Data Science and Nuclear Engineering: A Perfect Match

Data Science and Nuclear Engineering:

A Perfect Match

Dr. Madicken Munk

University of Florida

2020.02.20

About Me:

Nuclear Engineering, University of California, Berkeley

About Me:

What is Data Science?

“ [A] data scientist is someone who knows how to extract meaning from and interpret data, which requires both tools and methods from statistics and machine learning, as well as being human. They spend a lot of time in the process of collecting, cleaning, and munging data, because data is never clean. This process requires persistence, statistics, and software engineering skills—skills that are also necessary for understanding biases in the data, and for debugging logging output from code. ” - O'Neil and Schutt, 2013.

“ [An] academic data scientist is a scientist, trained in anything from social science to biology, who works with large amounts of data, and must grapple with computational problems posed by the structure, size, messiness, and the complexity and nature of the data, while simultaneously solving a real-world problem. ” - O'Neil and Schutt, 2013.

Differences between Data Science and Nuclear Engineering?

Data Science
Data Source: Human (taken from, targeted to)
Architecture: Cloud-based, distributed
Problem Types: Optimization
Privacy: Software, data proprietary

Nuclear Engineering
Physics (simulation or detection)
Local Machines, [Heterogenous] Clusters
Optimization, Understanding Physics
Export control

How about the Similarities?

Communication: Clear, readable results for domain and non-domain experts. Strong data visualization.

Domain Expertise: Deep understanding of the data and how it relates/applies to the problem

Heterogenous Tools: Full computational toolchain will involve multi-language tooling, expertise

Data Cleaning: All data needs to be clean!

Reproducibility: tools (git, hg, svn), analysis (jupyter notebooks), methods (papers, blogs), software (versioning, stability)

Scalability: Methods and analysis must scale from local machines to large, "production" compute nodes

Ethics: Use and/or implement tools/algorithms ethically

What about the Skills?

Programming, SQL, Math/Stats, ML Algorithms, DataViz, Communication, Cloud Computing, Software Engineering, Automated ML, Domain Expertise

Heterogenous data sources, trustworthy AI/methods, Automation, Privacy, Ethics

Packaging, Production Code Development, Version Control, Reproducibility, Sharing Data/Analysis

The Computational Landscape: Engineering

The Data Science Lifecycle

Key Takeaway:

Data Science and Nuclear Engineering (Scientific Computing) are Family!

The Computational Landscape

My work: Parametric study of design to maximize $^{99}$Mo
Result: Design patented, startup created, construction permit granted Data Science Skills: Reading/Parsing outputs, identifying relations, matlab scripting

https://patents.google.com/patent/US20120027152A1/en

Key Takeaways from the Rover Source

My work: Perform Parametric studies to maximize n flux, minimize shield material
Result: Passive neutron source designed with weight and flux constraints met
Data Science Skills: Parametric evaluation, Python scripting, optimization

The PB-FHR MK-1 Design

236 MWth core

300 C/HM fueled pebbles, 19.99% enrichment

FLiBe coolant, enriched to 99.999 wt% Li6

Power density 23.0 MW/$m^3$

Buoyant pebble fuel

Online refueling, annular core

Central reflector houses control rod guide tubes

Central Reflector Lifetime Estimates

Key Takeaways from the Lifetime Estimate

My work: Created a novel tool to couple neutronics/strucutral mechanics
Result: Lifetime estimated, reflector redesigned, Kairos power startup
Data Science Skills: Data Cleaning, Automation, Software Development
Data Science Potential: Use optimization techniques to converge on core component design that maximizes lifetime

Deep Dive: Why Variance Reduction?

Radiation shielding is important
"Analog" Monte Carlo is not ideal for these problems
- Lots of particles → good statistics
- Good shielding → very few particles

Image Credit: MCNP, X. Monte Carlo Team, MCNP–A General Purpose Monte Carlo N-Particle Transport Code, Version 5. LA-UR-03-1987, Los Alamos National Laboratory, April 2003.

