Related papers: An Unsupervised Network Architecture Search Method…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

This paper focuses on the PINNs algorithm by proposing the ALM-PINNs computational framework to solve various nonlinear partial differential equations and corresponding parameters identification problems. The numerical solutions obtained by…

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Differentiable Architecture Search (DARTS) is a simple yet efficient Neural Architecture Search (NAS) method. During the search stage, DARTS trains a supernet by jointly optimizing architecture parameters and network parameters. During the…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are…

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

Differentiable architecture search (DARTS) has emerged as a promising technique for effective neural architecture search, and it mainly contains two steps to find the high-performance architecture: First, the DARTS supernet that consists of…