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

A distinguished algebraic variety in $\mathbb{C}^2$ has been the focus of much research in recent years because of good reasons. This note gives a different perspective. (1) We find a new characterization of an algebraic variety $\mathcal…

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…

In this short note a differential version of the classical Weil descent is established in all characteristics. This yields a ready-to-deploy tool of differential restriction of scalars for differential varieties over finite differential…

Recovering clean and accurate geometry from images is essential for robotics and augmented reality. However, existing geometry foundation models still suffer severely from flying pixels and the loss of fine details. In this paper, we…

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…

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

Feature engineering, a crucial step of machine learning, aims to extract useful features from raw data to improve data quality. In recent years, great efforts have been devoted to Automated Feature Engineering (AutoFE) to replace expensive…

We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained…

Geometrical shape of airfoils, together with the corresponding flight conditions, are crucial factors for aerodynamic performances prediction. The obtained airfoils geometrical features in most existing approaches (e.g., geometrical…

We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…

The versatile Arbitrary-DERivative (ADER) scheme is cast in a multilevel framework (ML-ADER) for fast solution of system of linear hyperbolic partial differential equations. The solution is cycled through spatial operators of varying…

Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…

This is the continuation of the study of differential graded (dg) vertex algebras previously defined by the authors. The goal of this paper is to construct a functor from the category of dg vertex Lie algebras to the category of dg vertex…

Ptychography is a lensless imaging method that allows for wavefront sensing and phase-sensitive microscopy from a set of diffraction patterns. Recently, it has been shown that the optimization task in ptychography can be achieved via…

It has been conjectured that the Fisher divergence is more robust to model uncertainty than the conventional Kullback-Leibler (KL) divergence. This motivates the design of a new class of robust generative auto-encoders (AE) referred to as…

A computationally efficient high-order solver is developed to compute the wall distances by solving the relevant partial differential equations, namely: Eikonal, Hamilton-Jacobi (HJ) and Poisson equations. In contrast to the upwind schemes…

This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, "p-typical" Witt vectors of p-adic schemes of finite type are already reasonably well understood. The main point here is to generalize this…

Mumford defined a rational pullback for Weil divisors on normal surfaces, which is linear, respects effectivity, and satisfies the projection formula. In higher dimensions, the existence of small resolutions of singularities precludes such…

For a commutative algebra $A$ over $\mathbb{C}$,denote $\mathfrak{g}=\text{Der}(A)$. A module over the smash product $A\# U(\mathfrak{g})$ is called a jet $\mathfrak{g}$-module, where $U(\mathfrak{g})$ is the universal enveloping algebra of…