<p>Numerical simulation of time-domain wave propagation in heterogeneous materials with extreme eight-to-nine-order magnitude contrasts in conductivity and permeability poses significant stability challenges for grid-based finite difference time-domain methods. We present a localized mesh-free radial basis function-finite difference (RBF-FD) framework augmented with shape parameter adaptive damping tuning (DAT) to deliver robust and accurate solutions. DAT dynamically optimizes the mesh-free shape parameter <i>c</i> as our method’s local damping actuator using a neural network (NN) trained on datasets generated by an improved random walk algorithm. The NN predicts <i>c</i> based on local wave frequency, physical damping, and node density <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation>. Numerical experiments on 2D and 3D extreme-contrast models show order-of-magnitude reductions in numerical errors and improved efficiency versus conventional methods. Ablation studies confirm that only localized mesh-free <i>c</i>-tuning achieves higher accuracy, enabling stable multi-physics wave simulation in complex media with potential extensions to structural dynamics and coupled electromagnetic problems.</p>