Hybrid Physics-Machine Learning Models for Quantitative Electron Diffraction Refinements

Aug 5, 2026

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High-accuracy electron microscopy simulations for quantitative crystal structure refinement face a key bottleneck: physical interactions can be modeled theoretically, but experimental effects are difficult to capture analytically. A hybrid framework is presented that couples differentiable physical simulations with neural networks, enabling end-to-end gradient-based joint optimization of physical parameters and learned representations of experimental variables. Demonstrated on 3D-ED refinement, the method learns thickness distributions directly from diffraction data and achieves state-of-the-art results on synthetic and experimental datasets, recovering atomic positions, thermal displacements, and thickness profiles with high fidelity.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages26

Reading Time1 h 6 min

AccessFree to download

Abstract

Introduction

Differentiable physics and automatic differentiation

Motivation in electron microscopy

Hybrid Physics-Machine Learning Models for Quantitative Electron Diffraction Refinements Shreshth A. Malik 1†, Tiarnan A.S. Doherty 1,2*†, Benjamin Colmey2 , Stephen J. Roberts3 , Yarin Gal 1*, Paul A. Midgley2* 1 OATML, Department of Computer Science, University of Oxford, Wolfson Building, Parks Rd, Oxford, OX1 3QG, United Kingdom. 2 Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Rd, Cambridge, CB3 0FS, United Kingdom. 3 Machine Learning Research Group, Department of Engineering Science, University of Oxford, Eagle House, Walton Well Road, Oxford, OX2 6ED, United Kingdom. *Corresponding author(s). E-mail(s): [td404@cam.ac.uk](td404@cam.ac.uk) ; [yarin.gal@cs.ox.ac.uk](yarin.gal@cs.ox.ac.uk) ; [pam33@cam.ac.uk](pam33@cam.ac.uk) ; †These authors contributed equally to this work. Abstract High accuracy electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are challenging to model analytically. To address this gap, we present a novel hybrid physics–machine learning framework that integrates differentiable physical simulations with neural networks. By leveraging automatic differentiation throughout the simulation pipeline, our method enables gradient-based joint optimization of physical parameters and neural network components representing experimental variables, offering superior scalability compared to traditional second-order methods. We demonstrate this framework through application to three-dimensional electron diffraction (3D-ED) structure refinement, where our approach learns complex thickness distributions directly from diffraction data rather than relying on simplified geometric models. This method achieves state-of-the-art refinement performance across synthetic and experimental datasets, recovering atomic positions, thermal displacements, and thickness profiles with high fidelity. The 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 modular architecture proposed can naturally be extended to accommodate additional physical phenomena and extended to other electron microscopy techniques. This establishes differentiable hybrid modeling as a powerful new paradigm for quantitative electron microscopy, where experimental complexities have historically limited analysis. 1 Introduction Recent advances in scientific machine learning have demonstrated remarkable potential to complement traditional physics-based simulations across diverse domains of computational science. Hybrid physics–machine learning (ML) approaches, which combine quantitative physical models with the expressive capacity of neural networks [1–5], offer a principled framework for addressing complex phenomena that remain challenging for purely analytical methods. In these approaches, well-established physical theories that govern the forward model of a simulation are explicitly used to maintain theoretical rigor and interpretability, while neural networks are used as universal function approximators [6] to parameterize complex, system-specific effects that are difficult to model explicitly. Thus these hybrid methods bridge the gap between first-principles theory and experimental reality. In recent years, this approach has shown substantial promise infields ranging from dynamical systems [7–9] and atmospheric physics [10] to quantum physics [11, 12], where the learned components augment traditional simulators to improv

FAQs

What does the approach learn in the 3D-ED structure refinement application?

It learns complex thickness distributions directly from diffraction data, rather than relying on simplified geometric models, while also recovering atomic positions and thermal displacements.

Aug 5, 2026

Upload by Ophelia