FOSLS-deRhaNN: native de Rham neural classes for H(div) and H(curl) with applications to first-order system least-squares neural network methods for partial differential equations
math.NA, cs.LG, cs.NA
Submitted: 2026-10-06
Updated: 2026-10-06
Sources
- A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network
- Penalty-Free Natural Deep Ritz Method Based on de Rham Complex for High-Dimensional Dirichlet Boundary Value Problems
- Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
- ReLU$^k$ Neural de Rham Complexes
- Least-Squares Neural Network (LSNN) Method for Scalar Hyperbolic Partial Differential Equations
- First Order System Least Squares Neural Networks
- Goal-Oriented Error Estimation for Least-Squares Finite Element Methods via Physically Meaningful Adjoint PDEs
Related papers
- Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm
- A Neural-preconditioned Poisson Solver for Mixed Dirichlet and Neumann Boundary Conditions
- Operator learning meets inverse problems: A probabilistic perspective
- Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
- Windowed thinning and query complexity for the bouncy particle and Zigzag samplers
- Data-efficient Kernel Methods for Learning Hamiltonian Systems