Deeper Dive
This project was born in a class on fusion energy that I took at the Columbia University Science Honors Program. I asked the professor why well characterized reactors still had to be operated so conservatively. His answer was simple: We don’t know exactly how to predict the critical heat flux (CHF) in all regimes, and since CHF is the point of incipient cooling failure, we have to design conservatively to guarantee safe operation. I was outraged. One of the most important problems in the world is being held back, at least in part, by our inability to predict a boiling instability. CHF is the upper boundary for safe reactor operation, and because nobody can predict it precisely, it limits the performance and economics of commercial plants.
Because I wasn’t satisfied with living with this kind of uncertainty, I developed a neural network guided by physical theory to predict CHF in multiple regimes. It was trained on more than 10,000 experiments with bounds derived from hydrodynamic instability theory. It performs well in prediction on a fixed testing data set (R² = 0.986), while other widely used correlations produce errors an order of magnitude larger. Accurate predictions of CHF allow us to design and operate our nuclear plants based on what we know, not what we don’t, thus increasing the amount of clean electricity we produce without sacrificing safety.
While my model’s performance is part of my contribution, I believe another contribution that is often overlooked is the framework. I reformulated a physics-informed learning framework to handle difficult systems without a PDE. Rather than PDE residuals, physics is imposed through weighted regularization and mechanistic constraints. This is significant because much of engineering knowledge is encoded in the form of correlations and bounds rather than governing equations, and until now that knowledge was very difficult to incorporate into these models.
The project took about eight months, divided into the literature review, data collection and feature engineering, model and loss function formulation and statistical evaluation and paper writing. One problem I ran into was how to formulate a useful definition of physics informed when there was no governing PDE. Another was that the CHF dataset was very imbalanced, with the vast majority of points being subcooled or near saturated. The initial models would fit well in these high-density regions but would predict absurd values when extrapolating to high quality flow regions. I solved this by weighting the physics-based regularization based on how closely the different empirical correlations agreed for each individual sample and by adding a penalty to the loss function for any prediction that exceeded a known physical upper bound.
My third problem was performing the experiments in a statistically rigorous manner. Rather than evaluating performance with just the RMSE improvement, as I felt that wouldn’t be rigorous on its own, I did some research and decided to add bootstrap resampling and paired nonparametric tests. None of these topics were in any of my courses. All of the thermohydraulics, physics-informed machine learning and statistics were self-taught for this project. I developed all of the models and experiments on my own computer and used cloud resources such as Kaggle to run training. I had a mentor who provided guidance on the general research method, allowing me to go into this project confidently.
Each reactor operates under the requirement that it will be 95% confident that 95% of the fuel rods do not exceed the critical heat flux under any condition that could reasonably occur. This standard is nonnegotiable, as it should be for safety purposes. However, the amount of capacity that a power plant must curtail to satisfy this requirement is largely determined by the accuracy with which CHF can be predicted, and existing correlations predict CHF poorly, with errors of more than 60%. Reducing this error to roughly 5% doesn’t mean building a less safe reactor; it means building the same reactor for less money, which means cheaper carbon-free electricity from the plants that already exist and lower costs for the small modular reactors that will supply power to communities that have never had grid-scale power at all.
This limit also applies to fusion, where dealing with high heat fluxes is one of the main technical hurdles along with confining the plasma. No single model will achieve all of these goals by itself, but whenever a technological limit determines what is possible, an increase in the accuracy of that limit has the potential for societal impact. This is my effort to expand one such limit.