Flexi-VAE: Unified PDE Prediction Interface
🚀 Flexi-Propagator: Single-Shot Prediction for Nonlinear PDEs
Governing Equation (1D Burgers' Equation):
$$
\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} = \nu \frac{\partial^2 u}{\partial x^2}
$$
Key Advantages:
✔️ 50-100× faster than AE-LSTM baselines
✔️ Parametric control: Embeds system parameters in latent space
Physically Interpretable Latent Space - Disentanglement:
$$
Z_1 \text{ Encodes Peak Location, } Z_2 \text{ Predominantly Encodes Re (Sharpness)}
$$
425 2350
• Interpolation Zone: [822, 1022]
• Left Extrapolation: [400, 600]
• Right Extrapolation: [2200, 2400]
150 450
• Interpolation Zone: [340, 368]
• Left Extrapolation: [150, 178]
• Right Extrapolation: [398, 425]
🌪️ 2D Advection-Diffusion Visualization
Governing Equation: $$ \frac{\partial u}{\partial t} + c \frac{\partial u}{\partial x} = \nu \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) $$
1 10
• Interpolation Zone: [2.09, 2.99]
• Left Extrapolation: [1.0, 1.9]
• Right Extrapolation: [9.1, 10.0]
150 425
• Interpolation Zone: [364.7, 392.2]
• Left Extrapolation: [150, 177.5]
• Right Extrapolation: [397.5, 425]