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This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…

Numerical Analysis · Mathematics 2026-01-16 Wenbo Wang , Guangyan Jia

A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…

Optimization and Control · Mathematics 2026-03-11 Serge Gratton , Philippe L. Toint

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

Numerical Analysis · Mathematics 2020-09-15 Stefania Bellavia , Gianmarco Gurioli

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training…

Strongly Correlated Electrons · Physics 2019-09-11 Hai-Jun Liao , Jin-Guo Liu , Lei Wang , Tao Xiang

Computation methods for solving entropy-regularized reward optimization -- a class of problems widely used for fine-tuning generative models -- have advanced rapidly. Among those, Adjoint Matching (AM, Domingo-Enrich et al., 2025) has…

Machine Learning · Statistics 2026-02-17 Oswin So , Brian Karrer , Chuchu Fan , Ricky T. Q. Chen , Guan-Horng Liu

We establish that nonconvex definable parametric optimization problems with possibly nonsmooth objectives, inequality constraints, conic constraint systems, and non-unique primal and dual solutions admit an adjoint state formula under a…

Optimization and Control · Mathematics 2026-04-23 Jérôme Bolte , Edouard Pauwels , Cheik Traoré

The Heston model is a well-known two-dimensional financial model. Because the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging.…

Optimization and Control · Mathematics 2023-10-16 Anna Clevenhaus , Claudia Totzeck , Matthias Ehrhardt

There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been…

Machine Learning · Computer Science 2021-09-07 Marios Mattheakis , Hayden Joy , Pavlos Protopapas

Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such…

Statistics Theory · Mathematics 2018-07-19 Krishnakumar Balasubramanian , Jianqing Fan , Zhuoran Yang

Variance-based sensitivity indices have established themselves as a reference among practitioners of sensitivity analysis of model output. It is not unusual to consider a variance-based sensitivity analysis as informative if it produces at…

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…

Machine Learning · Computer Science 2021-11-09 Chenlin Meng , Yang Song , Wenzhe Li , Stefano Ermon

The open-source multiphysics suite SU2 features discrete adjoints by means of operator overloading automatic differentiation (AD). While both primal and discrete adjoint solvers support MPI parallelism, hybrid parallelism using both MPI and…

Mathematical Software · Computer Science 2025-04-23 Johannes Blühdorn , Pedro Gomes , Max Aehle , Nicolas R. Gauger

Chaotic dynamical systems are characterized by the sensitive dependence of trajectories on initial conditions. Conventional sensitivity analysis of time-averaged functionals yields unbounded sensitivities when the simulation is chaotic. The…

Numerical Analysis · Mathematics 2025-02-17 Pranshul Thakur , Siva Nadarajah

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…

Fluid Dynamics · Physics 2021-06-02 Niklas Kühl , Jörn Kröger , Martin Siebenborn , Michael Hinze , Thomas Rung

A generic framework for the solution of PDE-constrained optimisation problems based on the FEniCS system is presented. Its main features are an intuitive mathematical interface, a high degree of automation, and an efficient implementation…

Mathematical Software · Computer Science 2013-02-19 S. W. Funke , P. E. Farrell

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…

Machine Learning · Computer Science 2026-05-29 Qihong Yang , Yangtao Deng , Qiaolin He , Shiquan Zhang

High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…

Optimization and Control · Mathematics 2025-08-29 Brian K. Tran , Ben S. Southworth , David B. Cavender , Sam Olivier , Syed A. Shah , Tommaso Buvoli

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This…

Numerical Analysis · Mathematics 2019-12-09 Reza Najian Asl , Ihar Antonau , Aditya Ghantasala , Wulf G. Dettmer , Roland Wuchner , Kai-Uwe Bletzinger

We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the…

Optimization and Control · Mathematics 2021-04-06 Jolene Britton , Yat Tin Chow , Weitao Chen , Yulong Xing

Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn…

Machine Learning · Computer Science 2019-10-30 Nur Sila Gulgec , Zheng Shi , Neil Deshmukh , Shamim Pakzad , Martin Takáč