Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916032785940480 |
|---|---|
| author | DeGenaro, Dan Li, Xin Amo, Obed Pokojovy, Michael Bargal, Sarah Adel Lange-Hegermann, Markus Raiţă, Bogdan |
| author_facet | DeGenaro, Dan Li, Xin Amo, Obed Pokojovy, Michael Bargal, Sarah Adel Lange-Hegermann, Markus Raiţă, Bogdan |
| contents | 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 even for only 100 observations sampled from 3D space. These results suggest that moving governing structure from the loss into the hypothesis class can dramatically improve the trade-off between precision and optimization speed in scientific machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data DeGenaro, Dan Li, Xin Amo, Obed Pokojovy, Michael Bargal, Sarah Adel Lange-Hegermann, Markus Raiţă, Bogdan Machine Learning Numerical Analysis I.6.3; I.6.5; J.2 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 even for only 100 observations sampled from 3D space. These results suggest that moving governing structure from the loss into the hypothesis class can dramatically improve the trade-off between precision and optimization speed in scientific machine learning. |
| title | Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data |
| topic | Machine Learning Numerical Analysis I.6.3; I.6.5; J.2 |
| url | https://arxiv.org/abs/2605.20514 |