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Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…
I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…
The ability to automatically detect certain types of cells or cellular subunits in microscopy images is of significant interest to a wide range of biomedical research and clinical practices. Cell detection methods have evolved from…
Deep convolutional neural networks (CNN) have recently been shown in many computer vision and pattern recog- nition applications to outperform by a significant margin state- of-the-art solutions that use traditional hand-crafted features.…
This paper introduces a deep learning-based super-resolution (SR) framework specifically developed for accurately reconstructing high-resolution velocity fields in two-way coupled particle-laden turbulent flows. Leveraging conditional…
This work presents a quantum convolutional neural network (QCNN) for the classification of high energy physics events. The proposed model is tested using a simulated dataset from the Deep Underground Neutrino Experiment. The proposed…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
Convolutional Neural Networks (CNNs) have been recently employed to solve problems from both the computer vision and medical image analysis fields. Despite their popularity, most approaches are only able to process 2D images while most…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Detecting extreme events in large datasets is a major challenge in climate science research. Current algorithms for extreme event detection are build upon human expertise in defining events based on subjective thresholds of relevant…
The growing use of convolutional neural networks (CNN) for a broad range of visual tasks, including tasks involving fine details, raises the problem of applying such networks to a large field of view, since the amount of computations…
We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…
Deep learning architectures are showing great promise in various computer vision domains including image classification, object detection, event detection and action recognition. In this study, we investigate various aspects of…
In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
Over the past decade, deep learning research has been accelerated by increasingly powerful hardware, which facilitated rapid growth in the model complexity and the amount of data ingested. This is becoming unsustainable and therefore…
Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…
Deep learning based methods, especially convolutional neural networks (CNNs) have been successfully applied in the field of single image super-resolution (SISR). To obtain better fidelity and visual quality, most of existing networks are of…