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Applied Mathematics For Experimental Science J.A. Sethian
Mathematics Department LBNL and Department of Mathematics, UC Berkeley
A New Challenge: DOE Facilities in 2025: More Data, More Users, More Discovery
Experimental facilities will be transformed by high-
resolution detectors, advanced mathematical analysis
techniques, robotics, software automation, and
programmable networks.
Detectors capable of
generating terabit data
streams. Computational tools
for analysis, data
reduction & feature
extraction in situ,
using advanced
algorithms and
special-purpose
hardware.
Increase scientific
throughput from
robotics and
automation
software.
Data management
and sharing, with
federated identity
management and
flexible access
control. Post-processing:
reconstruction, inter-
comparison, simulation,
visualization.
Integration of
experimental and
computational
facilities in real time,
using programmable
networks.
DOE Facilities in 2025: More Data, More Users, More Discovery
Goal: Invent and Deliver the New Mathematics Needed to
(1) Accelerate our understanding of experimental data
(2) Reduce time and materials in the experimental cycle.
(3) Optimize, suggest, and steer experiment.
A Charge from LBNL:
Three years ago: Significant LBNL LDRD support
Plan of Attack:
(1) Formed teams of beam scientists, computational chemists,
computer scientists, and mathematicians
(2) Built teams: identified problems that needed to be
“mathematicized”, or for which current methods were inadequate
(3) Ran seminars (papers, external speakers, programmed
methods): to prioritize what needed to be done, and how.
CAMERA: Center for Applied Mathematics for Energy Research Applications
CAMERA
Pilot Partners
ALS
Foundry &
NCEM
Goal: Build applied mathematics that transform experimental data into understanding
computing
structure from
imaging
analyzing samples and
proposed new materials
designing new
possibilities
Tomorrow:
More data.
More quickly.
High resolution.
Today:
Facilities data
is time-
consuming
Critical need:
algorithms and
analysis for
understanding
LBNL approach:
Focused teams of
mathematicians/
domain scientists
New math to:
Guide and
optimize
experiments
Computational harmonic analysis Discrete Galerkin methods
Machine learning
Statistical sampling Clique analysis
Representation theory Bayesian analysis
PDE-based image segmentation
Graph theory Spectral clustering
Optimization methods Hamilton-Jacobi solvers
Maximum likelihood estimators
Discrete/continuous shape descriptors
Voronoi methods
Key: Leverage state-of-the-art mathematics
Mori-Zwanzig theory
Joint BES-ASCR Partnership (Steven Lee, Program Manager)
CAMERA: Mathematics and Algorithms for Designing New Materials
CAMERA
•What are the current projects?
ALS
Ptychographic Imaging
GISAXS (Grazing-incidence small angle scattering)
Image Analysis from Synchrotron Data
X-Ray Nanocrystallographic Reconstruction
Molecular Foundry
Electronic Structure Calculations
Searching Chemical Structure for New Materials
CAMERA: Mathematics and Algorithms for Designing New Materials
CAMERA
•Who is working on this? Advanced Light Source (ALS):
A. Hexemer (Beam Scientist/GISAXS)
S. Marchesini (Ptychography)
D. Parkinson (Beamline Scientist, Hard X-ray tomography)
D. Shapiro (Beamline scientist)
Molecular Foundry
D. Britt (Organic and Macromolecular Synthesis)
J. Neaton (Electronic Structure)
W. Queen (Inorganic Nanostructures)
National Center for Electron Microscopy (NCEM)
P. Ercius (Scanning transmission electron microscope)
Computational Research Division (CRD)
M. Haranczyk (Materials Design) T. Perciano (Image Analysis)
X. Li (GISAXS) H. Krishnan (Image Analysis/HPC)
L. Lin (Electronic Structure)
R. Martin (Materials Design)
C. Yang (Electronic Structure)
D. Ushizima (Image Analysis)
CRD Mathematics Department:
J. Donatelli (X-Ray Nanocrystallography)
C. Rycroft (Optimal Chemical Design)
J. Sethian (Director)
OVERVIEW OF
SOME OF THE
WORK UNDERWAY
Vision: Develop high-performance algorithms and software for analyzing X-ray scattering patterns.
