Foundation models are large artificial intelligence (AI) systems that learn from vast data and now play a central role in science and technology. Yet the complexity of how these models process information makes it difficult to recognize when their outputs are unreliable. This is especially challenging in safety-critical settings, such as health monitoring and smart homes. As hardware technologies evolve, new forms of data emerge from new sensors, and often do not align with past data used to train existing models. How these models encode information might also be disconnected from established scientific knowledge, such as human physiology. Current methods lack a systematic way to incorporate such information or assess when model outputs are unreliable. This research addresses this gap by reshaping how large AI models transmit information so that it becomes easier to assess their output reliably and easier to align with new data and scientific knowledge. The project’s novelties are this new representation of information flow and a unified framework for integrating diverse data with scientific knowledge. The project’s broader significance and importance are enabling trustworthy decision support in large AI systems and educating a workforce adept at leveraging these technologies. This approach treats the internal stages of a foundation model as snapshots of an information flow that captures how the statistical geometry of the model's internal features changes as information passes through it. Learning this flow makes it possible to track uncertainty in a more structured and lower-dimensional space, enabling scalable and accurate reliability estimates that previously did not extend to large-scale models. It supports adaptation to new modalities, such as signals from emerging sensors, and incorporation of scientific laws describing the processes that generate the data. These advances enable trustworthy foundation models that are adaptable and grounded in scientific la