Current signal processing algorithms excel at impairment compensation when the parameters of optical fiber systems are precisely defined. However, their effectiveness diminishes considerably in the presence of imprecise parameters. By integrating 'knowledge application from physics to neural networks (NN)' with 'information feedback from NNs to physics', this paper proposes a physics-regulated digital backpropagation (PR-DBP) algorithm, which shows great promise for impairment compensation with imprecise fiber parameters. The PR-DBP employs an optimization-estimation-initialization loop structure. The optimization process provides the network's adaptability by minimizing the loss value as in conventional NNs. The estimation process dynamically tracks physical parameters by extracting information from NNs to the physical domain. The initialization process offers a physics-based global control over the neural network, thereby mitigating the risk of overfitting by preventing an excessive focus on loss minimization. Moreover, a phase-shift weight function is applied to further improve algorithmic efficiency. Numerical analyses indicate that the PR-DBP significantly outperforms conventional methods in optical fiber systems with imprecise parameters, achieving a bit error rate reduction by an order of magnitude. As a mutually reinforcing part of impairment compensation, a high-accuracy and adaptive fiber parameter estimation is also demonstrated.