We present NewPINNs, physics-informing neural networks that couple traditional solvers into the training loop. Unlike physics-informed neural networks (PINNs) [1] that enforce physics through residual minimization, NewPINNs create a synergistic push-pull mechanism where the neural network learns solutions alongside the solver. NewPINNs eliminate customized loss functions based on equation residuals and boundary conditions, overcome convergence issues in PINNs [2], and leverage solver guarantees for accuracy and convergence. Like PINNs, only parameter inputs of the differential equations are required for training. For steady-state systems, we exploit the property that any initial state converges to the same equilibrium after sufficient solver iterations, enabling training with significantly fewer iterations per epoch while maintaining solution quality. We apply NewPINNs to parameterized nonlinear Poisson PDEs and 2D lid-driven cavity problems using a finite element solver. Once trained, NewPINNs predictions significantly reduce solver iterations needed for converged solutions. For transient systems, the neural network prediction serves as the initial state, which the solver advances in time to construct training targets. We demonstrate this on 1D Allen-Cahn and Kuramoto-Sivashinsky equations using MATLAB’s Chebfun package. This approach bridges traditional solvers with neural architectures, enabling the neural network to become a surrogate model of the numerical solver. [1] Raissi, M., Perdikaris, P., and Karniadakis, G. E., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations., Journal of Computational physics, 378, 686-707, 2019. [2] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., and Mahoney, M. W., Characterizing possible failure modes in physics-informed neural networks, Advances in neural information processing systems, 34, 26548-26560, 2021.