Related papers: Machine learning-based parameter optimization for …

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a…

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…

In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…

In Machine Learning, Artificial Neural Networks (ANNs) are a very powerful tool, broadly used in many applications. Often, the selected (deep) architectures include many layers, and therefore a large amount of parameters, which makes…

In the present paper a newer application of Artificial Neural Network (ANN) has been developed i.e., predicting response-function results of electrical-mechanical system through ANN. This method is specially useful to complex systems for…

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…

Terahertz (THz) sensing is a promising imaging technology for a wide variety of different applications. Extracting the interpretable and physically meaningful parameters for such applications, however, requires solving an inverse problem in…

Artificial neural networks (ANNs) have been successfully applied to solve a variety of classification and function approximation problems. Although ANNs can generally predict better than decision trees for pattern classification problems,…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we analyze the training dynamics of PINNs optimized with ANaGRAM,…

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…

Supervised classification is the most active and emerging research trends in today's scenario. In this view, Artificial Neural Network (ANN) techniques have been widely employed and growing interest to the researchers day by day. ANN…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

This study presents an innovative application of the Taguchi design of experiment method to optimize the structure of an Artificial Neural Network (ANN) model for the prediction of elastic properties of short fiber reinforced composites.…

Recent studies suggest that artificial neural networks (ANNs) that match the spectral properties of the mammalian visual cortex -- namely, the $\sim 1/n$ eigenspectrum of the covariance matrix of neural activities -- achieve higher object…

This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means…