Related papers: Combining physics-based modeling and deep learning…

We analyze the training dynamics for deep linear networks using a new metric - layer imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data…

Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for…

We introduce a new algorithm for regularized reconstruction of multispectral (MS) images from noisy linear measurements. Unlike traditional approaches, the proposed algorithm regularizes the recovery problem by using a prior specified…

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear…

This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…

This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…

We introduce a de novo elastography method to learn the elasticity of solids from measured strains. The deep neural network in our new method is supervised by the theory of elasticity and does not require labeled data for training. Results…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…

Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…

We propose a novel federated learning method for distributively training neural network models, where the server orchestrates cooperation between a subset of randomly chosen devices in each round. We view Federated Learning problem…

Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor…

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…

In terms of accuracy, deep learning (DL) models have had considerable success in classification problems for medical imaging applications. However, it is well-known that the outputs of such models, which typically utilise the SoftMax…

Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…