NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
Physics -Informed Neural Networks for Heat Transfer Problems
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A variational neural network using Kolosov-Muskhelishvili potentials solves 2D linear elasticity and fracture problems by minimizing total potential energy and embedding crack discontinuities into the ansatz, yielding higher accuracy and faster convergence than standard physics-informed networks.
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
PINNs with hard and soft boundary enforcement solve membrane form-finding PDEs to accuracy comparable with FEM, with hard-BC yielding smaller boundary errors.
A physics-informed neural network merges sparse LBM data with Navier-Stokes equations to predict unsteady flows in fractal-rough microchannels at 150-200 times lower data cost.
citing papers explorer
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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A Variational Kolosov--Muskhelishvili Network for Elasticity and Fracture
A variational neural network using Kolosov-Muskhelishvili potentials solves 2D linear elasticity and fracture problems by minimizing total potential energy and embedding crack discontinuities into the ansatz, yielding higher accuracy and faster convergence than standard physics-informed networks.
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MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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Physics-informed neural networks for form-finding of unilateral membrane structures
PINNs with hard and soft boundary enforcement solve membrane form-finding PDEs to accuracy comparable with FEM, with hard-BC yielding smaller boundary errors.
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Amalgamation of Physics-Informed Neural Network and LBM for the Prediction of Unsteady Fluid Flows in Fractal-Rough Microchannels
A physics-informed neural network merges sparse LBM data with Navier-Stokes equations to predict unsteady flows in fractal-rough microchannels at 150-200 times lower data cost.