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In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…
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…
This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…
This paper presents a fully data-free Physics-Informed Neural Network (PINN) capable of solving compressible inviscid flows (ranging from supersonic to hypersonic, up to Ma=15, where Ma is the Mach number) around a circular cylinder. To…
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…
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…
Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…
The development of techniques to measure accurately black hole spins is crucial to study the physics and astrophysics of these objects. X-ray reflection spectroscopy is currently the most popular method to estimate the spins of accreting…
In a quantum theory of gravity, fluctuations about the vacuum may be considered as Planck scale virtual black holes appearing and annihilating in pairs. Incident fields scattering from such fluctuations would lose quantum coherence. In a…
Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling…
We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations…
The continuum-fitting method is one of the two most advanced methods of determining the black hole spin in accreting X-ray binary systems. There are, however, still some unresolved issues with the underlying disk models. One of them…
Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…
A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…
Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…
Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often…
The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain…
Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…
Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…
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…