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In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…

Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be…

A maximally stable extreme region (MSER) analysis based convolutional neural network (CNN) for unified defect detection framework is proposed in this paper. Our proposed framework utilizes the generality and stability of MSER to generate…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

This paper addresses the problem of dense depth predictions from sparse distance sensor data and a single camera image on challenging weather conditions. This work explores the significance of different sensor modalities such as camera,…

We present Neural Shape Deformation Priors, a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements. State-of-the-art methods cast this problem as an optimization task,…

The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…

We explore the application of computer vision and machine learning (ML) techniques to predict material properties (e.g. compressive strength) based on SEM images. We show that it's possible to train ML models to predict materials…

Modern deep neural networks achieved remarkable progress in medical image segmentation tasks. However, it has recently been observed that they tend to produce overconfident estimates, even in situations of high uncertainty, leading to…

Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…

A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…

Morphological methods play a crucial role in remote sensing image processing, due to their ability to capture and preserve small structural details. However, most of the existing deep learning models for semantic segmentation are based on…

Model-based deep learning (MBDL) is a powerful methodology for designing deep models to solve imaging inverse problems. MBDL networks can be seen as iterative algorithms that estimate the desired image using a physical measurement model and…

Modern ConvNets continue to achieve state-of-the-art results over a vast array of vision and image classification tasks, but at the cost of increasing parameters. One strategy for compactifying a network without sacrificing much expressive…

This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual…

The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard…

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…

Mesh-free numerical methods offer flexibility in discretising complex geometries, showing potential where mesh-based methods struggle. While high-order approximations can be obtained via consistency correction using linear systems, they…