CAMERA: Faster Analysis for X-ray Scattering Data
CAMERA
Figur e 1: (a) The GISAXS experimental setup and the coordinate system used in HipGISAXS. The
incoming X-ray beam is propagated along the wave vector ki at an incidence angle α i with respect to the
sample axes as shown. A scat tered (outgoing) beam kf is also shown propagat ing toward the area
detector. (b) and (c) show respect ively the sample t ilt (“ t ilt ” ) and in-plane rotat ion (“ inplanerot ” ) angles.
• “ shape” : a 3D geometric form composed of a single or mult iple closed domains and
represents a full or part of a part icle in M . A shape may be exact ly defined by a
finite number of parameters and may have an analyt ical form factor expression (e.g.
cylinder) or may be a custom shape.
• “ grain” : is a collect ion of shapes arranged in a periodic lat t ice within a finite region
of space (i.e. a finite number of repet it ions).
• “ensemble” : is a collect ion of grains replicated according to some spat ial and orienta-
t ion distribut ion. Typically, ensembles are used to capture stat ist ical informat ion in
the sample (such as isotropy or radial averaging).
5
Figur e 12: Spherical nanopart icle hexagonal assemblies in a st rat ified medium (ABAB...) (a) simulated
at 10 keV using the slicing algorithm: (b) Comparison of computed (left ) and experimental (right ) [10]
data for the incidence angle α i = 0.12◦ and N J = 14 layers; (c), (d) and (e): the GISAXS images for
α i = 0.2◦ are computed for an increasing number of Au 2D layer to show the effect of slicing on the
structure of the Yoneda peak band. All pat terns are symmetric with respect to the qz axis; hence, only one
half of the image (negat ive) is shown.
distributed memory systems, the transpose operat ion between the two 1D FFTs requires
large amount of communicat ion. Therefore, parallel 3D FFT hardly scales beyond a few
thousands processors.
V . PER FOR M A N CE OV ERV I EW
HipGISAXS is a massively parallel software, which we have developed using C+ + , aug-
mented with MPI [15], Nvidia CUDA [18], OpenMP [2], and parallel-HDF5 [30] libraries, on
23
GISAXS scattering: probe nanoscale surface features
Forward Simulation (HipGISAXS)
Recover Structure (needs new and better algorithms)
Sample Structure GISAXS Image
Next Generation Computing for X-ray Science
• HipGISAXS simulation code based on DWBA
• Orders of magnitude faster than before
• Resulted from designing the mathematics to parallelize the algorithms.
GISAXS (forward simulation):
simulation: 20 sec 0.05 sec /frame
Reverse Monte Carlo (recover structure):
1 frame in 240 min 100 frames in 15 min
Current Focus: New mathematics and algorithms for structure recovery from noisy data
• Nonlinear optimization algorithms
• Genetic algorithms
• Pattern recognition, machine learning
before after
before after
• Work seeded by LBNL-LDRD (X. Li, 2011-2013).
• A. Hexemer (DOE Early Career 2013)
• Now part of CAMERA (GISAXS=grazing incidence small angle X-ray scattering)
Vision: Develop algorithms to advance reconstruction from x-ray nanocrystallographic diffraction.
Tools for determining crystal shape and size
Donatelli and Sethian, An algorithmic framework for x-ray nanocrystallographic reconstruction in the presence of the indexing ambiguity, PNAS, 2014
(2) Peak Shape Analysis
(3) Multi-Modal Modeling
CAMERA: Reconstruction Algorithms for X-ray Nanocrystallography
CAMERA
Structure Determination of PuuE Allantonaise
from simulated data
(1) Autoindexing
(4) Resolving Indexing Ambiguities
Techniques for orienting images up to crystal lattice symmetry
Periodicity analysis of reflections yields partial orientation information
Fourier analysis of finely sampled low angle data coupled with image segmentation reveals crystal features
Algorithms for removing orientation ambiguities resulting from crystal lattice symmetries
Multi-stage expectation maximization/scaling locates histogram modes from ambiguously oriented data
Clique analysis of a graph theoretical model of value concurrency resolves indexing ambiguities
X-ray Nanocrystallography Experimental Setup
Methods for reducing data variance in the presence of indexing ambiguities
Reconstruction via iterative phase retrieval Simulated diffraction pattern
J. Donatelli and J.A. Sethian (LBNL/UC Berkeley Math)
(1) DG discretization
(2) PEXSI evaluation
(3) Elliptic preconditioner for SCF
(4) Excited state calculation
Vision: Accelerate the computation of ground state and excited state
properties for large scale materials systems.
