Abstract: Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order ...

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Abstract: Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE ...

This paper presents the application of the unscented Kalman filter (UKF) for estimating the dynamic states of a maneuvering tank using a second-order Gauss-Markov process model. The proposed method is ...

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...

Phenomena such as mechanical vibrations, resonance and oscillations can be mathematically described by second-order differential equation systems, commonly referred to as second-order systems. Working ...

In geometrically nonlinear problems solved using the Finite Element Method (FEM), the structure response is directly influenced by the level of discretization and the nonlinear solution algorithm used ...

In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the ...