To address the issues of high computational and storage costs， poor stability of stiff systems， and difficulties in handling algebraic constraints in the traditional numerical methods for Integro-Differential-Algebraic Equations （IDAEs）， an Auxiliary Physics-Informed Neural Network （APINN）-based method for solving IDAEs， named APINN-IDAE， was proposed. The core idea of this method is to use the multi-task learning mechanism of APINN， introducing auxiliary network outputs to specifically approximate the integral history terms， so that the intractable integral constraints in the original IDAE system were transformed into differential relations that are easier to optimize， thereby avoiding the computationally expensive numerical integration in the traditional methods. The differential variables were handled by the main network output， while the integral terms and algebraic constraint residuals were processed by the auxiliary outputs， respectively. In addition， a unified weighted loss function was constructed， incorporating the differential equations， algebraic equations， auxiliary variable differential relations， and initial conditions. Experimental results on several typical IDAE examples （including nonlinear， variable-coefficient， and strongly coupled systems） show that the predicted solutions of the proposed method highly coincide with the exact solutions within the solution domain. And the relative L2 errors for both differential and algebraic variables reach the order of 10?3 to 10??， without observable error accumulation over time. It can be seen that APINN-IDAE retains the mesh-free and automatic differentiation advantages while using auxiliary variables to avoid explicit differentiation of integral terms， thereby reducing the computational complexity of integral operators and improving gradient stability， offering potential robustness for stiff or high-index IDAE systems， and providing a new perspective for solving multi-physics coupling problems.