Ground state calculation
(1) DG discretization
Using discontinuous basis functions to
represent continuous physical quantities
with low cost and high accuracy.
(2) PEXSI evaluation
Discontinuous
basis function for
3D Na
Nearly continuous
electron density
recovered
Represent Fermi
operator by pole
expansion
Massively parallel
distributed
memory selected
inversion
Reduce KSDFT cost calculation to at most
N^2 scaling without sacrificing accuracy.
PEXSI achieves two
order of magnitude
speedup for DNA
calculation.
(3) Elliptic preconditioner
Reduce the number of SCF iterations for
large scale inhomogeneous metallic system
Accelerate the SCF convergence of quasi-
1D Na system using elliptic preconditioner.
(4) Excited state calculation
After convergence of ground state calculation, evaluate excited
state properties using GW theory &Bethe-Salpeter theory. Compute
full-frequency dielectric function and self energy matrix efficiently.
Photoemission
experiment in molecular
foundry.
Improved integration rule for more
accurate self-energy calculations.
CAMERA: Mathematics and Algorithms for Designing New Materials
CAMERA L. Lin and C. Yang (LBL)
Vision: develop computer vision algorithms for 3D/4D quantitative analysis of experiments, addressing challenges posed by noise, artifacts, metrics, sheer size, and heterogeneous composition of materials.
ALS
Topological descriptors
Analysis
Segmentation (check-point)
Cmp with
simulation
Iron oxide coated quartz sand
Image
slices
750 um borosillicate
Next Generation Analysis for X-ray Science:
• Automated segmentation;
• Faster and multiplatform;
• Enable new metrics;
• Benchmark with simulations
Current focus:
• Pattern recognition/classification algorithms;
• Characterization of experimental data;
• Multiscale representation;
• PDE-based and graph-based image analysis; Work seeded by LBNL-LDRD
(Ushizima, 2011-2013).
Main ALS collaborators: Dula
Parkinson, Alastair Macdowell
Now part of CAMERA
Different materials
Image processing algorithms
Quant-CT
Ushizima et al. SPIE-DSP 2011, Ushizima et al. ImageJ Int. Conf. 2012, Ushizima et al. IEEE Trans Comp Graph Vis 2012, Ushizima et al Informs 2013
Reeb
graph
CAMERA: Quantitative Image Analysis of Micro-CT Samples
CAMERA D. Ushizima (LBNL)
Figure 1. Block diagram of the MRF approach proposed
in [1]. The process is composed by a low-level step (line
detection) and a high-level step (graph construction and
optimization). Figure 2. Graph modeling: (a) ridge detection (b) detection of connected
components and junctions (c) Addition of possible connections (d) generated
graph.
Filaments are fundamental structures
permeating materials. They define a channel
network that influences material porosity and
crack development. When detected from
images, the filaments enable essential
quantification and analysis of processes
related to the material. The challenge is the
extraction of this type of structure from
microscopic images due to filament complex
spectral and spatial characteristics. Our project
aims at developing and applying machine
learning techniques to tackle filament detection,
measurement, and classification of filament
networks.
The MRF theory provides a convenient and
consistent way to model context dependent
entities as image pixels or primitives. This is
possible through the characterization of mutual
influences between these entities. The
approach proposed in [1, 2] uses this idea to
detect thin structures from 2D images (see
Figures 1 and 2). We applied this algorithm to
extract filaments from 3D synthetic images [3].
The algorithm is applied to 2D slices of the 3D
images for recovering regions of interest that
are most likely to be filaments (see Figure 3).
The problem arising from the application of the
algorithm in 2D slices is that the complete 3D
contextual information is lost, which is essential
for the MRF approach. Lacking such
information, the algorithm poorly reconstruct
the complete filaments, and misclassify a few
artifacts as if they were regions of interest. To
overcome this drawback, we are developing a
3D extension of the algorithm where the MRF
model embeds the 3D contextual information of
the structures. In doing so, the 3D
characteristics will play a role in defining the
clique potentials for the energy function,
minimizing misclassification.
