Mahidhar Reddy Patukuri

Neural Network Solvers for Nonlinear ODEs: Benchmarking MLPs and B-Spline/Chebyshev KANs

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-splines, and a KAN whose edges are Chebyshev series. Each network is trained only on the residual of the equation and on its initial or boundary...