\(\text{Coordinates}\)

\(\text{Loss } (L)\)

\(\text{PDE Problem}\)

\((\boldsymbol{x}, t, \boldsymbol{\mu})\)

\(\text{ Parameters}\)

\( \text{and time}\)

\(\text{Smooth neural field MLP }(g_\theta)\)

\(\text{Backpropagation}\)

\(\text{ Intrinsic ROM manifold }(\Xi_\varrho)\)

\(\tilde{u}\)

\(\boldsymbol{x}\)

\(\boldsymbol{u}\left( \boldsymbol{x}, t; \boldsymbol{\mu} \right)\)

\(\mathcal{\tilde{U}}\)

\(\nabla_\theta L\)

\(\nabla_\varrho L\)

\(\nabla_\theta L\)