A single physics-informed neural network learns a continuous family of PDE solutions indexed by loss weights or coefficients by sampling the conditioning vector during optimization.
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PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
PINN residuals serve as an off-grid probe to adaptively refine meshes before a finite-difference solve, yielding lower error with fewer degrees of freedom than uniform refinement on the 1D Burgers equation.
A PINN with learnable loss balancing and transfer learning predicts heat transfer in miniature heat sinks to under 8% error using only 87 data points, outperforming standard baselines.
A diffusion-enhanced version of the NSCH-Oldroyd system is locally well-posed, with PINN numerics confirming energy decay for representative thrombus models.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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Local Well-Posedness of a Modified NSCH-Oldroyd System: PINN-Based Numerical Computation
A diffusion-enhanced version of the NSCH-Oldroyd system is locally well-posed, with PINN numerics confirming energy decay for representative thrombus models.