Drilling-fluid loss has always been one of the challenging issues in the field of drilling engineering. This article addresses the limitations of a single fluid-loss pressure mechanism model and the challenges in predicting positive drilling-fluid-loss pressure. By categorizing fluid losses of various types encountered during drilling, different geological formations associated with distinct mechanisms are considered. The actual drilling-fluid density in the wellbore at the time of fluid-loss occurrence is taken as a reference value for calculating the positive drilling-fluid-loss pressure of the already drilled well. Building upon this foundation, a combined model utilizing the Sparrow Search Algorithm (SSA) and Long Short-Term Memory (LSTM) neural network is constructed. This model effectively explores the intricate nonlinear relationship between well logging, logging engineering data, and fluid-loss pressure. By utilizing both data from the already drilled wells and upper formation data from ongoing drilling, precise prediction of positive drilling formation fluid-loss pressure can be achieved. Case studies demonstrate that the approach established in this paper, incorporating upper formation data, reduces the average absolute percentage error of fluid-loss pressure prediction to 2.4% and decreases the root mean square error to 0.0405. Through the synergy of mechanistic models and data-driven techniques, not only has the accuracy of predicting positive drilling formation fluid-loss pressure has been enhanced, but also valuable insights have been provided for preventing and mitigating fluid losses during drilling operations.