Geometry-informed deep learning surrogate models for flow prediction

Deep learning surrogate models have gained popularity in flow prediction, but they face limitations with diverse geometries. This led to 'geometry-informed' models, which adapt and predict flows across various shapes, crucial for design optimisation, real-time predictions, and multi-fidelity frameworks [1].

We introduce a framework combining Graph Neural Networks (GNNs) to represent mesh-based geometries and capture spatial relationships with Convolutional Autoencoders for compressed flow representations. The model is pre-trained on a 2D serpentine reactor with shape variants generated using sinusoidally-parameterised curves (Geometric parameters: p₁ ∈ [0.1, 0.5], p₂ ∈ [3.0, 4.0], p₃ ∈ [0, π/2], where p₁ = amplitude, p₂ = frequency, p₃ = horizontal offset). Transient CFD simulations track tracer concentration in water, generating over 100 cases using Latin-hypercube sampling. For each transient case, 140 datasets are recorded every 0.05 seconds.

Our GNN architecture employs graph convolution layers on the reactor mesh graph to capture spatial dependencies and geometric information. Key node features include x and y coordinates, tracer concentration, and velocity components. Pooling layers reduce dimensions, and the compressed representations are processed by fully connected layers to predict velocity and tracer concentration fields.

We demonstrate low mean squared errors on 10 unseen reactor geometries and a 100-fold speedup compared to CFD simulations. This geometry-informed approach significantly enhances accuracy and efficiency in predicting flow for complex reactor geometries.

References: [1] Bronstein, M. M., Bruna, J., Cohen, T., & Veličković, P. (2021). Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. ArXiv. /abs/2104.13478