# Rapid detection of rare events from _in situ_ X-ray diffraction data using
machine learning

Weijian Zheng  † Jun-Sang Park  † Peter Kenesei  Ahsan Ali  Zhengchun Liu  Ian
T. Foster  Nicholas Schwarz  Rajkumar Kettimuthu  Antonino Miceli  Hemant
Sharma ∗
Argonne National Laboratory, 9700 S Cass Ave, Lemont, IL, USA
∗To whom correspondence should be addressed<EMAIL_ADDRESS>
†Equal contributions

###### Abstract

High-energy X-ray diffraction methods can non-destructively map the 3D
microstructure and associated attributes of metallic polycrystalline
engineering materials in their bulk form. These methods are often combined
with external stimuli such as thermo-mechanical loading to take snapshots over
time of the evolving microstructure and attributes. However, the extreme data
volumes and the high costs of traditional data acquisition and reduction
approaches pose a barrier to quickly extracting actionable insights and
improving the temporal resolution of these snapshots. Here we present a fully
automated technique capable of rapidly detecting the onset of plasticity in
high-energy X-ray microscopy data. Our technique is computationally faster by
at least 50 times than the traditional approaches and works for data sets that
are up to 9 times sparser than a full data set. This new technique leverages
self-supervised image representation learning and clustering to transform
massive data into compact, semantic-rich representations of visually salient
characteristics (e.g., peak shapes). These characteristics can be a rapid
indicator of anomalous events such as changes in diffraction peak shapes. We
anticipate that this technique will provide just-in-time actionable
information to drive smarter experiments that effectively deploy multi-modal
X-ray diffraction methods that span many decades of length scales.

##  1 Introduction

Metals play a significant role in modern society. They are used in a wide
range of applications such as transportation; construction; energy generation,
storage and delivery; and security. The performance requirements for these
polycrystalline engineering materials have pushed the diversity and complexity
of processes and elements employed in those materials to optimize structure
and properties [1, 2]. Frameworks like integrated computational materials
engineering [3] and materials informatics [4] aim to accelerate material
discovery and process optimization so that new materials that meet performance
requirements can be deployed more quickly. Calibration and validation of these
frameworks rely on microstructure and associated attributes acquired across
multiple length scales at different conditions.

High-energy synchrotron X-ray ($>=$50 keV) diffraction methods are capable of
non-destructively characterizing metallic polycrystalline materials in their
bulk form. In particular, high-energy diffraction microscopy (HEDM) can
extract 3D microstructure information and grain-resolved attributes; it can
also track their evolution when combined with _in situ_ thermo-mechanical
loading capabilities [5, 6, 7]. The far-field HEDM (FF-HEDM) variant [8, 9]
can provide the center of mass, crystallographic orientation, and elastic
strain tensor for each constituent grain in a polycrystalline aggregate. These
FF-HEDM measurements are often combined with other measurement modalities such
as near-field HEDM and tomography to obtain a fuller picture of the
microstructure and state and their evolution in a polycrystalline material
[10, 11, 7, 12].

In a typical _in situ_ HEDM experiment, the macroscopic stimulus to be applied
on a sample is decided _a priori_ , based for example on a known response
relationship. For instance, in an _in situ_ HEDM experiment where a sample is
subject to various levels of mechanical loading to study the material response
heterogeneity at the mesoscale, the levels – at which the loading is paused to
deploy a higher resolution and more beamtime-consuming characterization method
– are often decided based on macroscopic milestones such as yield strength in
the macroscopic stress-strain curve of the material. Alternatively, such
experimental decisions to be made on-the-fly may require heroic efforts and
significant human involved processing during time-limited beam access to
reduce the full HEDM data set and identify when the scientifically interesting
phenomena occur [7, 13, 10, 14, 15, 16]. Hence, the high-level of reliable
automation is desirable and crucial for a successful study.

Here we propose a robust, self-supervised, machine learning-based framework
(Figure 1) that enables rapid identification of, and thus automated response
to, the minute changes in diffraction spots measured by FF-HEDM and probable
microstructural changes in polycrystalline metals. This framework is
particularly timely with the improved brilliance and coherence of the next
generation diffraction limited synchrotron X-ray sources and significant
advances in detector technologies capable of rapid and accurate measurement of
single photon events — developments that allow many mesoscale measurement
techniques like HEDM to be combined with nanoscale techniques like Bragg
coherent diffraction imaging (BCDI) and dark-field X-ray microscopy (DFXM) in
a single instrument [15, 17]. Our framework can provide quantitative
actionable information about material state and guide experimenters as to when
to deploy these higher resolution techniques. We refer to this actionable
information as rare event indicator (REI). Using a variety of _in situ_ FF-
HEDM data, we demonstrate that the proposed framework and REI is capable of
rapidly detecting mechanical yielding, an eventual but rare event that
experimenters often seek to capture through _in situ_ FF-HEDM experiments.

Figure 1: An illustration of the workflow for rapid inference of
microstructural deformation. A polycrystalline sample is subject to mechanical
loading while we acquire HEDM data. Bragg diffraction spots from the initial
material state are used to train an image representation model (encoder) and a
clustering model. These two models combined are sensitive to changes in the
diffraction spots. Using these models, the rare event indicators are computed
as we continue to apply mechanical loading to the sample and acquire HEDM
data. A significant increase in REI is quantitative actionable information
that the experimenters can use to steer the course of the experiment.

##  2 Results and discussion

We acquired four sets of _in situ_ FF-HEDM diffraction patterns using an area
detector. §4.3 provides the salient features of these HEDM experiments. The
first set of patterns was acquired with a 304L-stainless steel (304L-SS)
sample with a face-centered cubic crystal symmetry. The second set of patterns
was acquired with a Ti-6V-4Al (Ti64) sample with a hexagonal close-packed
crystal symmetry. These two data sets were acquired in uniaxial tension. The
third data set used a pack of sand with a trigonal crystal symmetry under
compression. The fourth data set was acquired on a Ti-7Al (Ti7Al) alloy sample
with a hexagonal close-packed crystal symmetry under continuous uniaxial
tension.

We anticipated the 304L-SS, Ti64, and Ti7Al samples to accommodate mechanical
yielding or plastic deformation by crystallographic slip [18] resulting in
diffraction spot smearing [19] while the sand sample to exhibit brittle
fracture with minimal diffraction spot smearing. For the sand sample, we
expected the number of diffraction spots to increase with the applied load as
the sand particles fracture into smaller but still coherent pieces, therefore
the shape of resulting diffraction spots was expected to exhibit minimal or no
smearing at all, while their intensity would show a dramatic decrease. With
these expectations, our rare event detection framework, which consists of an
image representation model and a clustering model, was trained using various
permutations of diffraction patterns acquired at zero load – zero strain state
(reference state) from each sample. These framework permutations were deployed
to assess whether yielding could be detected reliably. Furthermore, the
sensitivity of our framework and REI to instrumental changes was assessed
using the 304L-SS FF-HEDM patterns acquired using a variety of beam sizes and
incident X-ray photon flux levels.

