piecewise orthogonal function neural network: a general framework for function approximation

Accurate approximation and modeling of nonlinear dynamic systems remain a central challenge in computational intelligence and control theory. this paper introduces a general form of neural network architectures termed the piecewise orthogonal function neural networks (pofnns), which integrate the concept of orthogonal functional bases with localized piecewise representation. in the proposed framework, the input domain is partitioned into several subregions, each associated with a set of orthogonal basis functions that form locally independent subspaces. this structure enables the network to capture distinct nonlinear behaviors in different regions while preserving numerical stability and interpretability. the results confirm that the proposed framework provides a flexible, stable, and mathematically interpretable foundation for advanced neural modeling of nonlinear processes.