Related papers: Automatic differentiation for coupled cluster meth…
In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of…
Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…
Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
Differential machine learning (DML) is a recently proposed technique that uses samplewise state derivatives to regularize least square fits to learn conditional expectations of functionals of stochastic processes as functions of state…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
Boolean reaction networks are an important tool in biochemistry for studying mechanisms in the biological cell. However, the stochastic formulation of such networks requires the solution of a master equation which inherently suffers from…
Atom probe tomography (APT) is ideally suited to characterize and understand the interplay of chemical segregation and microstructure in modern multicomponent materials. Yet, the quantitative analysis typically relies on human expertise to…
Differentiable models of physical systems provide a powerful platform for gradient-based algorithms, with particular impact on parameter estimation and optimal control. Quantum systems present a particular challenge for such…
We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given…
We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the…
Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…
In this paper different types of ECG automatic delineation approaches were overviewed. A combination of these approaches was used to create sampling rate independent filtration algorithm for automatic ECG delineation that is capable of…
The exponential growth of the power of modern digital computers is based upon the miniaturisation of vast nanoscale arrays of electronic switches, but this will be eventually constrained by fabrication limits and power dissipation. Chemical…
The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together…
Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an…
The computation of first and second-order derivatives is a staple in many computing applications, ranging from machine learning to scientific computing. We propose an algorithm to automatically differentiate algorithms written in a subset…