###  2.1 _In situ_ FF-HEDM of stainless steel

The dotted yellow curve in Figure 2 shows the typical stimulus (stress) –
response (strain) relationship of a metallic material. At lower stresses, the
relationship between macroscopic stress and strain is nominally linear and
elastic, but at larger stresses, this is no longer the case. The level of
stress where the linear relationship between stress and strain breaks from
linearity is often referred to as the macroscopic yield point or yield stress
of the material (approximately 225 MPa in this case). Here, the stress–strain
curve was acquired during our _in situ_ FF-HEDM experiment under uniaxial
tension. The geometry of the 304L-SS sample was identical to that described in
[20] with $11\text{\,}\mathrm{mm}$ (length) $\times$ $1\text{\,}\mathrm{mm}$
(width) $\times$ $1\text{\,}\mathrm{mm}$ (thickness) in the gauge section.
Gold markers were attached along the gauge section [21] so that identical
material volume could be measured throughout the experiment.

In this _in situ_ FF-HEDM experiment, there were four target stress levels in
the elastic regime, five in the elastic-plastic transition regime (the so-
called “knee” of the stress-strain curve), and four in the plastic regime well
beyond the knee. Each target stress level was reached through a constant
displacement rate of
$1.1\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}\mathrm{/}\mathrm{s}$ to
achieve a nominal strain rate of $0.0001\text{\,}\mathrm{s}^{-1}$; once the
target stress level was reached, the applied stress was intentionally relieved
by approximately 10% before carrying out the FF-HEDM pattern acquisition to
prevent further changes to the material by stress relaxation during the
scans111The sample was under displacement control during FF-HEDM pattern
acquisition; applied stress level fluctuation was minimal during a FF-HEDM
scan even in the plastic regime..

An x-ray beam size of $2\text{\,}\mathrm{mm}$ $\times$
$0.4\text{\,}\mathrm{mm}$ was used for FF-HEDM pattern acquisition. The width
of the x-ray beam ensured that a $0.4\text{\,}\mathrm{mm}$-tall material
volume in the sample gauge section was always illuminated by x-rays during an
FF-HEDM pattern acquisition. At each target load level, four sets of FF-HEDM
pattern acquisition were executed illuminating a total of
$1.6\text{\,}\mathrm{mm}$ tall contiguous volume (4 layers) in the sample
gauge section. The gold markers in the gauge section ensured that the
identical material volume was interrogated across multiple target load levels
reached during _in situ_ loading.

At each target load level, FF-HEDM patterns were used to compute the
REI222Here, the FF-HEDM patterns acquired at the zero load - zero strain point
were used as the baseline data set to train the image representation model.
For more details on the image representation model, the readers are referred
to §4.1., average diffraction spot full-width at half maximum (FWHM) in the
azimuthal direction, and average axial lattice strain333The FWHM and axial
lattice strain are the more commonly used metrics to detect the rare event,
namely yielding in this case.; Figure 2 shows the evolution of these metrics
with applied stress denoted by the green dots, the orange dots, and the blue
dots, respectively. Here, the image representation model and the clustering
model to compute the REI were trained using the 304L-SS sample’s reference
state diffraction pattern. The FWHM and axial lattice strain were computed
using MIDAS [22, 23]. All three metrics, namely REI, average diffraction spot
FWHM in the azimuthal direction, and average lattice strain require the
extraction of diffraction peaks from 2D diffraction patterns, with the
subsequent steps being inference (for REI, requiring $\sim$2s computation
time), peak-shape fitting (for FWHM, requiring $\sim$100s computation time)
and full microstructure reconstruction (for lattice strain, requiring
$\sim$500s computation time).

We demonstrate in this paper that REI can provide actionable information
comparable to the traditional metrics for polycrystalline metallic alloys
subjected to mechanical loading. Figure 2 (b) is a magnified view of Figure 2
(a) near the elastic and elastic-plastic transition regime. In this regime,
researchers often need to make the difficult decision to pause the loading and
conduct higher resolution measurements and allocate precious beam time based
on limited _a priori_ knowledge about the material (such as stress-strain
curve obtained _ex situ_) or relying on FWHM or lattice strain metrics that
require FF-HEDM patterns acquired over a larger angular range, substantial
computing resources, and time. In general, the three metrics follow the trends
observed in the macroscopic stress-strain curve, with significant inflections
occurring near the knee of the stress-strain curve. REI and FWHM remain fairly
constant in the elastic regime. As the material approaches its macroscopic
yield point, REI and FWHM both start to increase, most notably in the region
highlighted by the purple ellipse, roughly coinciding with the macroscopic
yield point. They continue to increase substantially as the sample transitions
into the plastic regime. On the other hand, the average axial lattice strain
increases linearly in the elastic regime. It breaks from linearity near the
macroscopic yield point and then remains relatively constant in the plastic
regime444This is expected as lattice strain is measuring only the elastic
strain (change in the lattice spacing).. This figure illustrates that the REI
is a metric that is sensitive to material yielding accommodated by
crystallographic slip and delivers information comparable to the traditional
metrics while being at least 50 times faster to compute.

Figure 2: Applied stress, REI, average FWHM, and average axial lattice strain
vs. strain for (a) the entire _in situ_ FF-HEDM experiment (b) magnified view
near the elastic-plastic regime. The error bars for REI, FWHM, and lattice
strain at a target stress level indicate the range of respective metrics
observed in the four $0.4\text{\,}\mathrm{mm}$-tall material volumes. The
dotted yellow curve shows the stress-strain curve of the 304L-SS sample
measured during _in situ_ FF-HEDM experiment.

###  2.2 _In situ_ FF-HEDM of titanium alloy

Figure 3 shows the stress-strain curve and rare event indicator results for a
Ti-6V-4Al (Ti64) alloy, magnified in the elastic and elastic-plastic
transition regime. The dotted yellow curve shows the stress-strain curve of
the Ti64 material in uniaxial tension acquired during _in situ_ FF-HEDM
experiment; it shows similar characteristics as the stress-strain curve for
the 304L-SS sample (Figure 2) with the elastic-plastic transition occurring
approximately at 200 MPa. Here, the _in situ_ FF-HEDM experiment was conducted
using the Rotation and linear Axial Motion System (RAMS) load frame [6]. The
sample geometry was identical to the one presented in [24] with a
$1\text{\,}\mathrm{mm}$ $\times$ $1\text{\,}\mathrm{mm}$ cross section in the
gauge section. Gold markers were attached in the gauge section [21] to keep
the illuminated material volume consistent throughout the _in situ_
experiment. The experimental procedure was similar to that used for the
304L-SS sample; the nominal strain rate was $0.0001\text{\,}\sec^{-1}$ and
loading was temporarily paused to collect FF-HEDM patterns along multiple
layers in the sample gauge section.

