相关论文: An Introduction to Adjoints and Output Error Estim…

The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…

Driven by the advancement of GPUs and AI, the field of Computational Fluid Dynamics (CFD) is undergoing significant transformations. This paper bridges the gap between the machine learning and CFD communities by deconstructing…

Supported lipid membranes are useful and important model systems for studying cell membrane properties and membrane mediated processes. One attractive application of supported membranes is the design of phantom cells exhibiting well defined…

This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…

There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to…

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…

Recently, the alternating direction method of multipliers (ADMM) has found many efficient applications in various areas; and it has been shown that the convergence is not guaranteed when it is directly extended to the multiple-block case of…

Solving flow-related inverse problems such as topology optimization problems is intricate but significant in various engineering fields. The lattice Boltzmann method (LBM) and the related adjoint method are highly suitable to perform…

Quaternion-valued signal processing has received increasing attention recently. One key operation involved in derivation of all kinds of adaptive algorithms is the gradient operator. Although there have been some derivations of this…

In this fluid dynamics video, results from high fidelity numerical simulations are presented, which have been carried out to study the flow and droplet dynamics of liquid sheets formed by two impinging jets. A three-dimensional…

In computer vision, one is often confronted with problems of domain shifts, which occur when one applies a classifier trained on a source dataset to target data sharing similar characteristics (e.g. same classes), but also different latent…

Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an…

Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…

We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution of the adjoint problem, we show that error indicators in the…

Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…

The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…

We formulate, in lattice-theoretic terms, two novel algorithms inspired by Bradley's property directed reachability algorithm. For finding safe invariants or counterexamples, the first algorithm exploits over-approximations of both forward…

A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…