Adaptive Mixture-of-Experts with smooth routing based on PINNs for generalized nonlinear oscillators

This paper proposes an adaptiveMixture-of-Experts architecture based on physics-informed neural networks (AdaMoE-PINNs) for solving generalized nonlinear oscillators. The design couples three mechanisms: learnable Fourier features driven by the residual and protected from collapse via frequency repulsion, a C ∞ -smooth mollified router that enforces exact sparsity while supporting high-order automatic differentiation, and a physical Occam’s-razor objective with residual-aware pruning that distills the minimal active expert set. This approach will be helpful for overcoming the spectral bias of physics-informed neural networks (PINNs) and fractal multiscale PINNs’s (FMPINNs) inability to track out-of-band resonances with hand-prescribed features. We assess the efficiency of the proposed method on three nonlinear oscillators that present distinct spectral challenges, including Duffing oscillator, forced van der Pol-Duffing-Helmholtz oscillator and He’s fractal oscillator. Numerical comparisons across all benchmarks confirm that AdaMoE-PINNs outperform PINNs and FMPINNs, with the improvement attributed to its spectral-adaptive mechanism. The findings will provide an efficient approach for understanding the numerical behaviour of nonlinear or fractal oscillation systems.