Entropy stability is crucial for ensuring the robustness of numerical methods for hyperbolic conservation laws. Summation-by-parts (SBP) operators provide a general framework to systematically develop entropy-stable schemes by mimicking continuous properties on a discrete level. They have proven to be a powerful tool for providing stable and high-order accurate numerical solutions. Classically, they are developed to differentiate polynomials up to a certain degree exactly. However, in many cases alternative function spaces such as trigonometric, exponential, or radial basis functions (RBFs) better approximate the underlying solution space. The recently developed concept of function space SBP (FSBP) operators [1] provides a framework for SBP operators based on general function spaces, which has been extended to multiple dimensions in [2]. Especially in multidimensional problems with complex domains, RBFs offer excellent approximation properties on scattered data. However, RBF methods applied directly to hyperbolic problems often suffer from stability issues. Combining RBFs with SBP operators yields provably entropy-stable mesh-free discretizations. In [3], an optimization-based construction procedure for FSBP operators in one spatial dimension has been developed. In this talk, I will first discuss extensions of this optimization problem, which are especially of interest for global FSBP operators and highlight additional criteria that should be satisfied by the resulting operators and how these criteria can be incorporated in the construction. Secondly, I will show how the optimization-based construction approach can be generalized to arbitrary point distributions in multiple dimensions. Finally, I present results for one- and two-dimensional numerical examples that illustrate the performance of the constructed FSBP operators. REFERENCES [1] Glaubitz J., Nordström J., Öffner P., Summation-by-Parts Operators for General Function Spaces, SIAM Journal on Numerical Analysis, 61(2), 733–754, 2023. [2] Glaubitz J., Klein S.-C., Nordström J., Öffner P., Multi-Dimensional Summation-by-Parts Operators for General Function Spaces: Theory and Construction, Journal of Computational Physics, 491, 112370, 2023. [3] Glaubitz J., Nordström J., Öffner P., An Optimization-Based Construction Procedure for Function Space-Based Summation-by-Parts Operators on Arbitrary Grids, Journal of Scientific Computing, 105(3), 83, 2025.