FluidNeRF

Neural Radiance Fields for 3D Fluid Flow Visualization

FluidNeRF adapts Neural Radiance Fields (Mildenhall et al., ECCV 2020) for scientific volume rendering of 3D fluid flow data. Train a NeRF on volume-rendered snapshots of CFD simulations, then synthesize photorealistic flow visualizations from arbitrary camera angles in real time.

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The Idea

Traditional scientific visualization requires re-rendering entire volumetric datasets whenever the viewpoint changes. FluidNeRF learns a continuous neural representation of the flow field's appearance, enabling:

• Novel view synthesis of 3D flow structures from any camera angle
• Continuous resolution — query any point in space, not just grid vertices
• Compact representation — a few MB neural network replaces GB-scale volume data
• Interactive exploration — millisecond rendering after training

Architecture

Exact Mildenhall et al. (2020) NeRF, adapted for scientific data:

Position (x,y,z) → Positional Encoding (L=10, 60 dims)
    → 8-layer MLP (256 wide, skip at layer 4)
    → Density σ (ReLU, non-negative)
    → Feature + Encoded Direction → 1 layer → RGB (sigmoid)

Volume Rendering (Beer-Lambert):
    C(r) = Σᵢ Tᵢ · αᵢ · cᵢ
    αᵢ = 1 - exp(-σᵢ · δᵢ)
    Tᵢ = Πⱼ<ᵢ (1 - αⱼ)

Flow Fields

Training data from exact analytical solutions of Navier-Stokes/Euler equations:

• Taylor-Green Vortex: Decaying 3D turbulence (exact N-S solution)
• ABC Flow: Chaotic Beltrami flow (curl(V) = V, exact Euler solution)
• Lamb-Oseen Vortex: Viscous vortex tube (exact solution)
• Vortex Ring: Toroidal vortex with Gaussian core

All flows are divergence-free and satisfy the governing equations analytically.

Key Features

• Exact NeRF architecture with positional encoding, skip connections, hierarchical sampling
• Differentiable volume rendering with stratified ray sampling
• 4 physically correct analytical flow field generators (verified div(V)=0)
• Q-criterion and vorticity magnitude computation for vortex identification
• Scientific colormaps (coolwarm, jet) for physical quantity visualization

References

• Mildenhall, B. et al. (2020). NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. ECCV 2020.
• Taylor, G.I. & Green, A.E. (1937). Mechanism of the production of small eddies from large ones. Proc. R. Soc. London.
• Dombre, T. et al. (1986). Chaotic streamlines in the ABC flows. J. Fluid Mech.
• Hunt, J.C.R. et al. (1988). Eddies, streams, and convergence zones in turbulent flows. CTR Summer Program.

Author

Samarjith Biswas, Ph.D. Research Scientist III, University of Arizona, New Frontiers of Sound (NewFoS) Center