Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
We introduce FLASH-MAX, a shallow, exact-by-construction neural network architecture for predicting homogeneous electromagnetic fields from sparse pointwise observations. Each hidden neuron represents a separate exact solution to Maxwell's equations, so that the network satisfies the governing equations symbolically by construction and can be trained end-to-end from sparse data within seconds. We prove a universal approximation result showing that this exact model class remains universal on arbitrary domains. FLASH-MAX reaches sub-1% relative validation error from about 1K sparse pointwise observations in seconds, all while maintaining a zero PDE residual, and keeps single-digit errors ev...
| Authors | Dan DeGenaro, Xin Li, Obed Amo et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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