Related papers: Benchmarking Physics-Informed Neural Networks and …
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…
Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…
In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…
Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…
The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…
Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order…
Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
This research introduces an innovative application of physics-informed neural networks (PINNs) to tackle the intricate challenges of radiative transfer (RT) modeling in exoplanetary atmospheres, with a special focus on efficiently handling…
In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…
The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…
Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ)…
Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…
Domain-decomposed variants of physics-informed neural networks (PINNs) such as finite basis PINNs (FBPINNs) mitigate some of PINNs' issues like slow convergence and spectral bias through localisation, but still rely on iterative nonlinear…