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.

Future NASA mission objectives involving Cyber-Physical-Human (CPH) teams—such as maintaining lunar habitations or preparing for Martian landing—are ones we believe may benefit. Additionally, the methods described here could be adapted to accelerate learning from Scientist-in-the-Loop analysis of high-throughput collections of planetary science data. Next generation air operations safety could likewise benefit from tools that allow interrogation of uncertainty in representations of dynamic systems where high degrees of autonomy are involved.

CPH teams in defense applications (e.g., small-UAS maneuvers, long-range undersea surveillance) could benefit from the capabilities proposed here. Additionally, platooning of autonomous vehicles and enhanced safety of autonomous driver aids could be achieved through more robust uncertainty quantification of representations of dynamic processes in data.

This is early/mid-stage (TRL 2) — the most realistic path in is NASA SBIR/STTR, which funds small businesses and research institutions to develop technology aligned with NASA's needs (equity-free, phased funding). Check whether a current SBIR/STTR solicitation topic overlaps with this project's technology area, or contact the project directly (above) to ask.

None of these are guaranteed paths for this specific project — TechPort itself doesn't have an "apply" button. Reaching out to the contact(s) above with a specific question is usually the fastest way to find out what's actually open.