Related papers: The Discrete Adjoint Method: Efficient Derivatives…
Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. Here we provide a unified approach to the derivation of such methods for problems…
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a…
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face…
Iterative algorithms, like gradient descent, are common tools for solving a variety of problems, such as model fitting. For this reason, there is interest in creating differentially private versions of them. However, their conversion to…
We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are…
This paper uses deep learning to value derivatives. The approach is broadly applicable, and we use a call option on a basket of stocks as an example. We show that the deep learning model is accurate and very fast, capable of producing…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…
In this paper we study simulation-based methods for estimating gradients in stochastic networks. We derive a new method of calculating weak derivative estimator using importance sampling transform, and our method has less computational cost…
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face…
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…
This document, as the title stated, is meant to provide a vectorized implementation of adjoint dynamics calculation for Graph Convolutional Neural Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the gradient…