Explainable AI Offers a New Way to Understand One of Physics’ Most Puzzling Problems
Turbulence affects everything from airplane flights to industrial mixing systems, yet its underlying behavior is still considered one of the biggest unsolved problems in physics. A new study led by the University of Michigan and the Universitat Politècnica de València, published in Nature Communications, presents a fresh approach to understanding turbulent flows by using explainable artificial intelligence.
Instead of attempting to simply predict turbulence, the researchers focused on identifying which regions of a turbulent flow are actually the most influential. Their method combines high-fidelity simulations with AI tools to pinpoint these critical areas and challenge long-standing assumptions in fluid dynamics.
What Turbulence Really Is and Why It’s a Problem
Turbulence describes chaotic, swirling, irregular patterns in fluids such as air or water. It’s the reason airplanes experience sudden bumps during flights and why fluids mix thoroughly in industrial processes. Despite being something we observe constantly, scientists still lack a complete mathematical explanation for how turbulence evolves over time.
The core equations behind fluid motion, known as the Navier–Stokes equations, work when flows are smooth or only mildly disturbed. But in situations of strong turbulence, the complexity increases dramatically. Velocity gradients can become extremely large, and the flow patterns develop fractal-like spatial structures. While the equations are technically still valid, the computational effort required to resolve every detail becomes enormous.
This difficulty is so fundamental that the Clay Mathematics Institute has designated the existence and uniqueness of smooth solutions to the Navier–Stokes equations as one of the prestigious Millennium Prize Problems, with a $1 million reward for anyone who can solve it.
Why Traditional Approaches Fall Short
Over the last century, turbulence research has relied on either simplified models or visual cues — such as vortices, eddies, and other coherent structures that appear in experiments. These features are easy to identify but do not necessarily represent the true drivers of turbulence. Classical models also depend heavily on assumptions that may overlook or misinterpret important behaviors.
Modern supercomputers can model turbulence using a technique called direct numerical simulation (DNS), which calculates every detail of the flow without approximations. Unfortunately, DNS is extremely expensive. According to the study, simulating one second of flight for an Airbus A320 cruising at altitude would take the world’s fastest supercomputer around five months, and would require memory comparable to the amount of data transferred over the entire internet in a single month. That’s obviously impractical for routine research or engineering design.
The New Method: Explainable AI Meets Fluid Mechanics
The team behind the study developed a solution that uses DNS data but avoids the computation bottleneck. Their approach works in two major steps:
- Training an AI model — The researchers fed DNS data into a neural network trained to predict the behavior of a turbulent flow.
- Understanding the prediction using SHAP — Instead of treating the AI like a black box, they applied SHAP (SHapley Additive exPlanations), a method that determines how important each input is to the final prediction.
SHAP works by systematically removing one input at a time and measuring how much the model’s accuracy drops. It is similar to testing the importance of each player on a sports team by removing them from the lineup and observing how much the team’s performance suffers.
By analyzing the SHAP values across the turbulent flow, the researchers were able to determine which features — and which specific spatial regions — actually influence how turbulence evolves.
What They Discovered
The findings contradict several long-held assumptions in turbulence theory.
- Vortices, which have traditionally been considered central to turbulence behavior, turned out to have relatively low importance when far from the wall of a flow system.
- Reynolds stresses, which represent friction-like forces generated when fluid layers move at different speeds, emerged as highly influential, especially very close to and very far from the wall.
- Streaks, long structures of alternating fast- and slow-moving fluid, were the dominant factors at moderate distances from the wall.
In other words, each classical perspective captures only part of the turbulent story. When combined, they get closer to the truth, but the AI-based method revealed how these components interact and which ones matter most in different regions of the flow.
A Breakthrough With Practical Impact
This explainable AI method marks a significant milestone: for the first time, scientists can identify which exact structures and which regions are responsible for the behavior of a turbulent flow. This insight makes it possible to design more effective control strategies.
The team demonstrated this potential by combining SHAP analysis with deep reinforcement learning, achieving a 30% reduction in friction on an airplane wing in simulations. This level of drag reduction, if implemented in real aircraft, could result in lower fuel consumption and significantly improved efficiency.
Other potential applications include:
- Better turbulence forecasting for aviation, helping pilots avoid dangerous or uncomfortable turbulent zones.
- Improved combustion performance in engines by manipulating the most influential turbulent structures.
- Enhanced industrial mixing, such as in water treatment systems, by targeting regions that maximize mixing efficiency.
- Pollution reduction in urban environments through better airflow control around buildings.
The authors also emphasize that their approach is not limited to turbulence. Any physical system with complex interactions — climate models, plasma physics, material deformation, and more — could benefit from the combination of predictive AI with explainability tools.
A Broader Trend: AI in Fluid Dynamics
This study is part of a rapidly expanding movement in the scientific community where AI is being used not just to accelerate simulations but to gain genuine insights into complex physical phenomena. Machine-learning models, such as convolutional neural networks and reinforcement learning algorithms, have already shown promise in predicting flow behavior and optimizing engineering designs.
However, one major challenge has been the interpretability of these models. Without understanding why an AI reaches its conclusions, scientists are hesitant to use these systems to guide real-world decisions. The use of SHAP in this study provides a bridge between pure data-driven prediction and traditional physics-based understanding, making AI a more trustworthy tool in scientific research.
A Closer Look at the Importance of Reynolds Stresses
Since Reynolds stresses emerged as one of the most influential drivers of turbulence in the study, it’s worth expanding on what they actually represent.
When fluid moves at different speeds across adjacent layers, the interaction produces fluctuating forces that transfer momentum within the flow. These stresses are central to the energy cascade in turbulence — the process by which large-scale motions break down into smaller and smaller eddies. The discovery that Reynolds stresses dominate both near the wall and far from it suggests that the true mechanisms governing turbulence may be more distributed and less visually obvious than previously thought.
Why SHAP Matters in Scientific Research
SHAP has become popular in fields like finance, healthcare, and risk analysis because it offers a fair, mathematically grounded method for distributing “credit” among input features. Bringing SHAP into physics research is significant because it allows scientists to uncover hidden relationships within complex systems without depending on preconceived theories.
In this study, SHAP effectively peeled back the layers of turbulence to reveal which features drive the flow forward in time. This opens the door to new turbulence models that can be both accurate and explainable — a combination that has long been missing in fluid mechanics.
Research Paper
Classically studied coherent structures only paint a partial picture of wall-bounded turbulence
https://doi.org/10.1038/s41467-025-65199-9
