Uncertainty Quantification of Representations of Unknown Dynamic Systems through Universal Differential Equations

Cyber-Physical-Human (CPH) teams will drive future space missions, such as Artemis and future Martian exploration. Key to the success of CPH teams are trustworthiness and trust. In the context of machine agents on CPH teams, trustworthiness refers to whether a machine performs its intended task (and not prohibited actions) when faced with unknown physical processes. A need exists for methods that are flexible to encompass known and unknown elements of physical processes and produce outcomes that are interpretable for all members of CPH teams.Universal Differential Equations (UDEs) incorporate information from scientific models to constrain machine learning approximators. In the work proposed here, we aim to increase the reliability of UQ in UDEs to enable more detailed analysis of uncertainty in the learned representations of dynamic systems. The potential for inclusion of physics-based priors into the learning process for UDEs could enhance trustworthiness and trust in CPH teams because it is possible to extract a closed-form differential equation from UDE-based models. However, most UDE research has focused on deterministic solutions rather than a study of the sensitivity of the identified representation.In the work proposed here, we aim to increase the reliability of UQ in UDEs to enable more detailed analysis of uncertainty in the learned representations of dynamic systems. We will first conduct simulations of a semi-stable dynamic system in Simulink. We will demonstrate UDE learning of the equations of motion that describe the semi-stable system. Once this has been demonstrated, we will move onto the development of an advanced UQ framework for UDEs. We will build upon examples from literature (such as Bayes by Backprop), with a focus on human interpretability to increase the trust in the machine learned representation of the dynamic system.