The paper presents an adaptive physics-informed neural network (PINN) framework for solving the Blasius boundary‑layer equation. By combining gradient‑norm‑based loss weighting, nonuniform residual‑based collocation, and a sequential Adam–L‑BFGS optimization, the authors achieve a highly accurate prediction of the wall‑shear coefficient, with an absolute error of $1.896 imes10^{-5}$ for $f''(0)$. A comparative study of network architectures shows that a two‑hidden‑layer model yields the lowest wall‑shear error, while deeper networks reduce the weighted loss but increase physical error.
"whyItMatters":"The adaptive framework demonstrates that coordinated adjustments to loss weighting, collocation strategy, and optimization can substantially improve the physical accuracy of PINNs for classical fluid dynamics problems."
By Mehari Fentahun Endalew, Xiaoming John Zhang
arXiv:2606. 05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
The paper introduces ADE‑FEMU, an end‑to‑end differentiable framework that embeds a constitutive neural network within a JAX‑based finite element solver and learns its parameters by minimizing a measurement‑mismatch loss using automatic differentiation. It demonstrates two neural network architectures—a flexible grey‑box CANN and an interpretable white‑box CANN—for incompressible isotropic hyperelastic materials, and validates the approach on three experimental datasets, including full‑field DIC, reduced‑data stretch profiles, and a heterogeneous matrix‑inclusion system.
By Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen
The paper introduces a physics-informed neural network (PINN) framework for modeling fluid flow in dual‑network porous media, specifically addressing double porosity/permeability (DPP) systems. The framework embeds governing equations and boundary conditions into the loss function with adaptive weighting, employs dynamic collocation point selection, and uses shared trunk architectures to efficiently capture coupled pore‑network behavior. It is mesh‑free, accurately handles discontinuities across layered domains, and supports robust inverse analysis for parameter identification, with a systematic convergence study validating its stability and accuracy.
By V. S. Maduri, K. B. Nakshatrala
The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.
By Wenhao Chen, Alexandre M. Tartakovsky