Figure 3: The _in situ_ stress-strain curve of the Ti64 alloy sample (yellow
dots) and associated REI results (blue dots) in the elastic and elastic-
plastic transition regimes. REI remains roughly constant in the elastic
regime. As the material approaches its macroscopic yield point, REI also
starts to increase significantly highlighted by the purple ellipse, and
continues to increase as the plastic regime sets in. The abrupt change in REI
near 0.1% strain is due to a beam size change between two target load levels;
this is discussed further in §2.4.

The blue dots in Figure 3 show the evolution of REI when the image
representation model and clustering model were trained by using the 304L-SS
FF-HEDM patterns acquired at zero load-zero strain (reference state). The
overall evolution of REI is consistent with that observed in the 304L-SS
sample; REI remains relatively constant in the elastic regime and then starts
to increase near the knee of the stress-strain curve demonstrating that the
image representation model and the clustering model (and therefore REI) is
sensitive to materials accommodating plastic deformation through
crystallographic slip. Furthermore, Figure 3 illustrates that those models are
transferable between materials that share a similar deformation mode. The
abrupt decrease in REI at approximately 0.1% strain (or 150 MPa applied
stress) is due to a change made at this point in the beam size used for FF-
HEDM experiments in order to alter the vertical spacing between layers. The
robustness and sensitivity of REI are examined further in §2.4.

We computed several cases of REI in order to examine the performance of the
rare event detection framework and the choice of baseline and reference data
(Figure 4). Table 1 summarizes the permutations of training reference state
patterns to compute the REI cases. In all four cases, we used the optimized
hyperparameter values determined from the 304L-SS experiment. Naturally, the
absolute value associated with each REI case is different between the four
cases as the training data sets are different, however, the four cases all
share a similar trend in that they remain relatively constant in the elastic
regime, start to increase near the elastic-plastic regime, and continues to
increase in the plastic regime. The inflection point where the REI values
start to increase is consistently near the macroscopic yield point. This
highlights that the image representation and clustering models trained on a
data set that shares a similar deformation mode but collected on a different
sample or material are transferable. While it is recommended that the patterns
acquired before the beginning of _in situ_ loading be used as the training
set, such transferability can be useful when using REI to estimate the
material state, for instance in a high-throughput measurement setup.

Figure 4: The _in situ_ stress-strain curve and REI evolution for the Ti64 sample in the elastic and elastic-plastic transition regime. Four cases of REI using permutations of training reference state patterns (Table 1) are presented. REI Case |  Training reference state patterns for encoder |  Training reference state patterns for clustering model
---|---|---
1 |  Ti64 sample |  Ti64 sample
2 |  Ti64 sample |  304L-SS sample
3 |  304L-SS sample |  304L-SS sample
4 |  304L-SS sample |  Ti64 sample
Table 1: The reference state patterns employed to train the encoder and
clustering models for the REI cases presented in Figure 4.

###  2.3 _In situ_ FF-HEDM of sand

In §2.2, we established that the image representation and clustering models
trained using the 304L-SS FF-HEDM patterns acquired at reference state can be
used to detect rare events and anomalies in other material systems that share
a similar deformation modality. Here, we introduce a set of _in situ_
diffraction patterns acquired from a material system that does not accommodate
deformation by crystallographic slip.

Figure 5 shows the stress-strain curve and associated REI for an aggregate of
sand subject to compression. The dotted yellow curve shows the stress-strain
curve of sand aggregate in unaxial compression. The _in situ_ mechanical
loading procedure was similar to the one described in [25]. The sample
fractured catastrophically when compressed beyond 75 MPa. The sample also does
not exhibit the elastic, elasti-plastic transition, and plastic regimes that
were observed in the 304L-SS (Figure 2) and Ti64 (Figure 3) samples. Instead,
the stress-strain curve shows a constant increase and an abrupt decrease in
applied stress indicative of catastrophic failure. We consider two REI cases
similar to Figure 4. For REI Case 1 (green dots), the image representation
model and the clustering model are both trained using the 304L-SS reference
state patterns. For REI Case 2 (orange dots), these models are trained using
the sand reference state patterns. In both cases, the hyperparameters were
optimized based on the 304L-SS patterns. While the absolute magnitudes are
different, the two REI cases show minimal changes with respect to loading.
This implies that the underlying architecture in our rare event detection
framework is tuned to detect anomalies in diffraction spots induced by
crystallographic slip but it is insensitive to deformation carried by
fracturing of grains.

Figure 5: Stress-strain curve and REI evolution for the sand sample. Stress
and strain are compressive mimicking the compaction that sand is typically
subjected to. The stress-strain curve does not exhibit the characteristics
illustrated in Figure 2 and Figure 4. The orange dots show the REI case where
the sand reference state patterns were used as the training data set. The
green dots show the REI case where the 304L-SS reference state patterns were
used as the training data set. Both REI cases show minimal changes as the sand
sample is subject to compressive loads up to catastrophic failure of the
material system.

###  2.4 Robustness to experiment configurations

We have demonstrated that REI is sensitive to changes in plasticity in the
materials, but there are additional experiment configurations that can lead to
changes in REI too. Here we investigate the sensitivity of REI to different
configurations during the 304L-SS experiment in $\S$2.1. Figure 2 includes
data collected with the following configuration: 0.4 mm x-ray beam height,
rotation angle start at -180∘, rotation angle step 0.25∘, this was the
reference state for computing the absolute change in REI ($\Delta$REI). Table
2 shows $\Delta$REI as a result of different changes in experiment
configurations. For each $\Delta$REI calculation, the material deformation
state was constant, only the corresponding experiment configuration was
changed.

Changes in the starting rotation angle and rotation angle step change the
position and slicing of diffraction spots (3-dimensional) on individual frames
(2-dimensional). Since our model works with diffraction signals on individual
frames instead of 3-D shapes555Using 2-D spots instead of 3-D allows for
improvements in computation speed and working with streaming data., these
changes are expected to change REI as well. Table 2 shows that changing the
starting rotation angle 666Offsets of $\pm$0.125∘, $\pm$0.25∘, $\pm$0.314∘ and
$\pm$0.628∘ in starting rotation angle were used. has the smallest influence
on REI. We will use this $\Delta$REI as a baseline (denoted $\Delta$REIb) to
compare against other experimental parameters. Changing the rotation angle
step (0.1∘ vs 0.25∘) has more than 3 times larger $\Delta$REI as compared to
$\Delta$REIb.

