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Physics informed neural networks (PINNs) have drawn attention in recent years in engineering problems due to their effectiveness and ability to tackle the problems without generating complex meshes. PINNs use automatic differentiation to…

Time-domain simulations are crucial for ensuring power system stability and avoiding critical scenarios that could lead to blackouts. The next-generation power systems require a significant increase in the computational cost and complexity…

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 deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This…

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Physics-Informed Neural Networks (PINNs) have shown continuous and increasing promise in approximating partial differential equations (PDEs), although they remain constrained by the curse of dimensionality. In this paper, we propose a…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, and stable numerical algorithms for solving the phase…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…