To predict the fatigue life for oblique hyperbola-and bilinear-mode S-N curves of metallic materials with various strengths,a machine-learning approach for direct analysis was employed.Additionally,to determine the fatigue limit of the utilized materials (AISI 316,AISI 4140 and CA6NM series) with different S-N curve modes using finite-fatigue life data,a Bayesian optimization-based inverse analysis was performed.The results indicated that predictions of the fatigue life for the utilized datasets via the random forest (RF) algorithm for AIS14140 and CA6NM,and artificial neural network (ANN) for AISI 316,distribute within 2 factor error lines for most data.In the Bayesian optimization-based inverse analysis,the specific explanatory variabl.es corresponding to the optimized maximum fatigue life were treated as the fatigue limits.The predicted fatigue limits either approximated to or slightly underestimated the experimental results,except for several cases with large errors.Using the inverse analysis to predict the fatigue limit for both S-N curve modes is applicable for current employed data-set.However,the explored maximum fatigue lives via BO corresponding to the predicted fatigue limit were underestimated for AISI 4140 and CA6NM,and was overestimated for AISI 316 because of effect of shape of S-N curves.By combining the ANN or RF direct and BO inverse algorithms,whole S-N curves (including the fatigue limit) were evaluated for the S-N curve shapes of the oblique hyperbola and bilinear modes.