Changing the position of data acquisition in the sample (4 different
positions) results in 2 times larger $\Delta$REI than $\Delta$REIb. This is
attributable to local changes in the microstructure at any given sample state.
On the other hand, changes in other experiment configurations (with different
positions in the sample) lead to more than 4 times higher $\Delta$REI compared
to $\Delta$REIb: 4 times for changing x-ray beam size (0.1, 0.2, and 0.4 mm),
5 - 10 times for using sub-optimal incident x-ray flux for low and high
plastic deformation777Here, optimal incident x-ray flux is the setting in
which the full dynamic range of the area detector is utilized without
acquiring saturated pixels during a FF-HEDM scan; sub-optimal incident x-ray
flux means the dynamic range of the detector is underutilized.888High local
microstructure changes from deformation also contribute to high $\Delta$REI.
and $\sim$6 times higher for changing both x-ray beam size and flux.

Furthermore, for the titanium data set (Figure 3) the change in REI near 0.1%
strain by $\sim$1.3$\times$10-2 is because of a change in x-ray beam size from
0.4 mm to 0.2 mm.

$\Delta$REI for detecting the onset of plastic deformation in Figure 2 is
1.38$\times$10-2, the difference between REI of two sample states in the
purple ellipse. From Table 2, we can see that only changes in the starting
rotation angle and position in the sample yield a $\Delta$REI smaller than
this value. This indicates that an experiment utilizing REI as an indicator
can vary these two experiment configurations, namely, starting rotation angle
and position in the sample, but must keep the other experiment configurations
constant during the experiment: rotation angle step, x-ray beam size, and
x-ray beam flux.

|  $\Delta$REI | Average REI
---|---|---
Experiment change | $[\times 10^{-2}]$ | $[-]$
Different starting rotation angle | 0.52 | 0.27
Different rotation angle step | 1.7 | 0.28
Different position | 1.1 | 0.31
Different position and x-ray beam size | 2.1 | 0.28
Different position and x-ray beam flux | 2.7 | 0.29
Different position and x-ray beam flux, large plastic deformation | 5.2 | 0.52
Different position, x-ray beam size, and beam flux | 2.9 | 0.27
Table 2: Sensitivity to experiment parameters

###  2.5 REI using partial data set

The ability to monitor the material state changes and provide actionable
information in real-time predicates having a sufficient number of frames to
extract reliable REI quickly. To estimate the minimum number of detector
frames necessary to provide a reliable rare event indicator, we used the FF-
HEDM patterns from the 304L-SS sample acquired over $\omega$-range of
$360\text{\,}\mathrm{\SIUnitSymbolDegree}$. For the FF-HEDM patterns acquired
at a given target load level,

  1. 1.

A starting $\omega$ angle (or a frame in the stack of FF-HEDM patterns
acquired over $\omega$-range of $360\text{\,}\mathrm{\SIUnitSymbolDegree}$)
was chosen randomly,

  2. 2.

A contiguous segment of frames corresponding to a particular $\Delta\omega$
range starting from the chosen $\omega$ angle is extracted from the FF-HEDM
patterns,

  3. 3.

REI for the contiguous segment is computed, and

  4. 4.

This procedure is repeated 20 times with random starting $\omega$ angles to
estimate the range of REI values arising from using a partial FF-HEDM pattern
set.

Figure 6 presents a magnified view of the elastic and elastic-plastic
transition regime for $\Delta\omega$ of
$5\text{\,}\mathrm{\SIUnitSymbolDegree}$ (orange dots),
$10\text{\,}\mathrm{\SIUnitSymbolDegree}$ (blue dots),
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$ (purple dots),
$40\text{\,}\mathrm{\SIUnitSymbolDegree}$ (black dots), and full
$360\text{\,}\mathrm{\SIUnitSymbolDegree}$ FF-HEDM patterns (green dots). The
REI error bars show the range of REI values computed from 20 repeats. For
clarity, the REI values are intentionally shifted by -0.1, 0, 0.1, 0.2, and
0.3 for $\Delta\omega$ of $360\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$5\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$10\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$, and,
$40\text{\,}\mathrm{\SIUnitSymbolDegree}$, respectively. Table 3 shows the REI
calculation time for each $\Delta\omega$ case.

$\Delta\omega$ [deg] | Time for patch extraction [s] | Time for REI calculation [s]
---|---|---
5 | 1 | 0.31
10 | 2 | 0.33
20 | 4 | 0.35
40 | 8 | 0.41
360 (full) | 72 | 1.2
Table 3: REI calculation time for each $\Delta\omega$ case. Patch extraction
time is computed assuming $0.25\text{\,}\mathrm{\SIUnitSymbolDegree}$ $\omega$
steps when acquiring FF-HEDM patterns and 20 frames per second processing time
on the computing infrastructure used for this work.

In all four $\Delta\omega$ cases where a partial data set is used, the overall
trends in the rare event indicator are consistent with those observed when the
full data set is used to compute REI. Smaller $\Delta\omega$ results in larger
REI error bars, most likely due to limited sampling and scatter in the FF-HEDM
patterns. Nevertheless, the REI computed from $\Delta\omega$ of 40∘ is very
close to the benchmark REI. This implies that it is not necessary to acquire
and analyze a full FF-HEDM data set acquired over $\omega$-range of
$360\text{\,}\mathrm{\SIUnitSymbolDegree}$ to compute a reliable REI.
Furthermore, when combined with the REI calculation time (Table 3), this
observation shows that experimenters can consider a new mode of FF-HEDM data
acquisition where the sample is continuously rotated and loading is not
paused999The sample geometry and loading rate need to be moderated to a level
that matches the diffraction pattern acquisition and rare event indicator
determination rates. and diffraction patterns are streamed without
pausing101010Such experimental modality will also require a stage stack that
allows continuous $\omega$ rotation such as the RAMS load frame or one that
employs a slip ring system.. Given the quick turnaround time for REI
calculation, continuous quasi-static loading or even cyclic loading can be
possible. As diffraction patterns are streamed, REI can also be streamed
concurrently to provide a scalar actionable quantity to the experimenters to
steer the course of the _in situ_ experiment. This is a loading modality that
cannot be realized easily with the conventional metric such as FWHM or lattice
strain (Figure 2) that requires a full reconstruction or, at the minimum,
diffraction peak fitting.

Figure 6: The _in situ_ stress-strain curve and REI evolution. The _in situ_
stress-strain curve and REI evolution were computed using partial data sets
for the 304L-SS sample in the elastic and elastic-plastic transition regime.
For clarity, the REI values are intentionally shifted by -0.1, 0, 0.1, 0.2,
and 0.3 for $\Delta\omega$ of $360\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$5\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$10\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$, and
$40\text{\,}\mathrm{\SIUnitSymbolDegree}$, respectively.

