Fig. 4: Computational results for 1D beam structure.

a Randomly distributed training data for beam structures. b Verification for case 1 (simply supported beam). The boundary displacement ω constraint is given by ω | _x/l=0,x/l=1 = 0. The vertical uniform load q is set to −1. c Verification for case 2 (double-clamped beam). The displacement ω and turning angle θ at the ends of the beam are imposed with ω | _x/l=0,x/l=1 = 0 and θ | _x/l=0,x/l=1 = 0. The vertical uniform load q is −1. d Verification for case 3. The turning angles θ at the beam ends are constrained, namely, θ | _x/l=0,x/l=1 = 0, but the constraints of displacements ω are separately given by ω | _x/l=0 = 0 and ω | _x/l=1 = 1. e Verification for case 4. The constraints of displacements ω and turning angles θ are defined as ω | _x/l=0,x/l=1 = 0 and θ | _x/l=0 = 0 and θ | _x/l=1 = 1, respectively.