Online learning to accelerate nonlinear PDE solvers: applied to multiphase porous media flow

2025-04-25

AI Summary

Nonlinear PDE solvers for multiphase flow simulation in porous media suffer from slow convergence and high computational cost. Method: This paper proposes an online adaptive learning-based dynamic relaxation control strategy, coupling lightweight, dimensionless-feature-driven machine learning models (XGBoost/MLP) with real-time numerical relaxation factor tuning. It establishes a closed-loop optimization framework comprising offline training on 2D simplified models and online transfer to 3D realistic scenarios, integrated into open-source simulators (MRST/OPM). Contribution/Results: The method enables autonomous solver parameter adaptation, reducing computational time by up to 85% in 3D complex models and significantly decreasing nonlinear iteration counts. It achieves the first end-to-end deployment and validation, delivering an efficient, transferable intelligent acceleration paradigm for multiphase flow simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) for the offline training, (iii) dynamic control of a nonlinear solver tuning parameter (numerical relaxation), (iv) and online learning for real-time improvement of the machine learning model. This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter, the relaxation factor, and by adaptively learning the attributes of each numerical model on-the-run. Furthermore, this work performs a sensitivity study in the dimensionless parameters (machine learning features), assess the efficacy of various machine learning models, demonstrate a decrease in nonlinear iterations using our method in more intricate, realistic three-dimensional models, and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85% reduction in computational time.

Problem

• Accelerate nonlinear PDE solvers using online learning
• Optimize multiphase porous media flow simulations
• Reduce computational time via adaptive ML-driven relaxation

Innovation

• Online learning for nonlinear PDE solver acceleration
• Dynamic control of solver tuning parameters
• Dimensionless numbers as machine learning inputs