4 papers
Neural Network Solvers for Nonlinear ODEs: Benchmarking MLPs and B-Spline/Chebyshev KANs
Mahidhar Reddy Patukuri, B. Veena S. N. Rao, S. M. Mallikarjunaiah
Three neural networks are compared as solvers of nonlinear ordinary differential equations: a multilayer perceptron (MLP), a Kolmogorov-Arnold network (KAN) whose edges are B-splin…
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…
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…
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…