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In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
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…
In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional…
Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…
Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper…
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…
In this work, the hybrid intelligent computing method, which combines efficient Jaya algorithm with classical Runge-Kutta method is applied to solve the Falkner-Skan equations with various wedge angles, which is the fundamental equation for…
Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the…
The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…
The purpose of this paper is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarities and differences between them. The epitomal linear…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for analyzing nonlinear partial differential equations and identifying governing equations from observational data. In this study, we apply PINNs to investigate…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
To address the initial singularity inherent in solutions to fractional partial differential equations (fPDEs), we propose an accelerated Alikhanov discretization formulation implemented on nonuniform time grids. Based on the…
In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…
One of strengths in the finite element (FE) and Galerkin methods is their capability to apply weak formulations via integration by parts, which leads to elements matching at lower degree of continuity and relaxes requirements of choosing…
A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces…