Training ideas

Curricula, sampling schedules, pseudo-labeling and multi-task mixing, with the standard training recipe as the control.

2 ideas found

Category: Training ML: Graph nn Math: Numerical analysis Clear all

Unverified 2026

Stiffness-energy supervision without FEM labels

Train a finite-element surrogate by minimizing the assembled discrete potential energy rather than a loss against solved displacement labels. The objective uses only the sparse stiffness matrix and load vector, while its exact energy-gap identity makes it equivalent to supervised regression in the stiffness norm.

Useful6/10

Difficulty3/10

Novelty5/10

Training Sample efficiency Speedup Accuracy

Paper: Discrete energy as an exact label-free training objective for finite-element surrogates arXiv:2608.05437

✗ Mechanism failed 2026

Energy-Derived Nitsche Neural Fields

Represent a solution on an unfitted domain with local neural subnetworks and train them using one augmented energy containing the bulk physical energy, symmetric Nitsche boundary or interface terms, and a derivative-jump ghost penalty. Automatic differentiation of this scalar objective supplies all gradients and avoids independently tuning inconsistent PDE residual, flux, and boundary losses. The method is especially suited to moving geometries, cut-cell domains, and domain-decomposed neural…

Useful6/10

Difficulty5/10

Novelty6/10

Training Stability Accuracy Scalability

Paper: A Unified CutFEM Formulation for Finite-Strain Elasticity: Energy Minimisation and Corner Singularities arXiv:2607.02334