Viscous fingering during the displacement of a more viscous fluid (dark color) by a less viscous fluid (yellow color). Credit: Birendra Jha

Viscous fingering occurs when a thinner fluid pushes a thicker, more viscous fluid in a porous medium, like underground rock, creating unpredictable, finger-like patterns. For decades, this intricate dance between fluids has been a major headache in critical sectors like enhanced oil recovery, CO2 sequestration, and groundwater remediation. Predicting and controlling these “fingers” has remained an elusive goal for scientists, largely due to the sheer complexity of the fluid dynamics involved.

AI brings new hope to fluid modeling

A new approach led by USC Viterbi School of Engineering associate professor Birendra Jha is poised to change all that. The pioneering work, published in Physical Review Fluids, introduces a novel deep learning framework that can accurately predict and analyze viscous fingering with unprecedented speed and precision.

Traditional computer models, called Direct Numerical Simulations (DNS), have struggled to model viscous fingering accurately. Jha said these methods are time-consuming, expensive and computationally prohibitive.

“They can’t really simulate it, because it requires so many computational resources to be able to resolve those fingers, which are so nonlinear and curved and complex,” Jha said. “In my case, I remember one simulation that I did for a 2011 paper. It took two months to finish that simulation, which is just not acceptable in industry.”

Jha and his co-authors, graduate students Ramdhan Wibawa and Mohammed Alasker, could see that next-generation AI tools offered unprecedented scope to attack a problem that had puzzled mathematicians and physicists for almost a century. They were correct. After the AI model is trained, which in Jha’s case took about an hour with two GPUs (graphics processing units), results could be obtained in the time it takes to run a query on ChatGPT.

How the new AI framework works

At the heart of their innovation is a clever combination of technologies. First, they used a technique called “spatial embedding,” where a type of neural network called an autoencoder is trained to identify and simplify the complex, multi-scale patterns of the fluid fingers, compressing them into a concise digital signature. This is like teaching a computer to recognize the unique ‘handwriting’ of each finger as it forms and grows.

The real game-changer came with the integration of “Koopman-based temporal dynamics.” This advanced mathematical concept helps the AI understand the fundamental ‘rules’ governing how these finger patterns evolve over time.

Instead of wrestling with the fluid’s chaotic, nonlinear behavior directly, the Koopman operator transforms it into a simpler, linear system in a different mathematical space. This allows the AI to predict future states with remarkable accuracy, even for highly unpredictable flows.

“We are very proud and pleasantly surprised with the performance of the method, how we chose this AI architecture and trained it with high-quality data so that it’s able to perform and predict all these physical mechanisms of splitting one finger into two fingers, then merging and coarsening of fingers with time, and all the mixing that we see inside the domain,” Jha said.

“Our method is able to accurately predict multiple metrics of this problem.”

Implications for science and industry

The implications are immense. Not only are the new deep learning models faster than DNS, more importantly, Jha said, they offer improved accuracy, as they were not bound by the numerical errors that would arise in traditional computational models.

“It was a very pleasant discovery that, after the model was trained, not only was it able to meet the accuracy of the traditional method, we were surprised to see that it can actually fix some of the issues and errors that the traditional method had,” Jha said.

“For example, there is a region of less viscous fluid, where we don’t expect to see any presence of the more viscous fluid. And in the traditional method, there will be patches where it will show up, and it’s purely because of numerical error. In the proposed approach, we got rid of that error.”

Potential beyond energy and environment

Jha notes that beyond applications in the energy, subsurface technology and environmental remediation sectors, the new models could hold critical benefits for pharmaceutical and biomedical applications. Microfluidic devices, which are often used to test new drugs against biofluids like blood or sweat, can also be subject to viscous fingering complications when fluids of different viscosities interact.

“In microfluidic devices, you have very tiny spaces for the fluid to flow, and while it’s not a rock, viscous fingering is still a problem because the physics is the same,” Jha said.

Jha and his team are optimistic about further refining and expanding their models to cover a wider range of conditions and scenarios by adding more training datasets to better model the rock of underground environments.

The team’s research marks an important step in improving our ability to understand and manage fluid flow in Earth’s subsurface, paving the way for a more sustainable and resource-efficient future.

More information: R. Wibawa et al, Deep learning models of viscous fingering based on Koopman dynamics of dense embeddings, Physical Review Fluids (2025). DOI: 10.1103/knp4-cd89

Citation: A century-old mixing puzzle: AI helps predict and understand viscous fingering (2025, November 11) retrieved 11 November 2025 from https://phys.org/news/2025-11-century-puzzle-ai-viscous-fingering.html

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