相关论文: Jet Functors and Weil Algebras in Automatic Differ…

We compute the graded automorphisms of the upper triangular matrices, viewed as associative, Lie and Jordan algebras. We compute also the so called self-equivalences and Weyl and diagonal groups for every grading.

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…

Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic…

The Weil correspondence states that the datum of a Seiberg-Witten differential is equivalent to an algebraic group extension of the integrable system associated to the Seiberg-Witten geometry. Remarkably this group extension represents…

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…

The Harmonic Balance-Alternating Frequency-Time domain (HB-AFT) method is extensively employed for dynamic response analysis of nonlinear systems. However, its application to high-dimensional complex systems is constrained by the manual…

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement…

In this paper, we propose an effective unified control law for accurately tracking agile trajectories for lifting-wing quadcopters with different installation angles, which have the capability of vertical takeoff and landing (VTOL) as well…

We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive…

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing…

The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other…

We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical methods that use temporal and spatial…

We present a technique for applying (forward and) reverse-mode automatic differentiation (AD) on a non-recursive second-order functional array language that supports nested parallelism and is primarily aimed at efficient GPU execution. The…

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…

Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…

We develop a formulation for non-commutative derived analytic geometry built from differential graded (dg) algebras equipped with free entire functional calculus (FEFC), relating them to simplicial FEFC algebras and to locally…

The wind is one of the most increasingly used renewable energy resources. Accurate and reliable forecast of wind speed is necessary for efficient power production; however, it is not an easy task because it depends upon meteorological…

Automatic Differentiation (AD) allows to determine exactly the Taylor series of any function truncated at any order. Here we propose to use AD techniques for Monte Carlo data analysis. We discuss how to estimate errors of a general function…

Automatic generation of convex relaxations and subgradients is critical in global optimization, and is typically carried out using variants of automatic/algorithmic differentiation (AD). At previous AD conferences, variants of the forward…

We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…