Related papers: Data Driven Governing Equations Approximation Usin…
Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…
This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…
Regression neural networks (NNs) are most commonly trained by minimizing the mean squared prediction error, which is highly sensitive to outliers and data contamination. Existing robust training methods for regression NNs are often limited…
The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…
One of the methods used in image recognition is the Deep Convolutional Neural Network (DCNN). DCNN is a model in which the expressive power of features is greatly improved by deepening the hidden layer of CNN. The architecture of CNNs is…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…
Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…
DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…
Various powerful deep neural network architectures have made great contribution to the exciting successes of deep learning in the past two decades. Among them, deep Residual Networks (ResNets) are of particular importance because they…
We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a…
Forecasting complex system dynamics, particularly for long-term predictions, is persistently hindered by error accumulation and computational burdens. This study presents RefreshNet, a multiscale framework developed to overcome these…
In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…
Optimal decision-making in social settings is often based on forecasts from time series (TS) data. Recently, several approaches using deep neural networks (DNNs) such as recurrent neural networks (RNNs) have been introduced for TS…
Residual networks (ResNets) represent a powerful type of convolutional neural network (CNN) architecture, widely adopted and used in various tasks. In this work we propose an improved version of ResNets. Our proposed improvements address…
Many techniques have been developed, such as model compression, to make Deep Neural Networks (DNNs) inference more efficiently. Nevertheless, DNNs still lack excellent run-time dynamic inference capability to enable users trade-off accuracy…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…