This Case Study describes an approach to combining physical principles with Machine Learning (ML) for modeling and control of complex systems. Our approach was developed as part of a DARPA-funded research project. It was applied to oil reservoir management. While this Case Study provides an overview, technical details may be found in a separate publication [see reference 1 in full article PDF].
BACKGROUND
A physical process may be considered as a change in the state of a system with time – driven by physical phenomena that are internal or external to the system. Physicists and engineers attempt to model these processes employing conservation laws supplemented by phenomenological relationships. The resulting models are generally expressed as timedependent partial differential equations that are often coupled and non-linear. The solution to these equations, with appropriate initial and boundary conditions applied, describe the physical process. This physics-based paradigm has continued to be the primary approach for modeling complex physical systems ranging from chemical micro reactors to planetary climate.
However, simulations with such first-principles, high-fidelity models tend to be computationally intensive, and do not run in real-time. Hence, these models cannot be used in many real-world applications such as process control or tracking propagation of forest fires.
Over the past few decades, techniques have been developed to generate low-order models from high-fidelity models that enable simulations to be run in real-time or faster. These dynamic fast models attempt to accurately model the key physical state variables of interest while sacrificing accuracy on other state variables of less importance. Such fast low-order models may be developed mathematically e.g., proper orthogonal decomposition (POD), or developed using simplified physics that also judiciously reduce the number of states through aggregation. However, these fast models often cannot account for disturbances and process drifts. Additionally, the effect of unmodeled physics (left unmodeled intentionally or unintentionally) may be significant, including model parameters that may change often with time.
