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

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with…

Medical image segmentation supports clinical workflows by precisely delineating anatomical structures and lesions. However, medical image datasets medical image datasets suffer from acquisition noise and annotation ambiguity, causing…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…

Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent…

Deformable medical image registration is a fundamental task in medical image analysis. While deep learning-based methods have demonstrated superior accuracy and computational efficiency compared to traditional techniques, they often…

Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…

The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific…

We propose a model-based deep learning architecture for the reconstruction of highly accelerated diffusion magnetic resonance imaging (MRI) that enables high resolution imaging. The proposed reconstruction jointly recovers all the diffusion…

We develop in this paper a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may present in the response variable. The idea of EGM is to approximate the density…

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…

Electroencephalogram (EEG) classification has been widely used in various medical and engineering applications, where it is important for understanding brain function, diagnosing diseases, and assessing mental health conditions. However,…

Deep learning (DL) techniques have been extensively employed in magnetic resonance imaging (MRI) reconstruction, delivering notable performance enhancements over traditional non-DL methods. Nonetheless, recent studies have identified…

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…

EEG decoding systems based on deep neural networks have been widely used in decision making of brain computer interfaces (BCI). Their predictions, however, can be unreliable given the significant variance and noise in EEG signals. Previous…

Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While…

Computed ultrasound tomography in echo mode generates maps of tissue speed of sound (SoS) from the shift of echoes when detected under varying steering angles. It solves a linearized inverse problem that requires regularization to…

Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…