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The present study aims to configure and train a data-driven geometry-specific surrogate model (DD GSM) to simulate the load–displacement behavior until fracture in cylindrical notched specimens subjected to uniaxial monotonic tension tests. Plastic strain hardening that governs the load–displacement behavior and ductile fracture in metals are history-dependent phenomena. With this, the load–displacement response until ductile fracture in metals is hypothesized as time sequence data. To test our hypothesis, a long short-term memory (LSTM) based deep neural network was configured and trained. LSTM is a type of neural network that takes sequential data as input and forecasts the future based on the learned past sequential trend. In this study, the trained LSTM network is referred to as DD GSM as it is used to forecast the load–displacement behavior until ductile fracture for the cylindrical notched specimens. The DD GSM is trained using the load–displacement data until fracture, extracted from the finite element analyses of notched cylindrical test specimens made of ASTM A992 steel. The damage leading to fracture was captured using the Gurson–Tvergaard–Needleman (GTN) model. Finally, the trained DD GSM is validated by predicting the overall load–displacement behavior, fracture displacement, and peak load-carrying capacity of cylindrical notched ASTM A992 structural steel specimens available in the literature that are not used for training purposes. The DD GSM was able to forecast some portions of the load–displacement curve and predict the fracture displacement and peak load-carrying capacity of the notched specimens. Furthermore, the geometric sensitivity of the trained DD GSM was demonstrated by simulating the load–displacement response of an ASTM A992 steel bar with a central hole.