The need to implement complex physics systems is critical across various scientific and engineering domains. However, traditional numerical models for simulating these systems are computationally expensive, requiring significant time, resources, and cost. Recent advancements in AI present a promising alternative, with AI models demonstrating the ability to capture the dynamics of complex physical systems. Despite these successes, AI models suffer from key limitations, including challenges with generalization, vulnerability to bias, ethical concerns, and accuracy, particularly when applied to unseen tasks or variable-range predictions. These limitations are collectively viewed as issues of robustness. The TURING project aims to address these shortcomings by developing robust AI-driven solutions. It integrates multidisciplinary advancements from Machine Learning, Computer Engineering, Physics, and SSH to pre-train generative, multimodal foundation models capable of capturing the physics of dynamic systems that share common properties. Starting with a cautious approach, the models will incorporate representations of increasingly complex physical systems as robustness is ensured. Once pre-trained, these foundation models will be fine-tuned for specific tasks, enhancing their domain-specific robustness. The tasks will target critical engineering and physics problems in nuclear energy, particle physics, and meteorology, which are of high priority for the EU. The task-specific and foundation models, collectively termed "TURING models", will be developed in collaboration with partners from India, Canada, and Switzerland. To maximize the impact of TURING models, the project will ensure compliance of its activities with regulations such as the EU AI Act and then publicly release those models, along with the TURING Framework (MLOps SW tools and web-based app with conversational capabilities), enabling developers and end users to leverage this technology for their applications.