Pulse eddy current testing, as a non-contact, environmentally friendlynon-destructive testing method requiring no coupling agent, is widely usedto assess the structural healthof metallic pipelines. The timeliness and accuracy of pulse eddy current response estimation are severely constrained by electromagnetic modelling approaches for well casing pulse eddy current testing. Traditional mathematical modelling approaches demand substantial prior knowledge, entailing complex model construction and high computational cost.Meanwhile, purely data-driven neural network methods lack physical information constraints and exhibit insufficient robustness. Field operations frequently necessitate a pulsed eddy current modelling method balancing efficiency and precision. This research addresses this issue by proposing a novel physical information neural network surrogate model. Electromagnetic physical laws are embedded as prior knowledge within the objective loss function to guidethe training process of deep neural networks. Furthermore, sub-neural networks are introducedto estimate electromagnetic responses across distinct computational domains, separated according to their physical characteristics. An interface loss function is designed to compensate for discontinuities in output between networks when predicting results across dual computational domains, thereby enhancing the accuracy and robustness of electromagnetic response estimation. The performance of the proposed physio-informative neural network was validated using electromagnetic response data obtained via finite element analysis. Its capabilities were compared against conventional purely data-driven neural networks and interpolation algorithms. Results show that the physical information neural network model accurately estimates electromagnetic responses in oil casing eddy current testing, achieving a coefficient of determination exceeding 0.95. Furthermore, the inference speed of the physical information neural network model surpasses that of finite element analysis by over 52 times.