Load-dependent topology optimization has experienced rapid development over the past two decades. As an important branch of classical topology optimization, it not only faces the common bottleneck of finite element analysis in optimization algorithms, but also encounters additional computational challenges arising from dynamic changes in load positions. Although direct integration and indirect methods based on field/potential functions have become mature for small and medium-sized problems, their computational efficiency in large-scale complex scenarios or design processes requiring high-frequency real-time interaction has not been fully verified. To improve the overall computational efficiency of load-dependent topology optimization, this paper proposes a Two-Branch Problem-Independent Machine Learning (TB-PIML) model based on an extended multiscale finite element framework. This model first utilizes shared layers to transform the material distribution information of local substructures into a shared feature representation, and continues to learn through the shape function branch to obtain coarse and fine-scale displacement mapping relationship. Meanwhile, the load branch on the other end integrates the shared information with locally introduced unit load parameters to jointly output the energy equivalent load of the substructure. In this way, the model avoids the construction of related local parameters under the traditional framework, jointly achieving dual acceleration in structure-load coupled optimization. Furthermore, since the model always directly learns local information without introducing any global parameters, it is problem-independent and can naturally adapt to any design domain, displacement constraints, and load types without the need to regenerate samples or modify the model. Finally, a two-dimensional piston example with 7 million degrees of freedom is specifically presented, where each iteration takes only 5.5 seconds without resorting to parallel computing. Compared to the traditional fine-scale finite element method, this model achieves an overall speedup of 90.5%, with a relative error of only 0.69%, maintaining stable numerical accuracy.