Research
My current work focuses on scientific machine learning for fluid dynamics. I’m also developing research on knowledge representation, causality, and cognitive AI.
Research interests
Scientific machine learning
How can models use the laws of physics?
My work includes physics-informed and physics-inspired neural networks. I use mathematical and computational models to examine physical systems.
Causality
What changes after an intervention?
I’m interested in distinguishing causation from correlation, understanding the effects of interventions, and reasoning about what might have happened under different conditions.
Representation and cognitive AI
How can models represent and use knowledge?
I examine representation learning, knowledge representation, and their relation to planning, reasoning, and understanding.
Quantum machine learning
When can quantum models learn more efficiently than classical ones?
I’m interested in how quantum and classical models can work together, and which learning problems benefit from quantum computation.
Selected publications
Identifiability and Conditioning of Flux-Parameter Inversion for the Buckley–Leverett Equation
Physics alone cannot fix the viscosity ratio in a water-displaces-oil model. We show which measurements can, how much their errors are amplified, and why a good fitted field does not guarantee a good estimate.
Samson Dawit Bekele, Yerzhan Kenzhebek, Saltanbek Mukhambetzhanov, Saida Tastanova, Dagmawi Lemma, Timur Imankulov, Mathematics
Physics-Informed Neural Networks for Coupled Non-Isothermal Two-Phase Flow in Porous Media: Training Pathologies, Remedies, and the Role of Gradient Conflict
Conflict between training goals is a leading explanation for why physics-informed networks fail. On a hot-water flood with an exact solution, removing the conflict did not make training reliable, and two methods worked with it still present.
Yerzhan Kenzhebek, Timur Imankulov, Samson Dawit Bekele, Saltanbek Mukhambetzhanov, Machine Learning and Knowledge Extraction
Performance and stability of physics-informed Kolmogorov-Arnold networks for two-phase transport in porous media: A comparative study with physics-informed neural networks
Kolmogorov–Arnold networks promise accuracy with fewer parameters. On a sharp water front, ours used a third of the parameters but needed over twice the smoothing and about 50 times the training time.
Timur Imankulov, Yerzhan Kenzhebek, Samson Dawit Bekele, Darkhan Akhmed-Zaki, Results in Engineering
Coupled pressure and saturation prediction for two-phase flow in porous media using physics-informed neural networks (PINNs)
One physics-informed network trained on both the pressure and water-saturation equations got pressure right but misplaced the water front. Bigger networks and reweighting didn’t fix it; a small diffusion term with tuned weights did.
Yerzhan Kenzhebek, Timur Imankulov, Samson Dawit Bekele, Irina Panfilova, Darkhan Akhmed-Zaki, Computer Methods in Applied Mechanics and Engineering