<p>Computational inverse technology is a prevailing approach to solve engineering problems of complex structural systems, for which key parameters cannot be directly derived through conventional experimental or theoretical derivations. On the other hand, an inversion method applies forward solver iteratively for error minimization, which may entail intractable computational cost. Recently proposed two-way neural network with a direct-weight-inverse (DWI) approach theoretically constructs inverse neural network without expensive training and can significantly increase inversion efficiency. However, DWI can encounter potential out-of-bound input values when inversing the activation function. To fill in this gap, this study proposes full-range power activation functions to solve the out-of-bound issue. Three power activation functions, i.e., power activation functions, power-linear and power-quadratic activation functions, are constructed for DWI approaches. The necessary conditions for constructing inverse problem activation function are proposed. Numerical examples are used to demonstrate the efficacy and proficiency of the power activation functions in two-way neural network for inverse problems. The out-of-bound issue is successfully resolved with these new power activation functions. Especially, the inverse accuracy via the power-linear activation function is substantially improved. The constructed power activation functions remove a major obstacle in solving inverse problems using two-way neural network.</p>