Recently, the effectiveness of machine learning techniques in modeling the complex mechanical or thermo-mechanical coupled behavior of heterogeneous materials at the microscale has been demonstrated in an increasing number of publications. However, many data-driven approaches suffer from insufficient generalizability, high computational costs, and large data requirements due to the lack of physical constraints. To reduce the impact of these limitations, we present a novel spectral-based physicsinformed finite operator learning (SPiFOL) technique [1]. The SPiFOL approach combines a physicsinformed operator learning technique with spectral methods, which are commonly used for example either in FFT-based microstructure simulations or in FE-FFT-based two-scale simulations [2]. Since applying spectral methods inherently ensures equilibrium in combination with periodic boundary conditions and avoids the need for automatic differentiation (which is commonly used when building the physical loss functions in standard finite operator learning (FOL) techniques) through simple multiplications in Fourier space, the SPiFOL framework is significantly more accurate and efficient compared to standard FOL frameworks. In this work, we will investigate not only pure mechanical microstructural responses, but we will also apply the SPiFOL framework to solve multi-physical boundary value problems. Specifically, we will consider quasi-stationary thermo-mechanically coupled systems. Thus, the loss function is formulated in terms of the balance of linear momentum and the balance of energy in Fourier space, respectively (cf. [3]). To demonstrate the feasibility of the proposed framework, several numerical examples are provided. REFERENCES [1] Harandi A., Danesh H., Linka K., Reese S., Rezaei S., SPiFOL: A Spectral-based physics-informed finite operator learning for prediction of mechanical behavior of microstructures, JMPS, Vol. 203, 106219, 2025. [2] Gierden C., Kochmann J., Waimann J., Svendsen B., Reese S., A Review of FE-FFT-Based Two-Scale Methods for Computational Modeling of Microstructure Evolution and Macroscopic Material Behavior, ACME, Vol. 29, pp. 4115–4135, 2022. [3] Schmidt A., Gierden C., Fechte-Heinen R., Reese S., Waimann J., Efficient thermo-mechanically coupled and geometrically nonlinear two-scale FE-FFT-based modeling of elasto-viscoplastic polycrystalline materials, CMAME, Vol. 435, 117648, 2025.