###  2.6 REI with continuous loading

As alluded in §2.5, the ability to compute reliable REI from a partial FF-HEDM
data set allows a new loading modality where loading is not paused during an
_in situ_ FF-HEDM. We deploy our rare event detection framework on a
previously published FF-HEDM data set that employed this loading modality [26]
to quantify the crystallographic slip strength and study microcrack initiation
and propagation in a Ti-7Al alloy. The experimental setup and sample geometry
are similar to those used for the Ti64 data presented in §2.2. Another key
difference to note in this FF-HEDM data set is that the $\omega$ scan was
broken up into six $60\text{\,}\mathrm{\SIUnitSymbolDegree}$-segments so as to
test both the continuous loading modality and partial data REI.

Figure 7 shows the macroscopic stress-strain curve, REI values computed over
the course of the _in situ_ FF-HEDM, and incident x-ray flux. As anticipated,
the rare event detection framework is capable of capturing the elastic-plastic
transition from a partial FF-HEDM data set as indicated by the large increase
in REI when the material transitions into the plastic regime. Furthermore, our
rare event detection framework is capable of detecting changes in the incident
x-ray flux. For instance, the REI values increase significantly with a large
increase in the incident flux measured by an ion chamber installed in the
x-ray beam path immediately before the sample (purple ellipse in Figure 7). We
also observed a decay in REI consistent with the decay in the incident beam
flux associated with the 324 singlets (Non Top-Up) APS storage ring operation
modality when this data set was acquired. This trend is highlighted by the
blue and green dotted arrow lines for REI and incident flux, respectively.

Figure 7: Ti7 alloy is continuously deformed in uniaxial tension while
acquiring FF-HEDM patterns. REI shows significant changes in three different
ways. It increases significantly when the material undergoes elastic-plastic
transition. It also changes when the incident flux changes significantly, an
example of such an instance is highlighted by the purple ellipses.
Furthermore, REI is also sensitive to a gradual decay in the incident X-ray
flux, an example of such an instance is highlighted by the dotted green
(incident flux) and blue lines (REI).

This application example shows not only that our rare event detection
framework can track changes to the diffraction peaks induced by
crystallographic slip but also it is capable of detecting small changes to the
incident beam flux. This is particularly useful for newer FF-HEDM modes that
require much longer scan time (on the order of several hours) such as
stitching HEDM [27]111111Here, multiple field-of-view scans across a sample
cross-section are stitched to interrogate a sample cross-section larger than
the beam size available at the endstation or point focus HEDM [14]121212Here,
multiple scans across a sample cross section are conducted with a 2D focused
beam to acquire intra-granular microstructure and micromechanical state
information.. REI can be an independent metric that can indicate changes to
the FF-HEDM patterns due to incident beam characteristic changes or material
state changes (such as creep or relaxation) during these scanning techniques.

##  3 Outlook

We have demonstrated that our rare event detection framework is capable of
detecting changes to the FF-HEDM diffraction peaks due to material state
change and instrument changes such as incident flux and beam size. This
framework is based on the unsupervised image representation learning and
clustering algorithms. The resulting rare event indicator can be a metric that
experimenters can use to make informed decisions about the course of their _in
situ_ FF-HEDM experiment instead of solely relying on a conventional stress-
strain curve. Continuous loading combined with _in situ_ FF-HEDM can be more
accessible as experimenters do not have to rely on full reconstructions to
decide on when to stop the loading and deploy higher resolution techniques.

The rare event detection framework presented in this work can inform the
experimenter _when_ a possible rare event is occurring. If the rare event
detection framework can detect _where_ in the microstructure anomaly is
occurring, it will be an additional piece of information that experimenters
can use to steer their experiment. There are several avenues to identifying
the location. For instance, it can be accomplished by creating a subset of
patches from a particular set of _grains of interest_ and only monitoring the
REI from those grains.

It is also noteworthy that there are several petabytes of FF-HEDM data from
more than a decade of user operation at the APS 1-ID beamline covering a wide
range of alloy systems and multi-axial loading paths. Our intention is to use
these data sets to further evaluate our rare event detection framework and
report on the findings in the near future.

##  4 Methods

We describe our rare event detection workflow, hyperparameter tuning methods,
and high-energy diffraction microscopy experiments.

###  4.1 Rare event detection workflow

For several years, the field of event detection, also known as outlier
detection or anomaly detection, has been a vibrant and dynamic area of study
across diverse academic communities. Recently, the application of deep
learning has opened new avenues for event detection, emerging as a critical
and promising direction in this field [28]. A typical deep learning-based
event detection involves a three-phase process. First, in the data
preprocessing phase, the data is cleaned, normalized, and prepared for
modeling. Second, during model training, a deep learning model, such as an
autoencoder, is trained on a “normal” or “baseline” dataset to learn typical
data patterns and accomplish the feature extraction task. Finally, in the
event detection phase, this trained model is used to evaluate new data,
identifying “events” by measuring deviations from the learned patterns.

In this study, as shown in Figure 8, we employ the BraggNN model [29] as our
neural network model for feature extraction, specifically fine-tuned for image
representation. To facilitate the unsupervised training of our novel image
representation model, we adopt the BYOL (Bootstrap Your Own Latent) approach
[30]. Additionally, we utilize the K-means clustering algorithm to compute the
actionable information as a rare event indicator (REI). By separating the
feature extraction tool and the event detector into two independent modules,
our workflow can easily expand its support for event detection in various
applications. Furthermore, our current design demonstrates promising results,
showcasing the effectiveness of our event detection workflow on X-ray
diffraction data.

Figure 8: Rare event detection workflow with three phases. The first phase
(orange rectangle), trains an image representation model (Trained encoder)
using a baseline dataset for feature extraction. The trained encoder from the
first phase is applied to a reference dataset followed by K-means clustering
algorithm to obtain K centers to characterize the reference dataset in the
second phase (blue rectangle). The output of the trained encoder from the
first phase, and the clustering model from the second phase, applied on the
testing dataset, is thresholded to determine REI for the testing dataset in
the third phase (green rectangle). The different hyperparameters at each step
are shown in red text.

We provide in the following a comprehensive overview of the different building
blocks comprising our proposed workflow. §4.1.1 elucidates the preprocessing
steps involved in handling the HEDM diffraction images. §4.1.2 describes the
specifics of training the image representation model. We illustrate the
modules associated with processing the reference dataset and evaluating
subsequent experimental datasets in §4.1.3 and §4.1.4, respectively.

####  4.1.1 Data pre-processing

In the context of our workflow, a fundamental objective of data preprocessing
is to transform each dark-subtracted diffraction image extracted from a binary
file into a set of peak patches that represent individual peaks. To accomplish
this, we utilize the component analysis library provided by OpenCV [31]. A
dataset in our workflow is defined as the collection of peak patches (ranging
in number of thousands to millions) extracted from diffraction images
collected during a contiguous rotation segment (up to 360∘). Depending on the
material state during acquisition, datasets are labeled baseline, reference,
and testing datasets. The baseline and reference datasets are typically any
datasets collected before the start of the application of a macroscopic
stimulus to the material. The testing dataset is fed to the workflow as the
material undergoes microstructural change.

