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

Cyber-Physical-Human (CPH) teams are a key component of future space missions, such as the Artemis missions that will establish a lunar presence via autonomous agents, and future Martian exploration. To achieve mission goals, CPH teams will require machine agents with a high degree of autonomy.If an entire system encompassing a CPH team is to be considered trustworthy and to be trusted, all members of that systemboth human and machineneed to be considered trustworthy. This hinges on accurate and relevant data being provided to all members of that team in real-time to make a decision that impacts the system. Additionally, there can be issues in spacecraft operations due to the deep institutional knowledge required of SMEs with deeptraining and expertise. When SMEs leave an operations team, this institutional knowledge may not be passed onto other team members, and the training process can be time consuming and costly. This knowledge is not necessarily transferable to other systems, due to the specialized nature and architecture of each spacecraft and its mission. Developing efficient system modeling and decision-making algorithms that can be implemented on multiple platforms can overcome this challenge and reduce costs for operating teams. The potential for inclusion of physics-based priors into the learning process for UDEs has great potential for trustworthiness and trust in CPH teams. This is, in part, due to the fact that it is possible to extract a closed-form solution from UDE-based models. These equations arereadily interpretable by human scientists, engineers, or other collaborators who may need to investigate or validate the representation of datalearned by a machine teammate. We are focusing on how uncertainty quantification from two sources can be fused into one representationthat is conducive to decision-making. We will create and implement techniques for decision-making and control that build upon this work in integrated uncertainty quantification. Cyber-Physical-Human (CPH) teams will be a key component of future space missions, such as the Artemis missions and Martian exploration. To achieve future goals, these CPH teams will require machine agents with a high degree of autonomy. Key to the success of CPH teams are trustworthiness and trust. If an entire system encompassing a team is to be considered trusted, all members of that system—both human and machine–need to be considered trustworthy. This hinges on accurate and relevant data being provided to all members of that team at the time that they require it to make a decision that impacts the system. The potential for inclusion of physics-based priors into the learning process has great potential for trustworthiness and trust in CPH teams. This is, in part, due to the fact that it is possible to extract a closed-form solution from these models; readily interpretable by humans who may need to investigate or validate the data. We are developing uncertainty quantification from sources that can be fused into one representation that is conducive to decision-making. Objective 1: Simulation Data Creation and Curation - Implement a simulation framework that allows for the training and testing of our approaches; by incorporating existing open-source high-fidelity satellite simulation software to build an environment that can evaluate the performance metrics established in Phase 1 to compare traditional approaches with the two methods being investigated. Objective 2: Deep Ensemble Control Algorithms - Develop deep ensemble methods for use in the satellite predictive control of unstable dynamic systems, especially the competency metrics on uncertainty quantification of short to mid-term temporal horizons and system interrelations. Objective 3: Quantile Regression with Gradient-Boosted Trees - Develop quantile regression with gradient-boosted trees for satellite predictive control of unstable dynamic systems and uncertainty quantification of short to mid-term temporal horizons and system interrelations. Objective 4: Uncertainty Quantification and Decision-making - Leverage the uncertainty quantification in decision-making of satellites systems with a goal of maximizing the life expectancy of a low-earth orbit satellite and its mission objectives. Both approaches of uncertainty quantification will be analyzed for their performance bounds and specific applications will be identified for each.

Potential NASA applications cover a large number of domains due to the need to have trusted control, including satellite constellation proximity operations and mission performance optimization with cislunar operations and Artemis missions. It also applies to remote exploration vehicles in uncertain terrains and even safety-critical controls on air and space vehicles. Because of its application to safety critical control systems, this technology is also applicable for most critical infrastructure information monitoring and control systems. This can include mechanical systems seen in commercial aircraft, especially for engine monitoring, and in the control of nuclear power plants, electrical power grids, and water distribution and treatment.

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