Scientific machine learning (SciML) integrates machine learning (ML) into scientific workflows to enhance system simulation and analysis, with an emphasis on computational modeling of physical systems. This field emerged from Department of Energy workshops and initiatives starting in 2018, which also identified the need to increase "the scale, rigor, robustness, and reliability of SciML necessary for routine use in science and engineering applications" [5]. The field's subsequent growth through funding initiatives, conference themes, and high-profile publications stems from its ability to unite ML's predictive power with the domain knowledge and mathematical rigor of computational science and engineering (CSE). However, this surge in SciML development has outpaced good practices and reporting standards for building trust [66, 51, 109, 117]. SciML models must demonstrate trustworthiness to be safe and useful [44]. Organizational and computational trust definitions [92, 106] inform our criteria for trustworthy SciML: competence in basic performance, reliability across conditions, transparency about processes and limitations, and alignment with scientific objectives. These criteria span technical attributes (correctness, reliability, safety) and human-centric qualities (comprehensibility, transparency).

Rapid yet accurate simulations of fluid dynamics around complex geometries is critical in a variety of engineering and scientific applications, including aerodynamics and biomedical flows. However, while scientific machine learning (SciML) has shown promise, most studies are constrained to simple geometries, leaving complex, real-world scenarios underexplored. This study addresses this gap by benchmarking diverse SciML models, including neural operators and vision transformer-based foundation models, for fluid flow prediction over intricate geometries. Using a high-fidelity dataset of steady-state flows across various geometries, we evaluate the impact of geometric representations -- Signed Distance Fields (SDF) and binary masks -- on model accuracy, scalability, and generalization. Central to this effort is the introduction of a novel, unified scoring framework that integrates metrics for global accuracy, boundary layer fidelity, and physical consistency to enable a robust, comparative evaluation of model performance. Our findings demonstrate that foundation models significantly outperform neural operators, particularly in data-limited scenarios, and that SDF representations yield superior results with sufficient training data. Despite these advancements, all models struggle with out-of-distribution generalization, highlighting a critical challenge for future SciML applications. By advancing both evaluation methodologies and modeling capabilities, this work paves the way for robust and scalable ML solutions for fluid dynamics across complex geometries.

Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However, implementing SciML tools for optimization must be rigorously evaluated and performed with caution. This work proposes the deductions of a robustness test that guarantees the robustness of multiobjective SciML-based optimization by showing that its results respect the universal approximator theorem. The test is applied in the framework of a novel methodology which is evaluated in a series of benchmarks illustrating its consistency. Moreover, the proposed methodology results are compared with feasible regions of rigorous optimization, which requires a significantly higher computational effort. Hence, this work provides a robustness test for guaranteed robustness in applying SciML tools in multiobjective optimization with lower computational effort than the existent alternative.