We are seeking a highly motivated PhD candidate to contribute to the Engineering Digital Twins (EDT) program within Catalyst: the Reliable Hybrid Model Forge. The research focuses on developing new methods, algorithms, and tools that help designers correct model/data mismatches in digital twins of physics-dominated systems.
Modern modeling languages and tools allow engineers to build large-scale models directly from first principles of physics. Languages such as Modelica enable scalable modeling of complex cyber-physical systems, often using modeling paradigms such as port-Hamiltonian systems.
While assembling models from component libraries is relatively straightforward, practitioners often face major challenges in:
- parameter identification
- consistent model initialization
- fine-tuning of model dynamics
- integrating empirical models for poorly understood subsystems
This PhD aims to develop scalable methods that combine physics-based modeling with data-driven approaches to improve the reliability and accuracy of digital twin models.
A key challenge in digital twin engineering is the integration of experimental or simulated data into complex physics-based models.
Existing approaches typically rely on optimization-based data assimilation techniques, including:
- data reconciliation
- system identification
- deep learning approaches such as autoencoders
Although powerful, these methods often do not scale well to large dynamical systems involving thousands of variables.
This PhD proposes to address this challenge using structural analysis techniques for differential-algebraic equation (DAE) systems.
The core research idea is to transform the problem of data integration into the analysis of structurally overdetermined models. By leveraging structural analysis algorithms, it becomes possible to compute Minimal Structurally Overdetermined (MSO) subsystems, which can act as parity spaces to detect inconsistencies between model predictions and observed data.
These MSO subsystems can be solved using measured data, and the resulting residuals provide indicators of model inconsistencies. This approach enables the localization of model/data mismatches and supports targeted model corrections. Ultimately, the goal is to assist designers in discovering structural deficiencies in equation-based models, by identifying where the available data cannot be explained by the current set of equations.
The PhD research will investigate:
- Structural Analysis for Digital Twin Models: Adapting DAE structural analysis algorithms for model/data integration
- Parity Space Construction using MSOs: Identifying subsystems suitable for mismatch detection
- Scalable Algorithms for Large Systems: Leveraging graph-based algorithms with polynomial complexity
- Model Diagnosis and Correction: Using statistical analysis of residuals to localize inconsistencies
The proposed methods are particularly attractive because they scale well to large sparse systems, potentially containing millions of equations, and do not require prior knowledge of the reachable state space.
