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Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…

Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…

Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, Extended PINNs…

Holz & Wheeler (\cite{hw}) have recently proposed that a Schwarzschild black hole may act as a retro-lens which, if illuminated by a powerful light source, deflects light ray paths to large bending angles and a series of luminous arcs (or…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

We report on the nature of prominent sources of light and shadow in the Galactic Center. With respect to the Bremsstrahlung X-ray emission of the hot plasma in that region the Galactic Center casts a 'shadow'. The 'shadow' is caused by the…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

The dynamics of charged particles around magnetized black holes provide valuable insights into astrophysical processes near compact objects. In this work, we investigate the bound and unbound trajectories of charged particles in the…

We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter \(H(z)\) within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the…

We implement a Physics-Informed Neural Network (PINN) for solving the two-dimensional Burgers equations. This type of model can be trained with no previous knowledge of the solution; instead, it relies on evaluating the governing equations…

This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…

Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model described by a nonlinear PDE, we adopt Physics-Informed Neural…

Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems. Existing generalization analyses for PINNs and VPINNs…

We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO)…

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance…

This paper addresses the challenge of transient stability in power systems with missing parameters and uncertainty propagation in swing equations. We introduce a novel application of Physics-Informed Neural Networks (PINNs), specifically an…

Predicting the Remaining Useful Life (RUL) is essential in Prognostic Health Management (PHM) for industrial systems. Although deep learning approaches have achieved considerable success in predicting RUL, challenges such as low prediction…

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a…