Abstract Statistical Image Analysis and Machine Learning 3D Extension
References: [1] T. Perciano, F. Tupin, R. Hirata Jr., R. M. Cesar, A hierarquical Markov random field for road network extraction and its application with optical and SAR data. International Geoscience and Remote Sensing Symposium (IGARSS), 2011, 1159-1162.
[2] H. Sportouche, F. Tupin, J.-M. Nicoloas, C.-A. Deledalle, How to combine TerraSAR-X and Cosmo-SkyMed high resolution images for a better scene understanding?. International Geoscience and Remote Sensing Symposium (IGARSS), 2012, 178-
181.
[3] M. A. Galarreta-Valverde, M. Macedo, C. Mekkaoui, M. P. Jackowski, Three-dimensional synthetic blood vessel generation using stochastic L-systems, SPIE Medical Imaging, 2013.
Energy function for the optimization step:
Acknowledgements: this work was supported by the U.S. Department of Energy
under contract no. DE-AC03-76SF00098
Positive Negative
Positive 19.4% 9.2%
Negative 11.5% 59.9%
Precision = 67.8% Recall = 62.7% Accuracy = 77.9%
Positive Negative
Positive 21.5% 8.5%
Negative 12% 58%
Precision = 71.7% Recall = 64.2% Accuracy = 79.5%
Figure 3. Simulated filament network: original 3D images at left, noise-corrupted (N(0,15)) versions and recovered
structures at right; colors in figures at right are proportional to the likelihood of that voxel to belong to the structure.
CAMERA: Detection of Filaments from 3D Images using Markov Random Fields
T. Perciano and D. Ushizima (LBNL)
Vision: Accelerate the transition from virtual materials to real materials with specified performance goals. Enable users at the facilities to focus resources on the most promising materials.
+ =
Map building blocks to vertices and edges of topology graph
Final 3-D model exhibits desired topology
Tools for 3D assembly of porous polymer models from enumerated periodic graphs
Zeo++ - Voronoi decomposition-based tool for characterization of porosity
Fast discrete algorithms for calculation of guest-diffusion paths, pore size distributions and other properties with sub 0.1 A accuracy
Efficient material design with optimization algorithms
Haranczyk, and Sethian, PNAS, 2009; Willems, Rycroft, Kazi, Meza, Haranczyk, Microporous Mesoporous Mater. 2012; Martin, Haranczyk, Chem. Sci. 2013; J. Chem. Theory Comput. 2013
Optimization in abstract space representing a material reveals high-performing material designs
Abstract representation captures shape of real building block of a material
(1) Assembling Potential Materials (2) Analyzing Proposed Materials
Mathematics and Algorithms for Designing New Materials
CAMERA
Material structure
Monte Carlo sampled surface area
Simplified network representing void space.
Fast PDE-algorithms for more accurate calculations.
(3) Steering the Design
An Early Success: Designing Record-
Breaking High Surface Area Materials
Su
rface A
rea m
2/g
M. Haranczyk and R. Martin (LBNL), C. Rycroft, J.A. Sethian (LBNL and UC Berkeley Math)
Materials Informatics: Analysis, Discovery and Design of Porous Materials Richard L. Martin, Maciej Haranczyk
Computational Research Division, Lawrence Berkeley National Laboratory, CA 94720, USA
[email protected], [email protected]
Porous materials have a wide variety of applications in
industry, for instance as membranes, catalysts and
adsorbents. Discovering materials with the optimal porosity
for a particular application remains a great challenge,
largely due to the vast number of possible materials. Here,
we introduce new mathematical tools to facilitate high-
throughput computational analysis of materials, and more
efficient discovery and design.
We utilize the Voronoi decomposition to map the internal
pore network of materials, enabling the high-throughput
calculation of geometric properties of materials. Searching of
databases of materials is also enabled via novel structural
descriptors.
We also demonstrate prediction of crystal structures of
materials with a topology-based modeling approach. This
tool, combined with optimization algorithms, is demonstrated
in the automated design of new materials.
