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Adversarial Learning for Neural PDE Solvers with Sparse Data

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arxiv 2409.02431 v1 pith:ISJ7DI67 submitted 2024-09-04 cs.LG

Yunpeng Gong , Yongjie Hou , Zhenzhong Wang , Zexin Lin , Min Jiang This is my paper
classification cs.LG
keywords datamodelneuralaugmentationlearningnetworkpdessignificant
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Neural network solvers for partial differential equations (PDEs) have made significant progress, yet they continue to face challenges related to data scarcity and model robustness. Traditional data augmentation methods, which leverage symmetry or invariance, impose strong assumptions on physical systems that often do not hold in dynamic and complex real-world applications. To address this research gap, this study introduces a universal learning strategy for neural network PDEs, named Systematic Model Augmentation for Robust Training (SMART). By focusing on challenging and improving the model's weaknesses, SMART reduces generalization error during training under data-scarce conditions, leading to significant improvements in prediction accuracy across various PDE scenarios. The effectiveness of the proposed method is demonstrated through both theoretical analysis and extensive experimentation. The code will be available.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. GAMA: Geometry-Aware Manifold Alignment via Structured Adversarial Perturbations for Robust Domain Adaptation

    cs.CV 2025-05 reject novelty 5.0 of 10

    GAMA adds tangent-space adversarial perturbations and a geodesic alignment loss to domain adaptation training, but the paper's evidence is incomplete.

  2. FADE: Adversarial Concept Erasure in Flow Models

    cs.CV 2025-07 reject novelty 4.0 of 10

    FADE combines adversarial training with trajectory preservation to erase concepts from diffusion models, reporting state-of-the-art erasure on Stable Diffusion benchmarks, but the evidence is incomplete and the theore...

  3. Dynamic Modality Scheduling for Multimodal Large Models via Confidence, Uncertainty, and Semantic Consistency

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