Related papers: An Introduction to Adjoints and Output Error Estim…
The manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary-layer. The text is structured into three parts. The first part demonstrates,…
We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…
We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation…
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…
Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often…
In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…
Activity diagrams (ADs) have recently become widely used in the modeling of workflows, business processes, and web-services, where they serve various purposes, from documentation, requirement definitions, and test case specifications, to…
Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed and an explanation is provided by comparing a…
One of the crucial issues in federated learning is how to develop efficient optimization algorithms. Most of the current ones require full device participation and/or impose strong assumptions for convergence. Different from the widely-used…
High-fidelity computational fluid dynamics (CFD) is widely used for thermal-fluid design, but repeated CFD solves remain expensive for design optimization, uncertainty analysis, and digital-twin workflows. Recently, our team has…
Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic…
Automated code generation allows for a separation between the development of a model, expressed via a domain specific language, and lower level implementation details. Algorithmic differentiation can be applied symbolically at the level of…
As the core of recommender system, collaborative filtering (CF) models the affinity between a user and an item from historical user-item interactions, such as clicks, purchases, and so on. Benefited from the strong representation power,…
Computational Fluid Dynamics (CFD)-driven training combines machine learning (ML) with CFD solvers to develop physically consistent closure models with improved predictive accuracy. In the original framework, each ML-generated candidate…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…
Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…