NEFEM uses neural networks as adaptive enrichment functions inside the SGFEM framework, trained via the Ritz functional, to achieve better approximation with fewer degrees of freedom for problems with strong oscillations or weak interface discontinuities.
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math.NA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper supplies explicit hand-derived gradient formulas and a full training cycle for PINNs on a simple ODE, achieving 4.29e-4 relative L2 error against the analytic solution using only the physics loss.
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Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems
NEFEM uses neural networks as adaptive enrichment functions inside the SGFEM framework, trained via the Ritz functional, to achieve better approximation with fewer degrees of freedom for problems with strong oscillations or weak interface discontinuities.
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Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
The paper supplies explicit hand-derived gradient formulas and a full training cycle for PINNs on a simple ODE, achieving 4.29e-4 relative L2 error against the analytic solution using only the physics loss.