Problem
Research questions and friction points this paper is trying to address.
magnetization dynamics
energy-based model
latent neural evolution operator
Landau-Lifshitz-Gilbert equation
reduced-order model
An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamics
🤖 AI Summary
研究通过结合卷积自编码器和结构化潜神经常微分方程，开发了一种基于能量的简化模型来模拟微磁磁化动力学。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
energy-based model
latent neural ODE
conservative-dissipative structure
convolutional autoencoder
trajectory prediction
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