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The difficulty lies in the enormous range of motions present in turbulent flows. Large swirling motions continuously break down into smaller and smaller structures, creating a cascade of interacting movements across many different length and time scales. Capturing all these scales at once requires enormous computing power, making fully detailed simulations impractical for most real-world applications.

To make such simulations feasible, researchers often use a technique called large-eddy simulation (LES). Instead of simulating every tiny motion directly, LES resolves only the larger flow structures while estimating the effects of the smaller turbulent motions using mathematical models.

In recent years, machine learning has emerged as a promising way to improve these models by learning from highly-detailed direct numerical simulations (DNS). In these simulations, all turbulent motions - from large flow structures down to the very smallest scales - are explicitly calculated. However, while such AI models may appear accurate during training, they often become unstable once they are used inside a full simulation.

In his PhD research, investigated why AI turbulence simulations often become unstable and how these instabilities can be prevented. He defended his PhD thesis at the Department of Mathematics and Computer Science on Thursday, May 28, earning his doctorate cum laude.

Learning directly from the simulation

A central insight of Agdestein’s research is that turbulence simulations are not simply physics equations transferred onto a computer. The way that a simulation divides a flow into millions of small digital grid cells also affects the outcome of the calculation. This means that AI models must learn not only the physics of turbulence, but also how the computer simulation itself behaves.

Traditional machine learning models are often trained using idealized mathematical equations, while real simulations operate on these digital grids. As a result, a model that appears accurate during testing may still destabilize a simulation once deployed.

To address this problem, Agdestein developed AI models that are trained directly within the same computational framework in which they are ultimately used. By making the machine learning model aware of the digital grid and the numerical behavior of the simulation, the resulting models become both more accurate and more stable.

His research shows that accounting for how a simulation is represented on a computer is essential for building reliable AI turbulence models.

Embedding physical structure into AI models

Another part of Agdestein’s research explored how to incorporate fundamental physical rules directly into neural networks.

Fluid flows obey important physical principles. For example, the laws governing a flow should remain the same when the flow is rotated or mirrored. Standard neural networks do not automatically respect these properties, which can lead to physically inconsistent predictions.

Agdestein investigated neural network architectures that explicitly preserve these physical rules. By embedding these constraints directly into the models, the neural networks require less training data and produce more physically consistent results. They also avoid introducing artificial effects that depend on the observer’s viewpoint, improving the robustness of the simulations.

Open source turbulence simulations

To support the development of these methods, Agdestein also created , an open source software package for turbulence simulations that can run on both CPUs and GPUs.

The software combines fluid dynamics simulations and machine learning in a single framework, and it allows researchers to train neural network turbulence models directly inside the simulation itself.

Advanced turbulence simulations and machine learning experiments can even run on a standard desktop computer equipped with a graphics card, lowering the barrier for other researchers working in the field.