用精确守恒的神经网络提升冰流预测精度
Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fields
- 通过向量微积分实现局部质量守恒，强制物理约束
- 在比尔德冰川测试中，新方法比传统模型更可靠
- 结合大陆尺度卫星数据可显著提升所有模型性能
为准确预测未来海平面上升，冰盖模型需满足物理规律。将质量守恒等物理原理嵌入从稀疏且含噪观测中插值南极冰流矢量场的模型，不仅增强物理一致性，还能提高精度与鲁棒性。现有物理信息神经网络（PINNs）以软约束方式施加物理规则，虽灵活但无保证；本文提出无散度神经网络（dfNNs），利用向量微积分技巧精确实现局部质量守恒。在比尔德冰川冰通量插值任务中，dfNNs相较于PINNs和无约束神经网络表现更优。此外，引入方向引导学习策略——利用全大陆卫星速度数据进行训练，能普遍提升各类模型性能。
原文摘要 · Abstract (English)
To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy measurements not only promotes physical adherence but can also improve accuracy and robustness. While physics-informed neural networks (PINNs) impose physics as soft penalties, offering flexibility but no physical guarantees, we instead propose divergence-free neural networks (dfNNs), which enforce local mass conservation exactly via a vector calculus trick. Our comparison of dfNNs, PINNs, and unconstrained NNs on ice flux interpolation over Byrd Glacier suggests that "mass conservation on rails" yields more reliable estimates, and that directional guidance, a learning strategy leveraging continent-wide satellite velocity data, boosts performance across models.
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