发表机构
Wolfgang Pauli Institute; University of Vienna（沃尔夫冈·泡利研究所; 维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种基于能量的保守-耗散隐式神经演化算子，构建了微磁磁化动力学的降阶模型，通过对比不同隐式能量类型，发现反对称-耗散模型及深度二次能量在轨迹预测中表现更优，可实现低成本的高精度轨迹预测。
AI 中文摘要
我们开发了一种用于微磁磁化动力学的基于能量的降阶模型，该模型将卷积自编码器与结构化隐式神经常微分方程耦合。受Landau-Lifshitz-Gilbert方程的进动-耗散结构启发，隐式向量场由学习到的标量势的梯度通过反对称算子和对称半正定耗散算子生成。该势在非唯一隐式坐标中学习，不与吉布斯自由能量等同，但会沿自主连续时间解单调减小，而反对称分量允许沿其水平集运动。编码器、解码器、隐式能量及算子仅使用隐式和解码滚动损失在短轨迹窗口上联合训练，无需时间导数监督、物理能量标签或耗散惩罚。推理时，初始状态仅编码一次，在隐式空间中演化，并仅在请求的输出时刻解码，从而实现比用于生成训练数据的微磁求解器便宜得多的轨迹预测。我们在两个由场振幅参数化、针对NIST μMAG标准问题4的两个外加场方向生成的数据集上，比较了二次、深度及加性深度二次隐式能量。仅耗散模型与反对称-耗散模型在短训练式窗口上实现了相当的精度，但在连续滚动上差异显著，其中反对称-耗散模型提供了明显更准确的轨迹预测。深度二次能量在两个场方向上均实现了最佳整体精度，且当滚动扩展至训练 horizon 的两倍时，表现出更慢的误差增长。
英文摘要
We develop an energy-based reduced-order model for micromagnetic magnetization dynamics that couples a convolutional autoencoder to a structured latent neural ordinary differential equation. Motivated by the precessional-dissipative structure of the Landau-Lifshitz-Gilbert equation, the latent vector field is generated from the gradient of a learned scalar potential through an antisymmetric operator and a symmetric positive-semidefinite dissipative operator. This potential is learned in nonunique latent coordinates and is not identified with the Gibbs free energy, but decreases monotonically along autonomous continuous-time solutions, while the antisymmetric component permits motion along its level sets. The encoder, decoder, latent energy, and operators are trained jointly on short trajectory windows using latent and decoded-rollout losses alone, without time-derivative supervision, physical-energy labels, or dissipation penalties. At inference, an initial state is encoded once, evolved in latent space, and decoded only at the requested output times, enabling substantially cheaper trajectory prediction than the micromagnetic solver used to generate the training data. We compare quadratic, deep, and additive deep-quadratic latent energies on two datasets parameterized by field amplitude and generated for the two applied-field directions of the NIST $μ$MAG Standard Problem 4. Dissipative-only and antisymmetric-dissipative models achieve comparable accuracy on short training-style windows but differ substantially on uninterrupted rollouts, for which the antisymmetric-dissipative models provide markedly more accurate trajectory predictions. The deep-quadratic energy gives the best overall accuracy for both field directions and exhibits slower error growth when rollouts are extended to twice the training horizon.
Comments24 pages, 13 figures
