An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media

arXiv:2603.19561 · math.NA, cs.LG, cs.NA, physics.flu-dyn · Submitted 2026-03-20 · Read on arXiv

math.NA, cs.LG, cs.NA, physics.flu-dyn

Submitted: 2026-03-20

Updated: 2026-09-23

Project page: http://www.cive.uh.edu/faculty/nakshatrala

Terminology

• Adaptive Weighting — 15× in this paper · explained in 1 episode
• Accuracy — 14× in this paper · explained in 1 episode
• Adam — 14× in this paper · explained in 2 episodes
• Loss Function — 12× in this paper · explained in 2 episodes
• Trace — 12× in this paper · explained in 2 episodes
• Adaptive Sampling — 10× in this paper · explained in 1 episode
• alpha — 7× in this paper · explained in 1 episode
• Activation Function — 6× in this paper · explained in 1 episode
• Inverse Problem — 6× in this paper · explained in 2 episodes
• Consistency — 4× in this paper · explained in 3 episodes
• Neural Network Approximation — 4× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Multi-objective Optimization — 1× in this paper · explained in 4 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Network (PINN) — 1× in this paper · explained in 3 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Simple Moving Average — 1× in this paper
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Non-Asymptotic Stability and Consistency Guarantees for Physics-Informed Neural Networks via Coercive Operator Analysis
• Adam: A Method for Stochastic Optimization
• A Machine Learning-Enhanced Hopf-Cole Formulation for Nonlinear Gas Flow in Porous Media
• L-HYDRA: Multi-Head Physics-Informed Neural Networks

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