When you're testing the stability of a rocket, you can't just fire up a design.

Factors like temperature, pressure, and velocity impact a rocket's journey, and the parameters must be examined and modeled.

Even computational simulations are done for weeks or months with a supercomputer, given the stakes of such a complex and explosive application.

To speed up the design process, researchers from the University of Texas are finding more efficient ways to predict, or "learn," a rocket's behavior.

The system, developed at the Oden Institute for Computational Engineering and Sciences and and the Massachusetts Institute of Technology, uses "snapshots" of physics data to create reduced-order models — simulations that run very quickly and are therefore valuable for rocket builders looking to try out a variety of designs.

“In some important cases, these reduced-order models are the only means by which one can simulate a large propulsion system," said Ramakanth Munipalli, senior aerospace research engineer in the Combustion Devices Branch at Air Force Rocket Research Lab . "This is highly desirable in today’s environment where designers are heavily constrained by cost and schedule.”

The "scientific machine learning" approach, led by Oden Insitute director Karen Willcox, provides makers of rockets with a fast way to assess engine performance in a variety of operating conditions.

The snapshots, generated by an Air Force combustion simulation code known as General Equation and Mesh Solver (GEMS), serve as the training data for the system and the reduced-order models it produces. Each picture represents a variety of launch parameters, including pressure, velocity, temperature, and chemical content.

While the GEMS "training" takes about 200 hours of computer processing time, the reduced-order models can run the same simulation now in seconds, and can be run in place of GEMS to issue rapid predictions.

Beyond repeating the training simulation, the models also can predict how the combustor will respond to operating conditions that were not part of the data set.

Although not perfect, says Willcox, the models do an excellent job of predicting overall dynamics, and are particularly effective at capturing the phase and amplitude of the pressure signals — key elements for making accurate engine stability predictions.

“These reduced-order models are surrogates of the expensive high-fidelity model we rely upon now,” Willcox said. “They provide answers good enough to guide engineers’ design decisions, but in a fraction of the time.”

In an edited interview via email below, Director Willcox tells Tech Briefs about her team's efforts to quantify uncertainty for a system as complex as a rocket engine.

Tech Briefs: What is your simulation method doing better than alternative rocket design software?

Karen Willcox: We are addressing computational cost. To make good design decisions, engineers need good predictions of how the engine will respond. For example, we need to be able to understand how a change in injector geometry will alter the complex flowfield inside the injector.

Tech Briefs: What models are currently available? What are the drawbacks of traditional rocket design/simulation methods?

Karen Willcox: The community has high-fidelity computational models that aid in making these predictions, but those models are so complicated that they take a very long time to simulate. A single analysis can take days or weeks on a supercomputer. For the engineer that needs to study thousands of different possible design configurations (i.e., thousands of different analysis runs), this is clearly not practical. Our reduced-order models aim to provide answers much faster — in times fast enough to be useful in the design setting — while still retaining high levels of fidelity.

Tech Briefs: What is the training data, and where is that training data coming from?

Karen Willcox: The training data are solutions coming from a high-fidelity computational model; we call them "snapshots." This high-fidelity model is the model that we trust (sometimes called the "truth model"), and our goal is to get predictions that are close to as good as this model, but solved in a small fraction of the time. In our case, the high-fidelity model is a code called GEMS  that was developed by Purdue University and is used by the U.S. Air Force.

Tech Briefs: Can you take me through what a designer can learn from an example “snapshot?"

Karen Willcox: A snapshot is a glimpse of what is happening inside the engine at any point in time. A designer might look at the temperature profile to, for example, see pockets of heat release leading to regions exceeding a desired maximum temperature. Or they might look at the velocity field to see the character of the recirculation zone. Our reduced-order model can't recover all the fine details of a snapshot, but it captures enough of the general behavior to give the designer a good sense of what is going on.

a snapshot of pressure and temperature inside one injector of a rocket engine, from university of texas
These snapshots of pressure and temperature inside one injector of a rocket engine show that the new reduced-order models can predict complex physics with similar levels of accuracy as existing modeling techniques but in significantly less time and at a fraction of the cost. (Image Credit: UTexas)

Tech Briefs: What is the system “learning” exactly?

Karen Willcox: The system is learning a reduced-order model. The way we formulate the problem, this amounts to learning several matrices that define a dynamical system. This dynamical system is what we solve to get our reduced-order model predictions.

Tech Briefs: Is the system truly able to “learn” such complex physics?

Karen Willcox: If we were using standard machine learning (e.g., a neural network model), then my answer would be "most probably no." Standard machine learning is extremely reliant on having a large amount of training data. We don't have that; remember, we have to run an expensive model to generate training data.

What's more, even with a lot of training data, we would have no idea how a standard machine learning model would generalize — i.e., we would have no idea how good it would be at predicting conditions that weren't in the training data.

Tech Briefs: So what are you doing differently?

Karen Willcox: Two main things: We are embedding the physical governing equations, and we are exploiting the mathematical properties of projection onto a low-dimensional subspace. Without getting into details, this amounts to using the governing equations (conservation of mass, momentum, energy, and chemical balance) to identify structure, and then we reflect this structure in the form of the model we learn. The result is a method that enjoys the flexibility and ease-of-use of a non-intrusive data-driven machine learning approach together with the prediction power of a physics-based model.

Tech Briefs: What is most exciting to you about this system?

Karen Willcox: Most exciting to me is the way that this work blends machine learning and physics-based modeling. Machine learning is so powerful and has had many high-profile successes, especially in the retail and Internet worlds. But when it comes to complex problems in engineering, we can't afford to use models for which we have no idea of the quality of predictions— the consequences of being wrong are just too high. I like to say, "Big decisions need more than just big data, they need big models too ."

Of course, none of our models are perfect, but as engineers we think carefully about the uncertainties in our models and our associated confidence in the model predictions. We still have a long way to go to being able to rigorously quantify uncertainty for a system as complex as a rocket engine, but our approach that blends learning and physics is an important step to getting us there.

What do you think? Share your questions and comments below.