Iterations for active sampling in inelastic neutron scattering

<p>We combine Linear Spin Wave Theory with active-learning sampling, resulting in a Kalman Filter enhanced Adversarial Bayesian Optimization (KFABO) algorithm. This algorithm approximates the magnon spectrum using a minimal number of sampling points and iterations. Despite the limited iterations, the algorithm effectively addresses noisy neutron scattering data, providing reliable magnetic interactions that replicate the experimental spectra for 2D CrSBr. It can also reveal hidden or weak interactions, such as those induced by spin-orbit coupling.</p>
<p>The attached files illustrate the sampling process during different iteration scenarios. "Theoretical_SPINW_woDMI.gif" shows the iterations for the case including only Heisenberg exchange (J) interactions. "Theoretical_SPINW_wDMI.gif" displays iterations for the case including both Dzyaloshinskii-Moriya interactions (DMI) and Heisenberg exchange interactions. Finally, "Experimental_SPINW_wDMI.gif" represents the iterations during the fitting of the experimental spin wave data.</p>
<b>Methods</b>
<p>We combine Linear Spin Wave Theory (LSWT), Active Learning Sampling, and Adaptive Noise Reduction to form the Kalman Filter enhanced Adversarial Bayesian Optimization Algorithm (KFABO). This algorithm integrates two coupled Bayesian Optimization (BO) algorithms with a Kalman filter. The first BO algorithm, termed fBO, employs trust region Bayesian optimization (Turbo) on our linear response model to search for optimal parameters, aiming to minimize the difference between theoretically predicted and real LSW function values of the measured sample points. The second algorithm, termed sBO, is a standard BO that selects sampling points with maximum information gain relative to the current state, specifically, those points that can better characterize the real LSW function given the current samples and the fitted LSW function.</p>