Post by Aum Rawal

Geometric Deep Learning | Differential & Cartan Geometry | Topological Data Analysis | Bridging Advanced Mathematics & AI

What if a neural network could hand you an entire CFD flow field over a drone's wing / rotor without ever running the solver? 🚀 That's VolumeGEM, the volume surrogate at the core of my AeroForge project. Instead of solving Navier–Stokes from scratch per geometry, it learns the solution operator: a gauge-equivariant mesh CNN that maps a RANS mesh straight to the full interior flow field. On 200 held-out AirfRANS cases (~10M nodes), measured — not projected: → Velocity field: R² = 0.96 → Turbulence (νt): median per-case R² = 0.90 → ~1.3 s/case vs a multi-minute solve — ~473× faster → From a model of just ~13,000 parameters Integrating its OWN predicted field (no separate lift model) recovers a lift coefficient that tracks CFD at Spearman ρ = 0.91 — enough to rank competing designs end-to-end. The honest part: drag isn't there yet. Over half of it is viscous, set by a razor-thin near-wall layer the model still under-resolves at 50 epochs, so CD scatters against truth. A dedicated surface loss is the next milestone — I'd rather show you the failure mode than hide it. A brief introduction to the method with metrics is in the overview below. I'm posting this to find collaborators and get honest feedback. I'd especially love to connect with: → A CFD / meshing specialist — to help me make drag as trustworthy as lift. → A drone / UAV expert — to point this at real rotor-blade geometries. And if you work near aerodynamics or geometric deep learning: tell me where I'm wrong and what you'd try next. Comment, DM, or connect — I read everything. Patrick Nicolas Frédéric Barbaresco Reference paper : https://lnkd.in/dWYUuMcr. Taco Cohen, Max Welling #GeometricDeepLearning #CFD #Aerodynamics #MachineLearning #Drones #UAV #DeepLearning #AI

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