相关论文: Parameter Estimation with Dense and Convolutional …

In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…

Deep neural networks (DNNs) exhibit superior performance in various machine learning tasks, e.g., image classification, speech recognition, biometric recognition, object detection, etc. However, it is essential to analyze their sensitivity…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Neural Operators (NOs) are a powerful deep learning framework designed to learn the solution operator that arise from partial differential equations. This study investigates NOs ability to capture the stiff spatio-temporal dynamics of the…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

When fine-tuning Deep Neural Networks (DNNs) to new data, DNNs are prone to overwriting network parameters required for task-specific functionality on previously learned tasks, resulting in a loss of performance on those tasks. We propose…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

In this paper, deep neural network (DNN) is integrated with spatial modulation-orthogonal frequency division multiplexing (SM-OFDM) technique for end-to-end data detection over Rayleigh fading channel. This proposed system directly…

With the rising prevalence of cardiovascular diseases, electrocardiograms (ECG) remain essential for the non-invasive detection of cardiac abnormalities. This study presents a comprehensive evaluation of deep neural network architectures…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs…

We propose to impose symmetry in neural network parameters to improve parameter usage and make use of dedicated convolution and matrix multiplication routines. Due to significant reduction in the number of parameters as a result of the…

For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…

Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may…

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work,…