Deep Dive: Hybrid Methods

Deterministic solution used to create importance map

Importance map → Monte Carlo → improves solution, reduces time

Importance: contribution to a tally

Common solution: use deterministic solution to adjoint equation for importance map.

A Forward Problem

An Adjoint Problem

A Simple Labyrinth

General:

Point source
NaI detector, concrete barrier
Vacuum boundary conditions

Monte Carlo specific:

NaI reaction rate with track length tally (f4)
Tally energy binning consistent with XS library

Denovo specific:

27g19n XS library
QR quadrature
SC solver
P$_N$ order 3

Forward Flux

Adjoint Flux

Angle Isn't Captured

Explicit angle biasing is difficult

The $\Omega$ Flux

\[ \phi^{\dagger}_{\Omega}(\vec{r},E) = \frac{\int{\psi (\vec{r}, E, \hat{\Omega}) \psi^{\dagger} (\vec{r}, E, \hat{\Omega})}d \hat{\Omega}} {\int{\psi (\vec{r}, E, \hat{\Omega}) d \hat{\Omega}}} \]

Uses angular flux → More angular information is captured in importance map
Generates scalar flux → Can be used in existing methods
Weights by the forward flux → Direction of particle flow is captured

Adjoint Flux

Used by CADIS

$\Omega$ Flux

Used by CADIS-$\Omega$

Flux Anisotropies

Anisotropy Metric 2 ( $\phi^{\dagger}_{\Omega}/\phi^{\dagger}$ ) Distribution, Group 26 for Steel Beam in Concrete

Above: Anisotropy Metric 4 Distribution ( $\psi^{c}_{max:avg}/\psi^{\dagger}_{max:avg}$ ), by Energy Group, in Regions where the Contributon Flux is High

Below: Trend Results for Anisotropy Metric 4 as Related to the Ratio of Relative Errors $RE_{\Omega}/RE_{CADIS}$

Key Takeaways from the $\Omega$-methods

My work: Created and implemented a novel method to capture angle in ADVANTG, developed novel methodology to analyze anisotropy in problems
Result: New insight into shield designs, robust characterization of method
Data Science Skills: Python, build systems (make, cmake), version control (git), data formatting (hdf5), data cleaning, data visualization (matplotlib, yt, seaborn), algorithms
Data Science Potential: Use anisotropy metrrics to characterize beyond the $\Omega$-methods, build out suite of analysis tools

yt and widgyts

Project website
Project repository

↓

Analysis and Visualization

Domain Context System

Weather and Climate
Oceanography and Hydrology
Whole-earth seismography and tomography
Observational Astro
Nuclear Engineering
Neuroscience

Geographic Projections

orthographic projection of GEOS-5 global weather model from August 22, 2018

robinson projection of GEOS-5 global weather model from August 22, 2018

My slides and talk from SciPy 2018

Data Science In Nuclear Engineering

Nuclear Data: Detection --> Data Reduction --> Format --> Human-Readable/Machine-Readable --> Simulation

Coupled Reactor Multiphysics: High Dimensionality + Coupled Fields, data selection, minimization + visualization

Real-Time Grid Monitoring/Response: Multiply-Sourced, Time-Series Data --> Cleaning --> Response Metrics --> GUI for human interaction

Materials Selection and Design: Using ML optimization techniques to minimize compute time for parametric studies

The Perfect Match

...in Interdisciplenary Heaven

Using data science methods and best practices in scientific computing will help us do better, more reproducible, robust research

Practicing the skills we learn in scientific training will help us be better data scientists

Computing makes our lives better as scientists

Tools for your science

Effective Computation in Physics

PyNE

WholeTale

Binder

Version Control with Git

Jupyter Notebooks

Data Science for Fun

Creating A Twitter Art Bot

Computing 'Zines by Julia Evans

Effective Computation in Physics

Advanced Visualization Lab (for inspiration)

Data Science Roundup

"Best Practices in Software Engineering for Scientific Computing", talk given to Blue Waters graduate fellows, Madicken Munk

Acknowledgements

Matthew Turk
Rachel Slaybaugh

Tara Pandya
Seth Johnson
Steven Hamilton
Garret Baltz
David Krumwiede
Nathan Goldbaum
Britton Smith

Katy Huff
Denia Djokic
Lakshana Huddar
Alejandra Jolodosky
Patricia Schuster

Thank You!

