SpecFuser: A Hybrid Spectral Transformer Framework for Solid Mechanics

Solving solid mechanics problems of complex systems is notoriously demanding either in terms of time, computational resources, or data. Traditional numerical solvers require extensive modelling and fine-grained discretization for computational simulation. Scaling techniques serve as a fundamental strategy for managing computational overhead, including mass scaling which inflates material density, time scaling which compresses the event duration and so on. Nevertheless, a definitive trade-off between runtime and accuracy remains an inherent challenge. Deep learning solvers, on the other hand, are fast at inference, but they carry no physical prior and must recover the underlying mechanics from examples alone, which requires a lot of data and unreliable outside the distribution. To achieve the best of two worlds, we introduce SpecFuser, a hybrid spectral transformer framework that couples a numerical solver with a neural network. Specifically, the full-scaled model is first reduced by geometric scaling, and the numerical solver is run on this computationally cheaper, sub-scaled geometry. The resulting simulation is physically grounded yet geometrically compressed, capturing the essential low-frequency mechanical behaviour at a fraction of the original cost. The solver output, together with the geometric representations of both the sub-scaled and full-scale models, are then jointly encoded and passed to the network as structured input. A Fourier transform with a low-pass cut-off separates a physically exact low-frequency prior from scale-dependent residuals, the truncated spectrum is fused with spatial features and fed to a multi-head cross-attention transformer, which infers the full-scale solution. Because the solver has already supplied the low-frequency answer, the network is left with a low-dimensional residual rather than the full solution operator. This design for complex solid mechanics problems could not only significantly speed up the solving process, but also demonstrates superior capabilities in terms of generality and generalization.