Fig. 1 Initial microstructure of the Ti-2Al-9.2Mo-2Fe alloy: (a) low and (b) high magnification.

Fig. 2 Schematic illustration of the present DNN architecture.

Fig. 3 Instantaneous temperature of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and 1000?°C (f).

Fig. 4 Experimental flow curves of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and1000?°C (f).

Fig. 5 Average error with variation of (a) the number of hidden neurons, (b) number of iterations, (c) learning rate, and (d) momentum term for conventional ANN and present DNN models. The arrows indicate the minimum average error for each plot.

Fig. 6 Average error during optimization using the conventional ANN and present DNN models.

Fig. 7 Comparison of predicted and experimental flow stress during training (a) and (b) testing of the present DNN model.

Fig. 8 Comparison of experimental (solid line) and predicted (dashed line for ANN and dotted line for DNN) flow behaviors of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and 1000?°C (f).

Fig. 9 Processing maps for Ti-2Al-9.2Mo-2Fe alloy at a strain of 0.6 predicted by ANN (a) and DNN (b). The shaded areas, contour lines, and dotted rectangles represent the unstable domains, the efficiency of power dissipation, and optimum hot working conditions, respectively.

Fig. 10 Microstructures of alloys formed under different deformation conditions to validate unstable regions: (a)(b) 800?°C, (c)(d) 850?°C, (e)(f) 1000?°C; (a)(c)(e) 1 s-1, (b)(d)(f) 10 s-1.

Fig. 11 Inverse pole figure (IPF) maps for the β phase of the alloy deformed at a strain rate of 0.1 s-1 and temperatures of 800?°C (a), 900?°C (b), and 1000?°C (c). Black and white lines indicate high-angle (≥15°) and low-angle (2°-15°) grain boundaries, respectively. The arrows indicate typical DRXed grains. The inset in Fig. 11(a) shows an IPF map for the α phase.

Fig. 12 IPF maps for the β phase of the alloy deformed at a strain rate of 10 s-1 and temperatures of 800?°C (a), 900?°C (b), and 1000?°C (c), respectively. Black and white lines indicate high-angle (≥15°) and low-angle (2°-15°) grain boundaries, respectively. Maps were taken from areas outside the flow-localized band.