Madicken Munk

twitter:@munkium github:@munkm
https://munkm.github.io/2020-02-20-UF
This publication is supported in part by the Gordon and Betty Moore Foundation's Data-Driven Discovery Initiative through Grant GBMF4561 to Matthew Turk and by the Department of Energy under award number DE-NE0008286 to Rachel Slaybaugh.

Data Science and Nuclear Engineering: A Perfect Match by Madicken Munk is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://munkm.github.io/2020-02-20-UF.

Backup Slides: Computing

Nuclear Engineering helped Data Science Today

Backup Slides: NE Work

Central Reflector Lifetime Estimates

Use MCNP to get the fluence data for the reflector

↓

Use fluence and experimental data to calculate radiation-induced strain

↓

Use strain calculation to impose a pseudo-temperature distribution in FEM

↓

Use FEM and fluence buildup to determine lifetime

Implementing Radiation-Induced Swelling

\[ \begin{align} \varepsilon_{th} &= \alpha (T-T_{ref}) \\ \varepsilon_{\Phi} &= \varepsilon_{th} \\ T &= \frac{\varepsilon_{\Phi}}{\alpha} + T_{ref} \end{align} \]

\[ \begin{align} T_{ref} &= \mbox{ unstrained reference temperature }\\ T &= \mbox{ temperature inducing strain }\\ \varepsilon_{th} &= \mbox{ thermal strain }\\ \varepsilon_{\Phi} &= \mbox{ strain induced from neutron fluence }\\ \alpha &= \mbox{ coefficient of thermal expansion } \end{align} \]

Redesign of the PB-FHR Central Reflector

Future Work: Lifetime Estimate

Idea: Perform lifetime evaluations on core components in emerging reactor designs based on coupled physics

Deliverable: software, lifetime characterization

Collaborators: Kairos Power, Westinghouse, INL

Funding: DOE-NE, ARPA-E, SBIR

Image Credit: Westinghouse eVinci micro reactor link

Key Takeaways from the Lifetime Estimate

My work: Created a novel tool to couple neutronics/strucutral mechanics
Result: Lifetime estimated, reflector redesigned, Kairos power startup
Future Idea: Perform lifetime evaluations on core components in emerging reactor designs based on coupled physics
Data Science Application: Use optimization techniques to converge on core component design that maximizes lifetime

Backup Slides: The $\Omega$ Methods

The forward neutron transport equation:

\[ \begin{multline} \hat\Omega \cdot \nabla \psi (\vec {r} ,E,\:\hat\Omega)+\Sigma _{ t } (\vec{r},E)\psi (\vec { r } ,E,\:\hat\Omega) = \\ \int _{ 4\pi } \int _{ 0 }^{ \infty } \Sigma _{ s }(E'\rightarrow E, \hat\Omega'\rightarrow\hat\Omega)\psi (\vec { r } ,E',\: \hat\Omega')dE' \:d\hat\Omega' + q_{e}(\vec { r } ,E, \:\hat\Omega). \end{multline} \]

The adjoint neutron transport equation:

\[ \begin{multline} \hat\Omega \cdot \nabla \color{teal}{\psi^{\dagger}} (\vec {r} ,E,\:\hat\Omega)+\Sigma _{ t } (\vec{r},E)\color{teal}{\psi^{\dagger}} (\vec { r } ,E,\:\hat\Omega) = \\ \int _{ 4\pi } \int _{ 0 }^{ \infty } \Sigma _{ s }(\color{violet}{E\rightarrow E'}, \color{purple}{\hat\Omega\rightarrow\hat\Omega'})\color{teal}{\psi^{\dagger}} (\vec { r } ,E',\: \hat\Omega')dE' \:d\hat\Omega' + \color{teal}{q_{e}^\dagger}(\vec { r } ,E, \:\hat\Omega). \end{multline} \]

The adjoint solution can be used to make an importance map for a desired outcome.