• Accurate and rapid calculation of geometric properties of
porous materials
• Similarity searching and diversity selection capabilities for
automated materials discovery
• Topology-based crystal structure prediction
• Optimization-based design of outstanding new materials
References: [1] T. F. Willems, C. H. Rycroft, M. Kazi, J. C. Meza and M. Haranczyk, Microporous Mesoporous Mater., 2012, 149, 134-141.
[2] R.L. Martin, B. Smit and M. Haranczyk, J. Chem. Inf. Model., 2012, 52, 308-318.
[3] M. Pinheiro, R.L. Martin, C.H. Rycroft and M. Haranczyk, CrystEngComm, 2013, 15, 7531-7538.
[4] R.L. Martin and M. Haranczyk, Cryst. Growth Des., in press.
[5] R.L. Martin and M. Haranczyk, Chem. Sci., 2013, 4, 1781-1785 and J. Chem. Theory Comput., 2013, 9, 2816-2825.
[6] R.L. Martin and M. Haranczyk, Cryst. Growth Des., 2013, 13, 4208-4212.
Abstract Methods Results
Acknowledgments:
This work was partially supported by CAMERA: The Center for Applied Mathematics for Energy Research Applications at Lawrence Berkeley National Laboratory
supported by the U.S. Department of Energy underContract No. DE-AC02- 05CH11231.
This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department
of Energy under Contract No. DE-AC02-05CH11231.
Our computational geometry tool, Zeo++, enables high-throughput analysis and comparison of
porous material structures.
The Voronoi hologram is a descriptor that encodes local pore shapes within a material for efficient
comparison and sampling of structures.
In polydisperse systems, significant errors can arise in calculated
pore sizes. Introducing pseudo-atoms of uniform size mitigates
these errors, while retaining the high-throughput character of the
software.
By optimizing material structure with respect to
some property of interest, new materials can be
efficiently discovered without the computational cost
of enumerating large datasets
Advanced porous materials such as metal-organic frameworks (MOFs) typically exhibit high-
symmetry underlying crystal topologies; Zeo++ can rapidly predict the structure of new
hypothetical materials in a topology-driven manner
Crystal Structure Prediction High-throughput Structure Analysis
Optimization-based Design
Based on the shape and connectivity of molecular building blocks, how can they be arranged to
form a valid crystal structure? By positioning these components in space, and performing the
appropriate symmetry operations, Zeo++ can assemble a crystal structure that exhibits a
particular topology, or ‘net’
Square Triangle
+ =
+ =
By focusing on these five topologies, a range of optimal
compromises between gravimetric and volumetric
surface area can be achieved
tbo pts
pyr
cds
pcu
The achievable gravimetric and volumetric surface area
within many high-symmetry candidate topologies for
materials was compared
Volumetric surface area (m2/cm3)
Gra
vim
etr
ic s
urf
ac
e a
rea
(m2/g
)
Sets of related material structure can be automatically identified from within large datasets; conversely, maximally diverse subsets of materials can
be extracted for use as representative training sets
Similarity between materials can be quantified, in high-throughput,
by calculating similarity between Voronoi hologram descriptors
v
s
.
Edge length l
Lar
ger
nod
e
radi
i ra
Smaller node
radii rb
Quantit
y
r
b
r
a l
Voronoi holograms are histogram descriptors that encode the frequency of
occurrence of local cavity shapes within a material’s pore network
Zeo++ can calculate descriptors for material
characterization, such as pore size distributions
The super resolution revolution in x-ray imaging
•The inverse transform: globally convergent scalable algorithms •First theoretical guarantee in the field (40+ years problem) •Connection Graph Laplacian for good initial •Long range synchronization by spectral methods
•Lens design •Resolution and information throughput, multiplexing
•Experimental perturbations •Robust long range recovery by spectral methods
•Low latency ptychography •ALS has 1000 more throughput (more coherent scattering) •Scalable code used at 4 beamlines •real time feedback by reducing latency
S. Marchesini, D. Shapiro, H. H. Krishnan (LBL) (with H-T. Wu (Stanford))
The network in ptychography [1]
Lens design
CAMERA: Ptychographic Imaging
CAMERA
The ability to reconstruct a sample from its diffraction pattern
has been a standing issue for over 100 years. We recently
demonstrated the global convergence for any object of
interest under general experimental conditions such as
ptychography. We first show that a popular iterative method
cannot stagnate if the solution is unique. Second, we show
that all possible orbits in high dimensions converge globally to
the solution. Additionally, we show how to scale the
algorithms by exploiting synchronization and connection
graph Laplacians to handle the big imaging data in the
coming new light source era. Finally, we propose new lens
design to increase resolution, robustness and information
throughput.