####  4.1.2 Image representation model training

During the training phase of the image representation model, we utilize the
Bootstrap Your Own Latent (BYOL) method [30] on the preprocessed baseline
dataset. BYOL has emerged as a prominent self-supervised learning technique in
deep learning, addressing the challenge of training neural networks without
explicit labels or annotations. In Figure 8, depicted by the orange rectangle,
BYOL leverages two sets of neural networks: online and target networks. Each
network comprises an encoder and a projector. For the encoder, we refine the
BraggNN model by removing its fully connected layers. The projector, a two-
layer fully connected neural network, maps the encoder’s output to a lower-
dimensional space, enhancing the model’s generalizability.

The encoder’s role is to extract the features of each data patch, while the
projector aims to reduce the dimensionality of the encoder’s output,
facilitating improved model performance. During training, the online network
learns to represent each peak patch in a latent space, while the target
network maintains a moving average of the online network’s parameters. The
trained encoder is saved for use in subsequent phases. The core idea of BYOL
is to encourage the online network to generate latent representations similar
to those produced by the target network. By comparing these representations,
BYOL effectively learns powerful representations for the given task. This
approach has demonstrated remarkable success across various domains, enabling
models to achieve state-of-the-art performance without the need for costly
annotated data.

Even though our workflow only uses the trained encoder of the online network
from BYOL, due to the structure and training of BYOL, the dimensions of the
encoder, projector, and predictor networks, the number of epochs for training
are important hyperparameters, which can impact REI when applied to the
training dataset later on. §4.2 describes the hyperparameters in more detail.

Figure 9: For a randomly picked peak (left-most), the median cosine distance
between the peak and 10 transformed views (a) is 0.0058, while the median
cosine distance with 10 randomly picked peaks (b) is 0.051, nearly 10x
further.

In each epoch of training, as illustrated in Figure 8 with the orange
rectangle, we randomly select a peak patch from the preprocessed baseline
dataset. We then apply random transformations to the chosen patch. This
improves the robustness of the model by reducing its sensitivity to such
transformations, an example is shown in Figure 9. The median cosine
distance131313Median cosine distance is used as a metric to indicate
similarity between two patches. between a randomly selected peak and its
transformed views (Figure 9a) is 0.0058, nearly 10x better than the distance
(0.051) between the same peak and randomly selected different peaks (Figure
9b). The intuition underlying BYOL is to minimize the distance between the
output of the target network and the online network, ideally converging to
zero.

####  4.1.3 Reference dataset processing

In the reference dataset processing phase, our first step involves feeding all
patches from the reference dataset into the trained representation model
(encoder) and converting them into a collection of representation vectors.
These vectors capture the essential features and characteristics of each
patch.

Subsequently, we utilize the K-means clustering algorithm to group these
representation vectors into K centers. This clustering process allows us to
identify common patterns and clusters within the reference dataset. The
resulting K centers (another hyperparameter) serve as representative points
that summarize the distribution and variations present in the reference
dataset.

The output of the reference dataset processing phase, comprising the K centers
obtained through K-means clustering, is saved for the subsequent testing
dataset evaluation phase. These centers provide a reference point for
comparison and evaluation when analyzing the similarity and discrepancy
between the testing datasets and the reference dataset.

####  4.1.4 Testing dataset evaluation

During the testing dataset evaluation phase, we utilize the trained
representation model (encoder) to generate a collection of representation
vectors for the testing dataset. Each vector captures the essential
characteristics of a particular data instance (peak patch) within the testing
dataset.

Next, we compute the Euclidean distances between each representation vector
and the K centers obtained from the previous phase. This distance calculation
allows us to determine the closest center for each vector, enabling us to
assign it to a specific cluster. Additionally, we update the vector’s closest
center to obtain an assignment to K centers and its corresponding confidence
level.

To quantify the uncertainty in the assignments, we introduce the REI score.
This score is determined by calculating the percentage of representation
vectors whose confidence level is below a predefined threshold value, denoted
as $t$ (another hyperparameter). A lower confidence level indicates higher
uncertainty in the assignment to a specific center. Accordingly, the REI score
values will fall in between 0 and 1.

By repeating this procedure for all testing datasets, we obtain rare event
indicators for each dataset. These scores provide an indication of the level
of uncertainty associated with the assignment of data instances to the K
centers. Collectively, these rare event indicator values form a figure that
summarizes the uncertainty across all datasets, allowing for a comprehensive
assessment of the performance and reliability of the event detection workflow.

###  4.2 Hyperparameter tuning

Hyperparameters play a pivotal role in the machine learning workflow,
determining the configuration and behavior of a model. In our REI workflow,
the hyperparameters during model training are as follows (numbers in
parentheses are optimized values used here): dataset used for training the
encoder, dataset used for training the clustering model, encoder dimension
(32), projector dimension (64), predictor dimension (64), number of epochs for
training the encoder, confidence threshold, t, and number of clusters, K.

As shown in §2.4, REI is more sensitive to changes in beam size, beam flux,
and rotation steps than to changes in position and starting rotation angles.
Thus, the datasets used for training the encoder (baseline datasets) and for
training the clustering model (reference datasets) only included datasets with
fixed beam size, beam flux, and rotation steps.

To determine the optimal number of training epochs for our model, we employ a
confidence summation approach. The idea behind this method is straightforward:
a well-trained image representation model should be able to identify pairs of
transformed patches within a set of random patches.

Our confidence summation process unfolds as follows: At the conclusion of each
training epoch, we randomly select 100 patches from our dataset, convert them
into 100 representation vectors using our model, and calculate a confidence
score for each one. This score is derived from the distances between a
specific patch representation and 10 other patches. To compute the confidence
score, we use the formula:

$\text{Confidence}=\frac{|D_{1}-D_{2}|}{D_{2}},\\\ $ (1)

where $D_{1}$ and $D_{2}$ are the shortest and second shortest Euclidean
distances, respectively, among all pairs of representation vectors. If the
distance between two transformed patches is not the closest one among these 10
patches, we assign a confidence score of -1. This process enables us to
evaluate how well patches differ from their nearest neighbors in terms of
distance. Finally, we sum up all 100 confidence scores for all representations
of patches.

In our experiments using the stainless steel dataset described in Section 2.1,
we observe that the confidence score stabilizes after approximately 100
epochs, as depicted in Figure 10. Therefore, we opt to set the number of
training epochs to 100 for our image representation model.

Figure 10: Accuracy plot of the image representation model.

