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

richardluismartin@.lbl.gov, mharanczyk@.lbl.gov

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

Z

S

a

m

pl

e

R

C

o

ar

se

X

C

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ar

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Y

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or

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o

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Mi

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or

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