Related papers: A Least-Squares-Based Regularity-Conforming Neural…
As deep neural networks are increasingly used in applications suited for low-power devices, a fundamental dilemma becomes apparent: the trend is to grow models to absorb increasing data that gives rise to memory intensive; however low-power…
Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…
Deep reinforcement learning (DRL) methods such as the Deep Q-Network (DQN) have achieved state-of-the-art results in a variety of challenging, high-dimensional domains. This success is mainly attributed to the power of deep neural networks…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
This paper concerns solving the steady radiative transfer equation with diffusive scaling, using the physics informed neural networks (PINNs). The idea of PINNs is to minimize a least-square loss function, that consists of the residual from…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…
This paper proposes a novel algorithm for training recurrent neural network models of nonlinear dynamical systems from an input/output training dataset. Arbitrary convex and twice-differentiable loss functions and regularization terms are…
Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation,…
In this work we develop a novel algorithm, termed as mixed least-squares deep neural network (MLS-DNN), to recover an anisotropic conductivity tensor from the internal measurements of the solutions. It is based on applying the least-squares…
Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
Deep neural networks have exhibited remarkable performance in image super-resolution (SR) tasks by learning a mapping from low-resolution (LR) images to high-resolution (HR) images. However, the SR problem is typically an ill-posed problem…
In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…
Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…