To determine the optimum number of clusters, $K$, and threshold, $t$, we will
describe hyperparameter tuning as it was applied to the stainless steel
dataset described in $\S$2.1. The performance of the model is evaluated by
computing the change in REI when the material first undergoes plastic
deformation (two data points in the purple ellipse in Figure 2). REI
sensitivity, _REI_ sensitivity (shown in Figure 11) is maximized during
hyperparameter tuning, defined as follows:

$REI_{\textrm{sensitivity}}=\dfrac{REI^{\textrm{min}}_{\textrm{plastic}}-REI^{\textrm{max}}_{\textrm{elastic}}}{\Delta
REI_{\textrm{plastic}}},$ (2)

where $REI^{\textrm{min}}_{\textrm{plastic}}$ is the smallest REI value for
the data point after the onset of plastic deformation and
$REI^{\textrm{max}}_{\textrm{elastic}}$ is the largest REI value for the data
point before the onset of plastic deformation in the elastic regime and
$\Delta REI_{\textrm{plastic}}$ is the spread in REI (due to local
microstructure variations) among different volumes scanned for the data point
after the onset of plastic deformation.

Figure 11 shows a contour plot of _REI_ sensitivity as a function of number of
clusters and confidence threshold. Only positive values of _REI_ sensitivity
are shown.141414Negative _REI_ sensitivity means the model fails to detect the
onset of plastic deformation at that data point. It can be seen that a higher
number of clusters and higher confidence threshold results in higher _REI_
sensitivity. As depicted in Figure 11, the selection of K as 40 and the
threshold as 0.5 lead to the highest sensitivity of _REI_ sensitivity,
reaching 5.6.

Figure 11: Contour plot of REI sensitivity as a function of number of clusters
$K$ and threshold $t$.

###  4.3 High-energy diffraction microscopy experiments

The FF-HEDM data sets presented here were acquired at the 1-ID beamline of the
Advanced Photon Source (APS) at Argonne National Laboratory. The FF-HEDM
instrument geometry (Figure 12) is detailed in [9]. Its main features are:

  * •

Monochromatic, high-energy, synchrotron X-rays were used as the probe to
interrogate the material.

  * •

Transmission geometry with an area detector [32] was used to capture the
intensity of the diffraction spots in reciprocal space. Table 4 lists the
x-ray energies and sample-to-detector distances used.

  * •

The incident X-ray beam had a rectangular shape. The beam size along $x_{L}$
was sufficiently large to illuminate the cross-section of the sample in its
gauge section and the beam size along $y_{L}$ was varied depending on the
experiment’s main objectives and required resolution in between layers; it was
varied only when investigating the effect of beam size on the rare event
indicator.

  * •

Figure 12 shows an example sample geometry used for the uniaxial tension
testing. When possible, a set of $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$
cube gold markers [21] were attached on the sample gauge section surface so
that identical volume of material was interrogated throughout the _in situ_
HEDM experiment.

  * •

The sample was rotated about $y_{L}$ at a constant angular speed over an
$\omega$ range of $360\text{\,}\mathrm{\SIUnitSymbolDegree}$ while a set of
diffraction patterns were acquired. Typically, this set consisted of 1440
frames, each covering an angle of $0.25\text{\,}\mathrm{\SIUnitSymbolDegree}$.
It took approximately $6\text{\,}\min$ to acquire a set.

  * •

In a typical _in situ_ FF-HEDM experiment at the APS, Microstructural Imaging
using Diffraction Analysis Software (MIDAS) [22, 23, 33] is used to analyze
the set of diffraction patterns and extract a 3D map. At moderate deformation
levels, it takes approximately $8\text{\,}\min$ to acquire the 3D map from a
data set on a high performance computing cluster.

Figure 12: A schematic of the FF-HEDM instrument geometry. The stage stack consists of translation and rotation capabilities to align the $\omega$-rotation axis and the sample to the x-ray beam. The picture shows the setup and sample geometry used to acquire the _in situ_ FF-HEDM data for the 304L-SS sample. | X-ray energy (keV) | Sample to detector distance (mm)
---|---|---
304L-SS (§2.1) | 71.68 | 803
Ti-6-4 (§2.2) | 71.68 | 1163
sand (§2.3) | 71.68 | 1601
Ti-7 (§2.6) | 61.33 | 756
Table 4: FF-HEDM instrument parameters.

##  5 Acknowledgements

This research used resources of the Advanced Photon Source, a U.S. Department
of Energy (DOE) Office of Science user facility at Argonne National Laboratory
and is based on research supported by the DOE Office of Science-Basic Energy
Sciences, under Contract No. DE-AC02-06CH11357. This work was also supported
by the DOE Office of Science, Office of Basic Energy Sciences Data, Artificial
Intelligence and Machine Learning at DOE Scientific User Facilities program
under Award Number 08735 (“Actionable Information from Sensor to Data
Center”). We express our thanks to Professor Aaron Stebner of Georgia
Institute of Technology for sharing the 304L-SS material, Dr. Paul Shade and
his team at the U.S. Air Force Research Laboratory for fabricating the gold
markers for the 304L-SS sample, Professor Matthew Kasemer and his team at the
University of Alabama for sharing the Ti64 data, and Professor Ryan Hurley and
his team at Johns Hopkins University for sharing the sand data.

##  6 Code and data availability

The data used here is archived on the APS Data Management System and is
available on request. The code is available on request.

##  7 Author contributions

AA, HS, and ZL conceived the machine learning methods. AA, ZL, and WZ
developed the machine-learning software with guidance from IF and RK. JSP, PK,
and HS performed the synchrotron experiments for 304L-SS data set with
assistance from AM and ZL. WZ performed the data analysis under the guidance
of JSP, PK, and HS. All the authors discussed the results and wrote the
manuscript.

