Related papers: Model Based and Physics Informed Deep Learning Neu…

Physics-informed neural networks approach the approximation of differential equations by directly incorporating their structure and given conditions in a loss function. This enables conditions like, e.g., invariants to be easily added…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs…

Deep neural networks are becoming more and more popular due to their revolutionary success in diverse areas, such as computer vision, natural language processing, and speech recognition. However, the decision-making processes of these…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Graph neural networks (GNNs) are a type of deep learning models that are trained on graphs and have been successfully applied in various domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to…

Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Deep learning, as a highly efficient method for metasurface inverse design, commonly use simulation data to train deep neural networks (DNNs) that can map desired functionalities to proper metasurface designs. However, the assumptions and…

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…

This paper presents a systematic evaluation of Neural Network (NN) for classification of real-world data. In the field of machine learning, it is often seen that a single parameter that is 'predictive accuracy' is being used for evaluating…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

We use Deep Neural Networks (DNNs) to classify and reconstruct a large database of handwritten digits from the intensity of the speckle patterns that result after the images propagated through multimode fibers (MMF). Images transmitted…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…