aiqbench analysis
This research introduces a novel neural operator that embeds physical conservation laws—specifically precessional and dissipative structures from the Landau-Lifshitz-Gilbert equation—into latent space for micromagnetic simulations. By training solely on trajectory data without explicit energy labels, the model achieves significantly faster inference speeds while maintaining high accuracy over extended prediction horizons compared to standard solvers. The approach demonstrates that structuring neural ODEs with antisymmetric and symmetric operators can effectively capture complex magnetic dynamics, offering a promising path for accelerating computational physics in materials science.
An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamics
arXiv:2609.04530v1 Announce Type: new 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 $\mu$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.
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 $\mu$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.
Machine Learning (cs.LG); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
arXiv:2609.04530 [cs.LG]
(or arXiv:2609.04530v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.04530 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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