Abstract Alternating projections and its global covergence Phase Synchronization/ Graph Laplacian
the next 100 years…
1952
1914
How big can we go?
2001
NaCl
DNA
RNA
fie
ld o
f vie
w
diffraction
microscopy
ptychography
HOW TO FILL THE GAP BETWEEN
LENGTH-SCALES
100 years of phase retrieval
The imaging setup The mathematical framework
The Alternating projection algorithm
.
Main issue : No theoretical
guarantee of the convergence
of these algorithms!
To show the global
convergence, we need the
uniqueness result
Consider the nonlinear optimization
Satisfy
constraint Fit the data
Phase
Coherent
Diffraction
iteratively
shrinking the
support +
= S. Marchesini, H. He, H. N. Chapman
et al. PRB 68, 140101(R) (2003),
Resolution
minimize discrepancy with object in data
space
Any meaning ?
Yes ! Phase synchronization
i-th and j-th
patches overlap
Fourier Wigner
Distribution
And phase correction
Phase Synchronization network !
Long range phase synchronization In each iteration step (AP for
example),
• evaluate the “frame-wise”
phase
• update
Multiscale phase synchronization*! Synchronization kernel of
the Connection Graph
Laplacian
Long range synchronization
*quick, scalable
• Still non-convex. Try to relax.
• take the amplitude (image) into account
• the larger the amplitude is, the more
important its associated phase is
How to build good initial
syn
chr
o-
CG
8
0
x
A
P
4
0
x
A
P
3
x
A
P
A
P
• Global convergence of the alternating projection
(AP) algorithm is shown (40+)
• Phase synchronization (PS) and connection graph
Laplacian (CGL) are introduced to obtain a good
initial
First theoretically
guaranteed algorithm in
the field
(macro-scaled + atomic)
• Spectral method, can be scaled up to handle
BIG data
Several practical and
theoretical problems
left… Alternating Projection, Ptychographic Imaging and Phase Synchronization, Stefano
Marchesini, Yu-Chao Tu, Hau-tieng Wu, [arxiv:1402.0550].
Measure macro-scale samples at atomic resolution?
• Diffraction enables atomic resolution
• Scanning microscope enables imaging macro-scale objects
Called Ptychographic Image
technique
Diffractive imaging ab initio: Now being used at every x-FEL worldwide
Coherence Enables Diffractive imaging “ab-initio”
CAMERA: The Inverse Transform in Ptychography: Globally Convergent Scalable Algorithms
S. Marchesini (LBNL), Y-C Tu (Princeton Math), H-T Wu (Stanford Math, Princeton)
A practical issue in ptychographic reconstruction are the strict
requirements of the experimental geometry to achieve high quality data.
For example, the need for stable, well controlled coherent illumination
of the sample, limited detector speed and response function all
contribute to limit the specifications of a ptychographic microscope.
We approach the inverse problem in high dimensional data space (we
view every pixel of every frame as a dimension) by trying to make the
phases of all pixels consistent with each other under some constraints.
This motivates us to consider augmented projections and
synchronization strategies aimed at organizing local information in a
global way. We have developed numerical solvers to handle situations
when sample, illumination function, incoherent effects, as well
as positions, are all unknown parameters in high dimensions based on
spectral methods[2], conjugate gradient, Newton [4], and augmented
Lagrangian [3] methods, some of which are in production at 4
microscopes at the Advanced Light Source.
Abstract Experimental Perturbation in High Dimensions Convergence with perturbations
The imaging setup The mathematical framework
The Alternating projection algorithm
.
[1] Augmented projections for ptychographic imaging, S. Marchesini, A Schirotzek, C
Yang, HT Wu, F Maia, Inverse problems 2013
[2] Alternating Projection, Ptychographic Imaging and Phase Synchronization, Stefano
Marchesini, Yu-Chao Tu, Hau-tieng Wu, [arxiv:1402.0550].
