is a general and powerful procedure to calculate the QCD next-to-leading order corrections for collider observables. We clearly define a practical algorithm to use the dipole subtraction. The algorithm…

We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…