Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs

arXiv:2603.24002 · cs.LG · Submitted 2026-03-25 · Read on arXiv

cs.LG

Submitted: 2026-03-25

Updated: 2026-09-16

Comments: arXiv admin note: text overlap with arXiv:2412.00088, arXiv:2410.08989, arXiv:2307.12306 by other authors

Code: https://github.com/liangzhangyong/SDZE

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

Terminology

• Benchmark — 21× in this paper · explained in 2 episodes
• Accuracy — 17× in this paper · explained in 1 episode
• Trace — 14× in this paper · explained in 2 episodes
• Fine-Tuning — 7× in this paper · explained in 5 episodes
• Adam — 5× in this paper · explained in 2 episodes
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Stochastic Dimension Gradient Descent — 4× in this paper
• Physics-Informed Neural Networks (PINNs) — 3× in this paper · explained in 6 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Abstraction — 2× in this paper · explained in 1 episode
• DeepONet — 2× in this paper · explained in 2 episodes
• Hutchinson Trace Estimation — 2× in this paper
• PDE residual — 2× in this paper · explained in 2 episodes
• Stiefel manifold — 2× in this paper · explained in 2 episodes
• Stochastic Taylor Derivative Estimator — 2× in this paper
• Ablation Studies — 1× in this paper · explained in 1 episode
• Activation Function — 1× in this paper · explained in 1 episode
• Amortization — 1× in this paper · explained in 1 episode
• Common Random Numbers Synchronization — 1× in this paper
• Core — 1× in this paper · explained in 2 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Exchangeability — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Neural Surrogates — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Stochastic Dimension-free Zeroth-order Estimator — 1× in this paper
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Gradients without Backpropagation
• Johnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey
• Randomized Numerical Linear Algebra : A Perspective on the Field With an Eye to Software

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