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We provide the most complete analysis so far of quasinormal modes of rotating black holes in a general higher-derivative extension of Einstein's theory. By finding the corrections to the Teukolsky equation and expressing them in a simple…
In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…
A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schr\"{o}dinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution…
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…
Physics informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by PINNs in approximating the solutions of a large class of linear parabolic PDEs, namely…
We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the…
We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular…
The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…
The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…
The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based…
Previous research in the scientific field has utilized statistical empirical models and machine learning to address fitting challenges. While empirical models have the advantage of numerical generalization, they often sacrifice accuracy.…
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…
A Regge--Wheeler analysis is performed for a novel black hole mimicker `the regular black hole with asymptotically Minkowski core', followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order…
The study of the gravitational wave signatures of neutron star oscillations may provide important information of their interior structure and Equation of State (EoS) at high densities. We present a novel technique based on physically…
Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical…
Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive…
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing physics into neural-network training. Recent studies have shown that parameterized PINNs can learn…