Related papers: Neural Network Localized Orthogonal Decomposition …

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Diffusion models have emerged as powerful priors for image editing tasks such as inpainting and local modification, where the objective is to generate realistic content that remains consistent with observed regions. In particular, zero-shot…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

Diffusion models have achieved remarkable success in image and video generation. In this work, we demonstrate that diffusion models can also \textit{generate high-performing neural network parameters}. Our approach is simple, utilizing an…

A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and…

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently,…

Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse…

The embedded ensemble propagation approach introduced in [49] has been demonstrated to be a powerful means of reducing the computational cost of sampling-based uncertainty quantification methods, particularly on emerging computational…

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…

This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…

We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement…

In astrophysical simulations, nuclear reacting flows pose computational challenges due to the stiffness of reaction networks. We introduce neural network-based surrogate models using the DeePODE framework to enhance simulation efficiency…

Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…

Using the equivalent inclusion method (a method strongly related to the Hashin-Shtrikman variational principle) as a surrogate model, we propose a variance reduction strategy for the numerical homogenization of random composites made of…

Recently, several optimization methods have been successfully applied to the hyperparameter optimization of deep neural networks (DNNs). The methods work by modeling the joint distribution of hyperparameter values and corresponding error.…