An exact adjoint solution can be used to obtain a zero variance Monte Carlo solution.

Importance and the Adjoint

Notation:

$\langle ab \rangle = \int a(P)b(P) dP$

Detector response

$ \begin{align} R &= \langle \sigma_d \psi \rangle \\ &= \langle q^{\dagger} \psi \rangle \\ &= \langle q \psi^{\dagger} \rangle \\ \end{align} $

Point source

$q ( \vec{r}, E, \hat{\Omega}) = \delta(\vec{r}-\vec{r_0})\delta(\vec{E}-\vec{E_0})\delta(\vec{\hat{\Omega}}-\vec{\hat{\Omega}_0})$

Response = adjoint flux

$R = \psi^{\dagger} (r_0, E_0, \Omega_0)$

The CADIS method

Biased source distribution

Starting weight of the particles

Weight window target values

$\\ \hat{q}(\vec{r},E) = \frac{\phi^{\dagger}(\vec{r},E)q(\vec{r},E)}{R} \\$

$\\ w_{0}(\vec{r},E) = \frac{q(\vec{r},E)}{\hat{q}(\vec{r},E)} = \frac{R}{\phi^{\dagger}(\vec{r},E)} \\$

$\\ w(\vec{r},E) = \frac{R}{\phi^{\dagger}(\vec{r},E)}$

MCNP, X. Monte Carlo Team, MCNP–A General Purpose Monte Carlo N-Particle Transport Code, Version 5. LA-UR-03-1987, Los Alamos National Laboratory, April 2003.

Evans, Thomas M., et al. "Denovo: A new three-dimensional parallel discrete ordinates code in SCALE." Nuclear technology 171.2 (2010): 171-200.

Mosher, Scott W., et al. "ADVANTG—an automated variance reduction parameter generator." ORNL/TM-2013/416, Oak Ridge National Laboratory (2013).

Anisotropy Metrics

\begin{align} M_1 &= \frac{\phi^{c}}{\Phi^{c}} \\ M_2 &= \frac{\phi^{\dagger}_{\Omega}}{\phi^{\dagger}} \\ M_3 &= \frac{\psi^{c}_{Max}}{\psi^{c}_{Avg}} \\ \end{align}

\begin{align} M_4 &= \frac{\frac{\psi^{c}_{Max}}{\psi^{c}_{Avg}}}{\frac{\psi^{\dagger}_{Max}}{\psi^{\dagger}_{Avg}}} \\ M_5 &= \frac{\psi^{c}_{Max}}{\psi^{c}_{Min}} \\ M_6 &= \frac{\frac{\psi^{c}_{Max}}{\psi^{c}_{Min}}}{\frac{\psi^{\dagger}_{Max}}{\psi^{\dagger}_{Min}}} \end{align}

Steel Beam in Concrete

Above: Figure of Merit results for CADIS and CADIS-$\Omega$ for various tally regions of interest

Below: Timing results for CADIS and CADIS-$\Omega$

Above: Figure of Merit results for CADIS and CADIS-$\Omega$ for various tally regions of interest

Below: Timing results for CADIS and CADIS-$\Omega$

Future Work

Idea: Use anisotropy metrics to characterize beyond $\Omega$-methods, build out suite of novel analysis tools for nuclear engineering with PyNE+yt

Deliverable: Robust scheme to recommend method based on problem type, open-source package to calculate anisotropy metrics

Data Science Influence: Use methods from other domains (halo finding (astro)), cleaning and filtering methods

Future Work

Idea: Use LDO quadrature set to do angle biasing in Monte Carlo

Deliverable: Angle biasing in Monte Carlo for low angular refinement

Collaborators: ORNL, UC Berkeley Neutronics

Funding: DOE-NE, ORNL subcontract