Hybrid Model Combines Differentiable PDE Solvers and Neural Networks for Sparse Measurement Reconstruction

Jul 16, 2026

A new hybrid modeling pipeline integrates Radial Basis Function reconstruction, a neural network correction, and a differentiable partial differential equation (PDE) solver to reconstruct dense physical fields from sparse measurements. The approach enables training the neural network without access to fully-resolved simulation states, by embedding the differentiable PDE solver directly in the training loop. Evaluated on fluid mechanics benchmarks, the method outperforms existing statistical and machine-learning-based reconstruction techniques.

Why it matters: This method allows for physics-informed reconstruction from sparse data without requiring complete simulation examples, addressing a common limitation in real-world applications.

Full story at: arXiv Statistical ML ↗