Encoder-Decoder Neural Networks in Interpretation of X-ray Spectra

TL;DR

A network where the linear projection of ECA is used is developed, thus maintaining the beneficial characteristics of vector expansion from the latent variables for their interpretation, underline the necessity of information recovery after its condensation.

Abstract

Encoder--decoder neural networks (EDNN) condense information most relevant to the output of the feedforward network to activation values at a bottleneck layer. We study the use of this architecture in emulation and interpretation of simulated X-ray spectroscopic data with the aim to identify key structural characteristics for the spectra, previously studied using emulator-based component analysis (ECA). We find an EDNN to outperform ECA in covered target variable variance, but also discover complications in interpreting the latent variables in physical terms. As a compromise of the benefits of these two approaches, we develop a network where the linear projection of ECA is used, thus maintaining the beneficial characteristics of vector expansion from the latent variables for their interpretation. These results underline the necessity of information recovery after its condensation and identification of decisive structural degrees of freedom for the output spectra for a justified interpretation.

Figures (8)

• Figure 1: The principle of spectra prediction with encoder-decoder neural network (EDNN). Successful emulation of output for given input requires essential latent information to be condensed into the activation values of the neurons at the bottleneck, which may be only a few for reasonably accurate emulation of the structure--spectrum relationship.
• Figure 2: Spectra for structures from AIMD simulations for (a-c) the H2O molecule and (d) amorphous GeO2 at various pressures. Black line depicts the mean and grey areas $\pm \sigma$ cut to zero. For amorphous GeO2 colored lines represent mean spectra for different pressures and the intervals containing the studied peaks are marked with vertical dashed lines.
• Figure 3: Isosurface plots (a-c) of the one-component EDNN model activation values compared to (d-f) isosurfaces of metric $M$ defined in Equation (\ref{['eq:mdiff']}) a polynomial modelNiskanen2022 for the spectra of the H2O molecule. Drawn following Ref. Niskanen2022. The H--O--H angle, the length of the long O--H bond, and the length of the short O--H bond, are denoted as $\alpha$, $b_l$, $b_s$, respectively.
• Figure 4: The principle of implementing ECA as a simple encoder in the NNCA network with $k$=1. A broader bottleneck implies corresponding orthonormal set of vectors $\{\mathbf{v}_j\}_{j=1}^k$ for the projection of the input vector $\mathbf{x}$. The matrix operation after input has zero bias followed by linear activation.
• Figure 5: Mean-structural-parameter-based distances in each pressure from the central Ge atom (a) Reconstructed from the fitted NNCA components for both one and two-component models. Dashed lines correspond to the two-component model. (b) Known mean distances calculated from the atomic coordinates of the test dataset. Drawn following Ref. Vladyka2023