Discrete energy as an exact label-free training objective for finite-element surrogates

arXiv:2608.05437 · cs.CE, cs.LG, math.NA · Submitted 2026-08-05 · Read on arXiv

Ruifeng Cao, Xidan Song

The University of Manchester · Wuhan University

cs.CE, cs.LG, math.NA

Submitted: 2026-08-05

Comments: 9 pages. Theory note of the FE-JEPA programme

Code: https://github.com/HymnOfLight/FE-JEPA

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Verification — 6× in this paper · explained in 2 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Training Objective — 5× in this paper · explained in 3 episodes
• Decoder — 4× in this paper · explained in 2 episodes
• Joint-Embedding Predictive Architecture (JEPA) — 4× in this paper · explained in 4 episodes
• Representation Learning — 4× in this paper · explained in 3 episodes
• Surrogate Model — 3× in this paper · explained in 3 episodes
• Surrogate Models — 3× in this paper · explained in 3 episodes
• Expressivity — 2× in this paper · explained in 2 episodes
• Preconditioner — 2× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Incremental Updates — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Neural Operators — 1× in this paper · explained in 2 episodes
• Preconditioning — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Deep Ritz Method with Adaptive Quadrature for Linear Elasticity
• An operator preconditioning perspective on training in physics-informed machine learning

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