The Role of Structural Representation in the Performance of a Deep Neural Network for X-ray Spectroscopy

Abstract

An important consideration when developing a deep neural network (DNN) for the prediction of molecular properties is the representation of the chemical space. Herein we explore the effect of the representation on the performance of our DNN engineered to predict Fe K-edge X-ray absorption near-edge structure (XANES) spectra, and address the question: How important is the choice of representation for the local environment around an arbitrary Fe absorption site? Using two popular representations of chemical space—the Coulomb matrix (CM) and pair-distribution/radial distribution curve (RDC)—we investigate the effect that the choice of representation has on the performance of our DNN. While CM and RDC featurisation are demonstrably robust descriptors, it is possible to obtain a smaller mean squared error (MSE) between the target and estimated XANES spectra when using RDC featurisation, and converge to this state a) faster and b) using fewer data samples. This is advantageous for future extension of our DNN to other X-ray absorption edges, and for reoptimisation of our DNN to reproduce results from higher levels of theory. In the latter case, dataset sizes will be limited more strongly by the resource-intensive nature of the underlying theoretical calculations.

Enhancing the analysis of disorder in X-ray absorption spectra: application of deep neural networks to T-jump-X-ray probe experiments

“…In this Article, we have developed a DNN for the instantaneous prediction of XANES spectra at the Co K-edge, building on our recent work at the Fe K-edge. 46,47 We have demonstrated that our DNN can predict Co K-edge XANES spectra using nothing more than the local geometry of the X-ray absorption site with consistent qualitative accuracy and that it can, in many cases, deliver quantitative (sub-eV) accuracy on peak positions with respect to reference XANES spectra. The structure and performance of the DNN optimised in the present Article is comparable to that reported in our recent work at the Fe K-edge, 46,47 evidencing the potential transferability of our DNN to the K-edges of the other transition metal elements and, eventually, the extension of our model to encompass the rest of the periodic table.…”

“…4.5 Â 10 À2 (evaluated against unseen/'out-ofsample' spectra for which the post-edge has been normalised to unity), demonstrating two-fold-improved performance relative to our previous work at the Fe K-edge. 8,46,47 This is due -in partto the larger dataset that we work with here (40 700 local geometry/ spectrum pairs at the Co K-edge vs. 9040 local geometry/spectrum pairs at the Fe K-edge). Fig.…”

“…To address this, contemporary works have explored supervised machine learning/deep learning algorithms with a view towards mapping the relationship between XANES spectra and the electronic and geometric structures of the systems that they characterise. 8,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] For an ab initio MD-based approach like that described in the present Article, our own deep neural network (DNN; introduced in ref. 46) could be used to accelerate the prediction of the X-ray spectra for each of the ab initio MD snapshots (the bottleneck of the strategy), opening up a fast and cost-effective route to the quantitative interpretation of T-jump pump/X-ray probe experiments.…”

Machine learning activation energies of chemical reactions

“…Outside of chemistry, ML has been applied in many circumstances including: natural language processing 36–39 ; driverless vehicles 40–44 speech recognition 45–48 ; handwriting analysis 49–51 ; enhancing image resolution 52–55 ; robotics 56–60 ; and, famously, beating the human champions of the games chess 61 and Go 62 . Within chemistry, an incomplete list of applications include: evaluating potential energy surfaces of ground 63–66 and excited states 67,68 ; forming solutions to the Schrödinger equation 69,70 ; modeling molecular wavefunctions 71,72 ; accelerating TS optimization 73,74 ; finding exchange‐correlation functionals for DFT 75,76 ; predicting reaction rate constants 77,78 ; predicting the outcomes of organic reactions 79–84 ; X‐ray, 85–87 UV–Vis, 88 IR, 89–92 and NMR 93–95 spectroscopies; sequence‐based biomolecular function prediction 96,97 and predictions of protein structures 98–101 . Another very recent and exciting application of ML in chemistry is the prediction of activation energies.…”

Accurate, Affordable, and Generalisable Machine Learning Simulations of Transition Metal X-ray Absorption Spectra using the XANESNET Deep Neural Network

“…a "fingerprint" window sensitive to a particular property or observable) and developing a machine learning model to predict directly the resonances within this window; 48,49,[98][99][100][101][102][103] ii) representing the resonances via a Hamiltonian matrix associated with a closed set of secular equations and developing a machine learning model to predict the Hamiltonian matrix elements; 27,39,41,42,50 and iii) developing a machine learning model to predict directly the spectral lineshapes. [71][72][73][74]104,105 The latter approach, which we adopt in this Article and elsewhere where we have worked with machine learning models for XAS in theoretical 71 and practical 73,74 settings, circumvents the formidable challenge of predicting the huge number of resonances around the Xray absorption edge. 106 Sitting alongside the well-developed theory for XAS (e.g.…”