Physics-Informed Neural Embeddings of PDE Solution Families
We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network output by construction, these principal components measure the additional variability the network le...
| Authors | Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas et al. |
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| Primary category | cs.LG |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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