## References

  * [1] Greenfield, A. & Graedel, T.  The omnivorous diet of modern technology.  _Resources, Conservation and Recycling_ 74, 1–7 (2013).
  * [2] Graedel, T. E., Harper, E. M., Nassar, N. T. & Reck, B. K.  On the materials basis of modern society.  _Proceedings of the National Academy of Sciences_ 112, 6295–6300 (2015).
  * [3] Olson, G. B.  Designing a new material world.  _Science_ 288, 993–998 (2000).
  * [4] Rajan, K.  Materials informatics.  _Materials Today_ 8, 38–45 (2005).
  * [5] Lienert, U. _et al._ High-energy diffraction microscopy at the Advanced Photon Source.  _JOM_ 63, 70–77 (2011).  URL http://dx.doi.org/10.1007/s11837-011-0116-0.
  * [6] Schuren, J. C. _et al._ New opportunities for quantitative tracking of polycrystal responses in three dimensions.  _Current Opinion in Solid State and Materials Science_ 19, 235–244 (2015).  URL http://www.sciencedirect.com/science/article/pii/S1359028614000862.  Opportunities in Mesoscale Science.
  * [7] Naragani, D. _et al._ Investigation of fatigue crack initiation from a non-metallic inclusion via high energy x-ray diffraction microscopy.  _Acta Materialia_ 137, 71–84 (2017).  URL https://linkinghub.elsevier.com/retrieve/pii/S1359645417305888http://www.sciencedirect.com/science/article/pii/S1359645417305888.
  * [8] Bernier, J. V., Suter, R. M., Rollett, A. D. & Almer, J. D.  High-energy X-ray diffraction microscopy in materials science.  _Annual Review of Materials Research_ 50, 395–436 (2020).
  * [9] Park, J.-S., Sharma, H. & Kenesei, P.  Repeatability and sensitivity characterization of the far-field high-energy diffraction microscopy instrument at the Advanced Photon Source.  _Journal of Synchrotron Radiation_ 28, 1786–1800 (2021).  URL http://scripts.iucr.org/cgi-bin/paper?fv5137https://journals.iucr.org/s/issues/2021/06/00/fv5137/https://scripts.iucr.org/cgi-bin/paper?S1600577521008286.
  * [10] Suter, R. M. _et al._ Probing microstructure dynamics with X-ray diffraction microscopy.  _Journal of Engineering Materials and Technology_ 130, 21007 (2008).  URL https://doi.org/10.1115%2F1.2840965.
  * [11] Turner, T. J. _et al._ Crystal plasticity model validation using combined high-energy diffraction microscopy data for a Ti-7Al specimen.  _Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science_ 48, 627–647 (2017).  URL http://dx.doi.org/10.1007/s11661-016-3868-x.
  * [12] Sangid, M. D. _et al._ A complete grain-level assessment of the stress-strain evolution and associated deformation response in polycrystalline alloys.  _Acta Materialia_ 201, 36–54 (2020).  URL https://linkinghub.elsevier.com/retrieve/pii/S135964542030745X.
  * [13] Ravi, P., Naragani, D., Kenesei, P., Park, J.-S. & Sangid, M. D.  Direct observations and characterization of crack closure during microstructurally small fatigue crack growth via in-situ high-energy X-ray characterization.  _Acta Materialia_ 205, 116564 (2021).  URL https://linkinghub.elsevier.com/retrieve/pii/S1359645420310016.
  * [14] Li, W. _et al._ Resolving intragranular stress fields in plastically deformed titanium using point-focused high-energy diffraction microscopy.  _Journal of Materials Research_ 38, 165–178 (2023).
  * [15] Maddali, S. _et al._ High-energy coherent X-ray diffraction microscopy of polycrystal grains: Steps toward a multiscale approach.  _Physical Review Applied_ 14, 024085 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevApplied.14.024085.
  * [16] Simons, H. _et al._ Dark-field X-ray microscopy for multiscale structural characterization.  _Nature Communications_ 6, 1–6 (2015).  URL http://www.nature.com/ncomms/2015/150114/ncomms7098/full/ncomms7098.htmlhttp://dx.doi.org/10.1038/ncomms7098.
  * [17] APS upgrade project final design review report (2019).  https://www-dev.aps.anl.gov/APS-Upgrade/Documents.
  * [18] Taylor, G. I.  Plastic strain in metals.  _Journal of the Institute of Metals_ 62, 307–324 (1938).
  * [19] Obstalecki, M., Wong, S. L., Dawson, P. R. & Miller, M. P.  Quantitative analysis of crystal scale deformation heterogeneity during cyclic plasticity using high-energy X-ray diffraction and finite-element simulation.  _Acta Materialia_ 75, 259–272 (2014).  URL http://www.sciencedirect.com/science/article/pii/S1359645414003103https://linkinghub.elsevier.com/retrieve/pii/S1359645414003103.
  * [20] Wang, L. _et al._ Developing ductile and isotropic Ti alloy with tailored composition for laser powder bed fusion.  _Additive Manufacturing_ 102656 (2022).  URL https://linkinghub.elsevier.com/retrieve/pii/S2214860422000628.
  * [21] Shade, P. A. _et al._ Fiducial marker application method for position alignment of in situ multimodal X-ray experiments and reconstructions.  _Journal of Applied Crystallography_ 49, 700–704 (2016).  URL http://scripts.iucr.org/cgi-bin/paper?S1600576716001989.
  * [22] Sharma, H., Huizenga, R. M. & Offerman, S. E.  A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup.  _Journal of Applied Crystallography_ 45, 693–704 (2012).
  * [23] Sharma, H., Huizenga, R. M. & Offerman, S. E.  A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. II. Volume, centre-of-mass position, crystallographic orientation and strain state of grains.  _Journal of Applied Crystallography_ 45, 705–718 (2012).
  * [24] Menasche, D. B. _et al._ Deep learning approaches to semantic segmentation of fatigue cracking within cyclically loaded nickel superalloy.  _Computational Materials Science_ 198, 110683 (2021).  URL https://linkinghub.elsevier.com/retrieve/pii/S0927025621004109.
  * [25] Hurley, R. C. _et al._ In situ grain fracture mechanics during uniaxial compaction of granular solids.  _Journal of the Mechanics and Physics of Solids_ 112, 273–290 (2017).  URL https://doi.org/10.1016/j.jmps.2017.12.007http://www.sciencedirect.com/science/article/pii/S0022509617308967.
  * [26] Pagan, D. C. _et al._ Modeling slip system strength evolution in Ti-7Al informed by in-situ grain stress measurements.  _Acta Materialia_ 128, 406–417 (2017).  URL https://linkinghub.elsevier.com/retrieve/pii/S1359645417301337.
  * [27] Johnson, Q. C. _et al._ Mapping 3d grain and precipitate structure during in situ mechanical testing of open-cell metal foam using micro-computed tomography and high-energy X-ray diffraction microscopy.  _Materials Characterization_ 195, 112477 (2023).  URL https://linkinghub.elsevier.com/retrieve/pii/S1044580322007598.
  * [28] Pang, G., Shen, C., Cao, L. & Hengel, A. V. D.  Deep learning for anomaly detection: A review.  _ACM computing surveys (CSUR)_ 54, 1–38 (2021).
  * [29] Liu, Z. _et al._ BraggNN: fast X-ray Bragg peak analysis using deep learning.  _IUCrJ_ 9 (2022).  URL https://doi.org/10.1107/S2052252521011258.
  * [30] Grill, J.-B. _et al._ Bootstrap your own latent: A new approach to self-supervised learning (2020).  URL https://arxiv.org/abs/2006.07733.
  * [31] Bradski, G.  The openCV library.  _Dr. Dobb’s Journal: Software Tools for the Professional Programmer_ 25, 120–123 (2000).
  * [32] Lee, J. _et al._ Characterization and application of a GE amorphous silicon flat panel detector in a synchrotron light source.  _Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment_ 582, 182–184 (2007).  URL https://linkinghub.elsevier.com/retrieve/pii/S0168900207017937.
  * [33] MIDAS.  https://www.github.com/marinerhemant/MIDAS.