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Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws directly into the loss function. However, as a fundamental optimization issue,…

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…

Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems,…

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce…

Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we…

PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Electrical Impedance Tomography (EIT) is a highly ill-posed inverse problem, with the challenge of reconstructing internal conductivities using only boundary voltage measurements. Although Physics-Informed Neural Networks (PINNs) have shown…

This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

Physics-Informed Neural Network (PINN) has become a commonly used machine learning approach to solve partial differential equations (PDE). But, facing high-dimensional secondorder PDE problems, PINN will suffer from severe scalability…

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Since the introduction of deep learning for solving partial differential equations (PDEs), there has been growing interest in real-time system responses, where the kernel function plays a key role. Physics-informed neural networks (PINNs),…

When solving time-dependent partial differential equations(PDEs), traditional physics-informed neural networks (PINNs) have inherent limitations: due to the lack of temporal causality, the network is forced to learn the later-time control…

The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by…

For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…

Machine learning-based seismic processing models are typically trained separately to perform specific seismic processing tasks (SPTs), and as a result, require plenty of training data. However, preparing training data sets is not trivial,…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is 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…

While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces…