Sanderse has been awarded a €50,000 Open Competition Domain Science – XS grant, which is intended to support promising ideas and to facilitate innovative and more speculative initiatives. The proposed research is both ground-breaking and high-risk. What counts is that all results, whether positive or negative, must contribute to the advancement of science.
With his research proposal, Sanderse aims to discover the hidden mathematical equations behind turbulence using a class of models known as neural stochastic differential equations.
Why turbulence is hard to simulate
Turbulence refers to the irregular, unpredictable motion in fluid flows - such as water, air or plasma - where small changes in initial conditions can lead to wildly different outcomes. Scientists typically describe such systems using differential equations, which mathematically express how quantities like velocity or pressure evolve over time. Although the exact form of these equations is known, the equations cannot be solved for most real-world cases because of the immense computational costs.
Machine learning has opened up new possibilities. In recent years, researchers have explored neural differential equations, which combine data-driven neural networks with the structure of traditional mathematical models. These methods offer a hybrid approach, but struggle when applied to inherently chaotic problems. “Simulating turbulence is notoriously difficult due to its chaotic nature,” says Sanderse.
Introducing randomness into the equations
To address this challenge, Sanderse and his team are adding stochastic (random) components to the equations, resulting in neural stochastic differential equations. These allow the model to account for uncertainty, making it possible to represent not just one possible outcome, but a distribution of possible turbulent behaviours.
“We propose a new stochastic approach that is inspired by recent advances in generative models,” Sanderse explains. Generative models, best known for their use in creating realistic images or text, can also be applied to physical systems to help uncover the dynamics hidden in data.
From turbulence to broader applications
“We will use the grant to partially employ a postdoctoral researcher to develop new probabilistic turbulence models,” says Sanderse.
While the focus is currently on turbulence, the method has broader relevance. Sanderse: “The proposed combination of physical laws and generative machine learning is an important research direction with many applications beyond turbulence.”
Picture: Andrei Armiagov/Shutterstock
