# Future Directions for Electric Propulsion Research
## 5 Strategies for Addressing Technical Challenges for Electric Propulsion Development
### Predictive Models for Incompletely-Understood Systems  
Validated and predictive numerical models could be a key enabler for addressing challenges related to both mature and immature concepts. As an example, for technologies higher on the s-curve where the relevant physical processes are well understood, numerical models are critical for performing lifetime assessments. For technologies lower on the s-curve, numerical models can help guide the rapid advancement of the technology by exploring underlying physical operation to a level of detail unattainable in laboratory experiments. With that said, many of the technologies both higher and lower on the s-curve have aspects of their operation that remain poorly understand. As discussed in the preceding sections, a few notable examples include electron transport in Hall thrusters; many aspects of the operation of electrosprays, such as the onset of failure modes and instability; and the problem of detachment in magnetic nozzles. The lack of understanding of these processes has precluded the development of predictive models.  
Ideally, future directions in the field of electric propulsion will include dedicated and detailed physics-based studies to produce predictive models that will help mature modern systems. However, this need should be balanced against the fact that some incompletely-understood physical processes in EP devices have been studied for several decades and still remain unresolved. This poses a practical challenge for leveraging numerical tools to address the outstanding and pressing open questions for technology development. As an alternative method to more rapidly advance EP technologies, one emerging strategy is to leverage data-driven methods to develop improved predictive models. As demonstrated in Figure 18, a machine learning regression algorithm may be used to derive functional forms for poorly-understood phenomena like electron transport in Hall thrusters based on available sets of training data. This helps \"fill in\" pieces of the missing physics, which assists in overcoming some of the hurdles that have prevented the development of self-consistent predictive models to date.  
A similar direction has recently been taken with electrospray research, using data-driven techniques to understand the lifetime and failure modes of large-scale arrays in the absence of predictive simulations [33]. These techniques can also be used to optimize existing thruster designs. Figure 19 shows an example of a two-frequency optimization experiment at the University of Michigan  
Figure 18: A notional machine-learning process to estimate electron transport given experimental plasma information based on a set of training data.  
from [146], in which the floating potential in the plume of an ECR thruster is maximized through data-driven optimization of applied microwave frequencies.  
Despite the incredible promise of data-driven analysis to close gaps in the modern understanding of electric propulsion systems, there are several caveats that must be acknowledged. First, because their results are not based on first principles, data-driven analyses may miss important physics that cannot be distinguished from the training data. Similarly, it is difficult to determine whether a learned expression is applicable outside of the training dataset. For example, a description of electron transport in Hall thrusters may be successfully formulated from machine learning with training data of moderate-power devices, but there is no guarantee that this description is extensible to low- or high-power designs.