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Magnetic Hamiltonian parameter estimation using deep learning techniques.

ABSTRACT: Understanding spin textures in magnetic systems is extremely important to the spintronics and it is vital to extrapolate the magnetic Hamiltonian parameters through the experimentally determined spin. It can provide a better complementary link between theories and experimental results. We demonstrate deep learning can quantify the magnetic Hamiltonian from magnetic domain images. To train the deep neural network, we generated domain configurations with Monte Carlo method. The errors from the estimations was analyzed with statistical methods and confirmed the network was successfully trained to relate the Hamiltonian parameters with magnetic structure characteristics. The network was applied to estimate experimentally observed domain images. The results are consistent with the reported results, which verifies the effectiveness of our methods. On the basis of our study, we anticipate that the deep learning techniques make a bridge to connect the experimental and theoretical approaches not only in magnetism but also throughout any scientific research.

SUBMITTER: Kwon HY

PROVIDER: S-EPMC7518863 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Magnetic Hamiltonian parameter estimation using deep learning techniques.

Kwon H Y HY Yoon H G HG Lee C C Chen G G Liu K K Schmid A K AK Wu Y Z YZ Choi J W JW Won C C

Science advances 20200925 39

Understanding spin textures in magnetic systems is extremely important to the spintronics and it is vital to extrapolate the magnetic Hamiltonian parameters through the experimentally determined spin. It can provide a better complementary link between theories and experimental results. We demonstrate deep learning can quantify the magnetic Hamiltonian from magnetic domain images. To train the deep neural network, we generated domain configurations with Monte Carlo method. The errors from the est ...[more]

PMID: 32978161

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Project description:BACKGROUND: Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system's states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes. RESULTS: We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions. CONCLUSION: Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Dataset Information

Magnetic Hamiltonian parameter estimation using deep learning techniques.

Publications

Magnetic Hamiltonian parameter estimation using deep learning techniques.

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