Related papers: Physics-Informed Neural Networks for Parametric Co…

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"…

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…

Physics-informed neural networks approach the approximation of differential equations by directly incorporating their structure and given conditions in a loss function. This enables conditions like, e.g., invariants to be easily added…

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…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

Physics-informed neural networks have emerged as a coherent framework for building predictive models that combine statistical patterns with domain knowledge. The underlying notion is to enrich the optimization loss function with known…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a…

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…

Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose…

The Vlasov-Poisson system is employed in its reduced form version (1D1V) as a test bed for the applicability of Physics Informed Neural Network (PINN) to the wave-particle resonance. Two examples are explored: the Landau damping and the…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and CO$_2$, H$_2$, and wastewater injection operations. This challenge…

We propose a physics-informed neural network as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the…

Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel…

We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that the underlying PDE residual can be made arbitrarily small…

The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems but with low computational cost and low runtime. Various techniques have been explored within…

Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted…

Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…

Gaining and understanding the flow dynamics have much importance in a wide range of disciplines, e.g. astrophysics, geophysics, biology, mechanical engineering and biomedical engineering. As a reliable way in practice, especially for…