PIML4LBM

Physics-Informed Machine Learning for LBM Simulation

This project aims to develop a machine learning approach for the 2D-Q9 Lattice Boltzmann Method (LBM) using four different modeling strategies. The models are validated using the Taylor-Green Vortex and lid-driven cavity tests.

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🔧 Methods Implemented

1. Naive BGK model
2. Symmetric lattice fetching
3. Mass & momentum conservation
4. Combined symmetry and conservation

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🧠 Approach Overview

The pipeline consists of the following steps:

1. Data generation
2. Collision operator construction
3. Dataset building
4. Model training and validation

Each model version reflects a different level of physical constraint:

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1. Naive Method

• Enforces only mass conservation (continuity equation).
• Computationally expensive and does not guarantee physical constraints.

2. Symmetric Condition

• Enforces D8 symmetry by averaging over group operations to ensure φ_NN is equivariant.
• Fails to conserve mass & momentum (violates Postulate 3).

3. Mass and Momentum Conservation

• Enforces conservation in x and y directions.

• Fails to ensure equivariance (violates Postulate 2).

  • 3.1: Algebraic Reconstruction (biased for rows 2, 5, 8)
  • 3.2: Symmetric Algebraic Reconstruction using group averaging
  • 3.3: Soft constraint in the loss function to penalize mass and momentum mismatches

4. Combined Symmetry + Conservation

• Satisfies all 4 physical postulates.
• Reduces degrees of freedom from 90 → 18 for D2Q9, improving efficiency.

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🧪 Tests

• Taylor-Green Vortex for flow validation
• Lid-driven cavity to assess physical accuracy

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Feel free to clone, explore, and adapt the models for more complex LBM simulations or different lattice types.