Related papers: Automatic differentiation for error analysis

Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…

When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…

In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

With the widespread application of Large Language Models (LLMs) in various tasks, the mainstream LLM platforms generate massive user-model interactions daily. In order to efficiently analyze the performance of models and diagnose failures…

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus…

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…

Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…

Machine learning (ML) methods are widely used in industrial applications, which usually require a large amount of training data. However, data collection needs extensive time costs and investments in the manufacturing system, and data…

It is needed to ensure the integrity of systems that process sensitive information and control many aspects of everyday life. We examine the use of machine learning algorithms to detect malware using the system calls generated by…

We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…

Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal…

This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…

This paper presents a novel methodology for enhancing Automated Program Repair (APR) through synthetic data generation utilizing Large Language Models (LLMs). Current APR systems are constrained by the limited availability of high-quality…

Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…

In the Monte Carlo simulation of both Lattice field-theories and of models of Statistical Mechanics, identities verified by exact mean-values such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well known…

Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…

The current generation of software analytics tools are mostly prediction algorithms (e.g. support vector machines, naive bayes, logistic regression, etc). While prediction is useful, after prediction comes planning about what actions to…