flowinGN

This repo contains code for the paper titled "Graph Networks as Inductive Bias for Genetic Programming: Symbolic Models for Particle-Laden Flows". In this work, we model thirty particles of a particle-laden flow and their mutual interactions as a graph. Hereby, one particle corresponds to a node, and particle-particle interactions are represented by edges between two nodes. A graph network (GN) is trained to approximate the underlying relations between particles and predict the fluid-induced force $F_{\textrm{fluid}}$ on the center particle. The edge messages are captured during training of the GN, and used as training data for the genetic programming (GP) algorithm. This reduces the complexity of the problem, and thus facilitates the search process for fitting equations. We supply code for two underlying interaction types, where $N_i$ includes all neighboring particles of particle $i$:

• $y = g(x) = \sum_{j \in N_i}{m_{i,j}}$
• $y = f(g(x)) = f(\sum_{j \in N_i}{m_{i,j}})$

The core of this repo constitutes the following files:

• "GN_flowing.ipynb": Code to train a graph network for the problem at hand.
• "GP_flowing.py": Code to identify symbolic models using genetic programming, which replace the network blocks of the GN.

The folder structure is the following:

• "data_inhouse": Training data for 30 particles, as generated by the in-house flow solver. We provide datasets for the Stokes flow (i.e., $Re = 0$) for varying particle-volume fractions $\phi \in$ {0.064, 0.125, 0.216, 0.343}.
• "GN_results": GN models and recorded edge messages for each dataset and algorithm variant.
• "GP_data": Recorded edge messages during GN training, later used as training data for GP to replace network blocks by symbolic models.
• "GP_results": Equation files for various combinations of algorithms and datasets.

Requirements

I recommend to set up two virtual environments to run this code:

• pytorch_env: For the GN part, install PyG (PyTorch Geometric) and all its dependencies. For me, the conda installation on macOS for M1 worked well.
• pysr_env: For the GP part, PySR as well as its Julia (not my name, the programming language) distribution is required. I had a positive experience with the pip installation on macOS for M1.

Contact

For any inquiries related to this repo, please feel free to contact me at julia.reuter@ovgu.de.

Acknowledgment

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Priority Programme "SPP 2331: Machine Learning in Chemical Engineering". The project titled "Improving simulations of large-scale dense particle-laden flows with machine learning: a genetic programming approach" is supervised by Sanaz Mostaghim and Berend van Wachem at Otto-von-Guericke-University Magdeburg, Germany.