A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers

arXiv:2609.07437 · math.NA, cs.LG, cs.NA, physics.flu-dyn · Submitted 2026-09-07 · Read on arXiv

math.NA, cs.LG, cs.NA, physics.flu-dyn

Submitted: 2026-09-07

Updated: 2026-09-07

Code: https://github.com/guoxing0809/neuropde_analysis

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

Terminology

• Accuracy — 1× in this paper · explained in 1 episode
• Graph Neural Network (GNN) — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes

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