用于瞬态冰流模拟的物理增强神经求解器
Physics-enriched neural solvers for transient ice-flow simulation
- Université de Lausanne（洛桑大学）
- Universität Zürich（苏黎世大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出物理增强神经求解器，通过低阶冰流平衡输入改进瞬态高阶冰流模拟，在真实冰川上显著提升稳健性和精度-运行时间权衡，大幅降低计算成本。
AI中文摘要：
高阶冰流的瞬态冰川模拟需要在几何演化过程中反复求解非线性问题。在Instructed Glacier Model的在线模式中，速度场由神经网络表示，其权重从前一时间步热启动，并通过少量优化器迭代进行更新。我们表明，向网络提供由低阶冰流平衡导出的廉价输入场可改进该在线求解器。与基于残差的物理信息神经网络（通过损失中的控制方程惩罚项纳入物理）不同，我们的方法保持控制能量目标不变，通过网络输入添加物理结构。在三个真实冰川配置上，增强求解器对求解器设置明显更稳健。在两个高山案例中，它还改善了调优精度-运行时间权衡，在固定运行时间内将表面速度误差减少2至4倍，并仅用10^4至10^5个可训练参数达到百分之几的相对误差，远少于可比原始输入基线。随后，300年的Aletsch模拟在单块GPU上不到一分钟内完成，更大的Valais区域约两分钟完成——这一预算曾专用于更简单的浅冰模型。对于快速海洋终止冰川，增益较小，因为非局部应力耦合倾向于更大或谱网络。更广泛地，结果表明，用降阶物理丰富神经求解器的输入可使重复高阶求解更便宜，且无需训练数据和离线训练。
英文摘要：
Transient glacier simulations with higher-order ice flow require the repeated solution of a nonlinear problem as the geometry evolves. In the online mode of the Instructed Glacier Model, the velocity field is represented by a neural network whose weights are warm-started from the previous time step and updated with a few optimizer iterations. We show that supplying the network with inexpensive input fields derived from low-order ice-flow balances improves this online solver. Unlike residual-based physics-informed neural networks, which incorporate physics through governing-equation penalties in the loss, our approach leaves the governing energy objective unchanged, adding physical structure through the network inputs. Across three real-world glacier configurations, the enriched solver is markedly more robust to solver settings. On the two alpine cases, it also improves the tuned accuracy--runtime trade-off, reducing surface-velocity errors by factors of two to four at fixed runtime and reaching few-percent relative errors with only $10^4$--$10^5$ trainable parameters, far fewer than comparable raw-input baselines. A 300-year Aletsch simulation then completes in under one minute, and the larger Valais domain in about two minutes, on a single GPU---a budget once reserved for much simpler shallow-ice models. Gains are smaller for the fast marine-terminating glacier, where nonlocal stress coupling favors larger or spectral networks. More broadly, the results suggest that enriching a neural solver's inputs with reduced-order physics can make repeated higher-order solves much cheaper, with no training data and no offline training.
