TL;DR
This study systematically compares PINNs preprocessing methods, with particular focus on three universal approaches (the non-dimensionalization, inner normalization layers, and synergistic normalization method for data and equation), and provides a practical reference for selecting preprocessing methods in different physical scenarios.
A robust and critical assessment of PINNs for solving the elastic wave equation in seismology is provided and it is demonstrated that this novel architecture enhances accuracy when applied to the acoustic wave equation, underlying the versatility of the network.
This study examines the influence of six collocation point sampling strategies—random uniform, uniform grid, Latin hypercube sampling, Sobol sequence, staggered triangular lattice, and a hybrid combined approach—on the performance of PINNs applied to the one-dimensional Burgers’ equation.
A novel framework that combines Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods (DGM) is proposed to overcome difficulties in solving PDEs using AI, and it is shown that both techniques are highly accurate in the comparative analysis for a variety of parameter regimes.
As nonlinearity strengthens, the accuracy advantage of discretization-based constraints becomes increasingly pronounced, with smaller optimization errors compensating for the truncation errors, and the more complex the nonlinearity and boundary conditions, the greater the advantage of GNN over MLP.
This paper presents a comprehensive study of deep learning-based numerical solutions for nonlinear PDEs in fluid dynamics, and proposes a proposed framework that integrates neural network architectures with physics informed constraints to accurately approximate fluid behavior while reducing computational complexity.
Novel physics-informed feature decomposition in residual dense block neural networks (PI-RDB-NN), which embeds physical constraints directly into the network architecture rather than relying solely on soft constraints, improves aerodynamic force predictions and CFD agreement.
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