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math.NA2026
Mesh-Free Numerical Approximation of the Biharmonic Equation via Optimized Kolmogorov--Arnold Neural Networks
B. Veena S. N. Rao
A mesh-free numerical framework based on \textit{Kolmogorov--Arnold Physics-Informed Neural Networks} (KAN-PINNs) is developed for the approximation of fourth-order elliptic bounda…
math.NA2026
AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations
B. Veena S. N. Rao
A controlled comparative study of a mesh-free Kolmogorov--Arnold Physics-Informed Neural Network (KAN-PINN) applied to nonlinear strain-limiting partial differential equations is p…
math.NA2025
Neural solver for sixth-order ordinary differential equations
Janavi Bhalala, B. Veena S. N. Rao
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural so…