KernelMO: New kernel method slashes operator learning costs while matching neural PDE models
KernelMO achieves state-of-the-art PDE accuracy with closed-form training, no backprop needed.
A new paper introduces KernelMO, a kernel-based encoder-decoder framework for learning operators with multiple inputs and outputs. It separates observation, representation, learning, and reconstruction, and uses closed-form training and inference. The framework’s approximation theory shows convergence rates are governed by the hardest subproblem, not the total number of inputs and outputs. Tested on five families of parametric PDEs, KernelMO achieves competitive or state-of-the-art predictive accuracy while reducing training and inference costs relative to neural operator architectures and deep learning models.
- KernelMO supports multi-input, multi-output operator learning with convergence rate independent of total input/output dimension
- Closed-form training and inference eliminates backpropagation, reducing computational overhead vs neural operators like DeepONet and FNO
- Matches or beats state-of-the-art accuracy across five parametric PDE families while cutting training and inference costs
Why It Matters
Faster, theoretically grounded operator learning could accelerate PDE surrogates and scientific simulations without expensive GPU training.