TL;DR
Experimental results confirm that the sampling strategy can effectively enhance the solution accuracy and provide reliable technical guidance for the optimization of sampling mechanisms in PINNs.
Adaptive computational grids improve the accuracy and efficiency of numerical simulations by concentrating nodes in regions of particular interest, but classical adaptation methods based on differential equations are often computationally expensive and geometry-dependent. This study proposes a physics-informed neural n...
Physics-informed neural networks (PINNs) are employed to solve the Navier–Stokes equations with a standard k–ω turbulence model for flow over a period, focusing on how the spatial placement of training points and hyperparameters affect accuracy. Wall-bounded turbulence modeling includes challenges because variables lik...
Simulating dispersive shock waves (DSWs) using physics-informed neural networks (PINNs) presents significant numerical difficulties. In particular, the square-root initial condition exhibits singularity near the origin, making it difficult to fit accurately. This initial fitting error is amplified through nonlinear evo...
This paper considers a model describing population dynamics where diffusion is nonlocal and habitat boundaries expand based on population flux. The population distribution is governed by a nonlocal Fisher–KPP equation with free boundaries. We propose a Front-Tracking method coupled with a fourth-order Runge–Kutta sch...
This work proposes and compares several approaches to solve the Boltzmann equation with uncertain parameters, including multilevel Monte Carlo and multifidelity methods that employ an asymptotic-preserving-hybrid scheme for the deterministic Boltzmann model and provides practical guidelines for selection between APH-ba...
The paper considers the application of Physics-Informed Neural Networks (PINN) to solving a two-dimensional Poisson equation with inhomogeneous mixed boundary conditions. The PINN method combines neural network approximations and physical laws, including the residual of the equation and errors at the boundary, into a s...
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