Gap with
constraint Fit the data
Phase
minimize discrepancy with object in data
space
Consider the nonlinear optimization
The relationship graph
Overlapping frames
are related to each
other
what if the
assumptions are
wrong?
D. Shapiro, Nanosurveyor/Ptychography Update
(August-October 2012)
https://docs.google.com/open?id=0B74dHuNh4CtiNzJP
UE5SS2RfUjA
i
n n x1
x2 i x3
Large dimensional
data
Lower dimensional
space
Consider a simple problem, what if the intensity of every
frame fluctuates? (1 extra scalar per frame)
•Build the K x K ”framewide” connection graph laplacian
•Compute the largest eigenvalue
•Largest eigenvalue provides fluctuating intensities [1]
overlapping
frames
Similar techniques can be applied to fluctuating intensity with
incoherent multiplexing (partial coherence, detector response,
vibrations)
Position refinement in high dimensional space
•Taylor expansion of the illumination
•Minimize the gap at first order
•Solve sparse KxK linear problem
•Missing pixels, beamstop
•Probe recovery
•I0 fluctuations (100%),
•vibrations( 100% probe width),
•partial coherence (>10 modes)
•Incoherent multiplexing
•background (bias)
•drifts
•Convergence without and with
correction
H is obtained by computing pairwise dot products between frames as in
the framewide CGL
Lens Design illumination lens
Band limited random lens
Large beam in both realand reciprocal
space
•increased aperture
•flat dynamic range
•more FOV and resolution per shot
•better use of many pixels
The network is more
connected, therefore
more robust
Numerical tests
From [2] we know how to solve this
We have developed numerical solvers to handle situations when sample, illumination
function, incoherent effects, as well as positions, are all unknown parameters in high
dimensions based on spectral methods[2], conjugate gradient, Newton [4], and
augmented Lagrangian [3] methods, some of which are in production at 4 microscopes at
the Advanced Light Source.
CAMERA: Robust Ptychography: Algorithms for Noisy Data
S. Marchesini (LBNL). H-T Wu (Stanford), C. Yang (LBNL), F. Maia (Uppsala)
With the ever increasing brightness of x-ray sources, it is now possible
to see what no one was ever able to see before: macroscopic
specimens in 3D at wavelength resolution. By combining diffraction with
microscopy and the computational power of GPUs, one can quickly turn
high throughput "imaging by diffraction" techniques into the sharpest
images ever produced. To sustain high throughput processing (~>TB/h)
we use a small cluster and developed distributed code that exhibit
strong scaling over dozens of nodes. In the near future, low latency
feedback will be made possible by streaming detector packets through
our distributed machine directly into the analysis backend computer.
Abstract Strong Scaling tests on an experimental
dataset show that the code is scalable
Toward real time feedback
Fast Implementation of Split and Overlap Kernels.
Higher level parallelization is necessary for real -time performance
Full Image Combine
1600 frames 260x260 pixels
C
C
D S
a
m
p
l
e
Zone
Plate
Piez
o
Scan
ner
S
a
m
pl
e
X
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S
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Figure 2 The user friendly interface is based on the STXM control software packaged developed by the ALS. There is a universal interface across all STXMs while still providing access to high level scanning routines for ptychography and fastCCD control.
Tratditional STXM ptychography Truth (SEM)
First results show large improvement over STXM
Interface Instrument
Uses GPUs to achieve high performance.
Use Thrust and Cusp whenever possible.
Split can be easily parallelized as all the operations are independent.
Overlap requires a reduction at every pixel which needs more careful
planning.
low latency feedback will be made
possible by streaming detector packets
through our distributed machine
directly into the analysis backend
computer.
CCD 100 Hz Raw data
CAMERA: Low Latency Ptychography Imaging by High Performance Computing
H. Krishnan (LBNL), F. Maia (Uppsala), S. Marchesini (LBNL), D. Shapiro (LBNL)
BUILD, TEST, EXPORT:
•Build the new mathematics required to partner with
experimental facilities
•Together with experimental partners, test algorithms on data
and “on the shop floor”
•Export codes, software to other DOE Facilities, Labs, and to
advanced computing environments (HIPGISAXS, MicroCT,
PytchoPS, PEXSI, ZEO++,…)
CAMERA:
CAMERA
camera.lbl.gov