Proves an n^{-1/(d+2)}-type convergence rate for weak PINNs approximating entropy solutions of geometry-compatible conservation laws on d-dimensional manifolds, with network complexity independent of the ambient dimension.
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks.Journal of Machine Learning Research, 20(1):2285–2301, 2019
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
background 1
citation-polarity summary
fields
math.NA 1years
2025 1verdicts
REJECT 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds
Proves an n^{-1/(d+2)}-type convergence rate for weak PINNs approximating entropy solutions of geometry-compatible conservation laws on d-dimensional manifolds, with network complexity independent of the ambient dimension.