[Paper Review] Point-particle drag, lift, and torque closure models using machine learning: hierarchical approach and interpretability

B. Siddani, S. Balachandar|arXiv (Cornell University)|Jul 18, 2022

Model Reduction and Neural Networks4 citations

TL;DR

This paper proposes a hierarchical machine learning framework using rotation and reflection equivariant neural networks to predict point-particle drag, lift, and torque in dispersed multiphase flows. By modeling pairwise and trinary particle interactions, the approach achieves up to 96% accuracy in torque prediction and improves streamwise torque accuracy by 16% when including trinary interactions, despite data scarcity.

ABSTRACT

Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest in recent times from dispersed multiphase flow community. The robustness of neural models for this complex multi-body problem is hindered by the availability of particle-resolved data. The present work addresses this unavoidable limitation of data paucity by implementing two strategies: (i) by using a rotation and reflection equivariant neural network and (ii) by pursuing a physics-based hierarchical machine learning approach. The resulting machine learned models are observed to achieve a maximum accuracy of 85% and 96% in the prediction of neighbor-induced force and torque fluctuations, respectively, for a wide range of Reynolds number and volume fraction conditions considered. Furthermore, we pursue force and torque network architectures that provide universal prediction spanning a wide range of Reynolds number ($0.25 \leq Re \leq 250$) and particle volume fraction ($0 \leq ϕ\leq 0.4$). The hierarchical nature of the approach enables improved prediction of quantities such as streamwise torque, by going beyond binary interactions to include trinary interactions.

Motivation & Objective

• Address the challenge of data paucity in training machine learning models for particle-resolved hydrodynamic forces and torques in dispersed multiphase flows.
• Overcome limitations of traditional mesoscale models that average over particle configurations and fail to capture particle-to-particle variations.
• Develop a physics-informed, hierarchical machine learning framework that captures multi-body interactions (pairwise and trinary) for improved force and torque prediction.
• Ensure model robustness and interpretability by enforcing rotation and reflection equivariance in the neural network architecture.
• Enable universal prediction across a wide range of Reynolds numbers (0.25 ≤ Re ≤ 250) and particle volume fractions (0 ≤ φ ≤ 0.4) using minimal training data.

Proposed method

• Employ rotation and reflection equivariant neural networks to ensure physical consistency and improve generalization under data scarcity.
• Implement a hierarchical machine learning approach that models interactions beyond binary pairs, including trinary interactions for improved accuracy.
• Use neighbor-truncation analysis to evaluate the impact of including increasing numbers of neighboring particles (M₂ = 26, M₃ = 5 or 10) on model performance.
• Train models on particle-resolved simulation data from a static, steady-state system with a uniform pressure gradient and triply periodic boundary conditions.
• Formulate force and torque predictions as functions of relative particle positions, Reynolds number, and volume fraction, enabling generalization across flow and packing conditions.
• Use R² scores to evaluate model performance on test sets, comparing training and test performance to assess generalization and data scarcity effects.

Experimental results

Research questions

• RQ1 Can a hierarchical machine learning model that includes trinary interactions outperform pairwise interaction models in predicting particle forces and torques?
• RQ2 How does the inclusion of rotation and reflection equivariance improve model accuracy and generalization in the presence of limited training data?
• RQ3 To what extent do neighbor-truncation effects impact the prediction accuracy of drag, lift, and torque components across varying Reynolds numbers and volume fractions?
• RQ4 Can a single universal model trained on diverse conditions predict forces and torques across the full range of Re (0.25–250) and φ (0–0.4) with high fidelity?
• RQ5 Why is the streamwise torque component particularly sensitive to higher-order interactions, and how does this affect model design?

Key findings

• The trinary-interaction torque model achieves a 16% improvement in streamwise torque prediction accuracy when increasing the number of neighbors from 5 to 10, despite data scarcity.
• The model achieves a maximum test R² of 0.96 for torque prediction, indicating high accuracy in capturing neighbor-induced torque fluctuations.
• For drag and lift, the model achieves test R² values of 0.75–0.80 across all conditions, with a maximum test R² of 0.803 for lift under specific Re and φ conditions.
• The training-to-test performance gap (e.g., R² drop from 0.862 to 0.803 in lift) indicates significant data paucity, especially for high-Re and high-φ conditions.
• The streamwise torque component shows the highest sensitivity to higher-order interactions, necessitating trinary models for accurate prediction.
• The hierarchical approach enables improved prediction of complex, anisotropic torque components by capturing non-additive, multi-body hydrodynamic effects beyond binary interactions.