Functionally graded materials (FGMs) are a class of advanced composite materials whose properties vary continuously by combining two or more constituent materials. This smooth spatial variation in material properties significantly enhances structural strength and thermal resistance compared to conventional composites [1]. For the effective application of FGMs, it is crucial to identify an optimal spatial distribution of material constituents within the domain based on the intended operating conditions. Existing FGM design approaches commonly employ schemes such as power-law, sigmoidal, and exponential distributions. However, these methods offer limited flexibility in representing the design space and are typically restricted to simple, regular geometries such as rectangular or square domains. In this study, a novel methodology for generating FGM profiles based on Gaussian Process Regression (GPR) and Gaussian Random Fields (GRF) is proposed [2]. Unlike conventional approaches, the proposed framework is capable of handling both regular and irregular geometries, including complex domains such as elliptical plates with circular holes. This enhanced geometric adaptability makes the method more versatile for practical engineering applications. Additionally, the GPR-based approach enables the incorporation of diverse boundary conditions, including region-specific material constraints that are often required in real-world designs. The proposed GPR-based profile generation scheme is applied to design the FGMs subjected to thermo-mechanical loading. To perform the optimization, the GPR-based profile generation scheme is integrated into a Genetic Algorithm (GA) optimization framework. Numerical examples, such as a square plate with a circular hole and an elliptical plate with two circular holes, are presented to demonstrate the efficacy of the proposed approach.