Advances in machine learning and reduced-order modeling are rendering construction of digital twins for complex systems possible. We are using these tools to perform scientific discovery, design optimization, and data-informed decision making in diverse applications. In this talk we (1) show how graphs may be used to build robust digital twins in high-consequence engineering settings and (2) present ongoing work developing them to perform AI-enhanced scientific discovery. The long-term objective of this work is to use ML not just to identify patterns/surrogates from data, but to emulate human-like cognition linking physics to interpretable causal mechanisms.

First, ML-accelerated multiphysics models require mathematical foundations (stability/accuracy/structure-preservation) to reliably couple component models together into a digital twin. We introduce a finite element exterior calculus to discover structure-preserving Whitney forms. This learning framework reveals physically-relevant control volumes with accompanying integral balance laws which naturally encode physical structure in terms of a graph. The resulting models provide speedups of 10000x for multiscale problems while providing stability and conservation guarantees associated with traditional finite element-based simulation. With a predictive digital twin in hand, we next sketch how they can be used to reveal causal relationships in large multimodal datasets. Multimodal scientific data may be combined and embedded into directed acyclic graphs which encode interpretable causal relationships. Unsupervised discovery of causal graphs provide a means of identifying exploitable scientific relationships or precursors to failure/rare events.