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 out
Lineage graph
Paper → model → repo connections mined from source citations (Tier-1 exact match).
Why these links exist
Every edge carries a method, confidence, and the source snippet that justified it — so bad links are debuggable.
- PossiblePossibly related (embedding) · 60%SciML/NeuralPDE.jl →
- PossiblePossibly related (embedding) · 53%NVIDIA/physicsnemo →
- PossiblePossibly related (embedding) · 48%Hamiltonian Neural Networks from a Differential Geometry Perspective [D] →
- PossiblePossibly related (embedding) · 47%arogozhnikov/hep_ml →
- PossiblePossibly related (embedding) · 47%Principled approaches for extending neural architectures to function spaces for operator learning →
- LinkedLinked via arxiv author · 85%Raul Jimenez →
“Physics-Informed Neural Embeddings of PDE Solution Families”
- LinkedLinked via arxiv author · 85%Svitlana Mayboroda →
“Physics-Informed Neural Embeddings of PDE Solution Families”
- LinkedLinked via arxiv author · 85%Pavlos Protopapas →
“Physics-Informed Neural Embeddings of PDE Solution Families”