九州⼤学 IMI 共同利⽤・研究集会（Ⅱ）

Fiber Topology Meets Applications
⽇時︓
場所︓2021年1⽉6⽇（⽔）14:30 〜 2021年1⽉8⽇（⾦）16:45
九州⼤学 伊都キャンパス ウエスト1号館 D棟4階
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１⽉６⽇（⽔）
14:30-15:15
Title︓Fiber Topology Meets Applications: Where We are Heading
Speaker︓Daisuke Sakurai (Kyushu University)
15:15-16:00
Title︓Why Topology is Necessary at Exascale - And Why it's Not Easy
Speaker︓Hamish Carr (University of Leeds)
16:00-16:45
Title︓Modeling semiconductor epitaxy for next generation power device
application
Speaker︓Yoshihiro Kangawa (Kyushu University)
１⽉７⽇（⽊）
14:30-15:15
Title︓Data Parallel Hypersweeps for in Situ Topological Analysis
Speakers︓Petar Hristov (University of Leeds), Gunther Weber (Lawrence
Berkeley National Laboratory and University of California, Davis), Hamish
Carr (University of Leeds), Oliver Rübel (Lawrence Berkeley NationalLaboratory) and James Ahrens (Los Alamos National Laboratory)
15:15-16:00
Title︓Design of Multimodal Test Problems in Multiobjective Optimization
Using Fiber Topology
Speakers︓Reiya Hagiwara (Kyushu University), Takahiro Yamamoto (TokyoGakugei University), Naoki Hamada (KLab Inc.), Daisuke Sakurai (KyushuUniversity)
16:00-16:45
Title︓Eco-efficient Flight Trajectory Exploration by Using theChemistry-climate Model EMAC
Speakers︓Hiroshi Yamashita and Bastian Kern (German Aerospace Center)
１⽉８⽇（⾦）
14:30-15:15
Title︓Elimination of B2 singularities
Speaker︓Takahiro Yamamoto (Tokyo Gakugei University)
15:15-16:00
Simplifying Indefinite Fibrations on 4-manifolds
Speaker︓Osamu Saeki (Kyushu University)
16:00-16:30
Title︓An Efficient Triangulation for Extruded Spatiotemporal Prism Meshes
Speakers︓Akito Fujii, Kenji Ono and Daisuke Sakurai (Kyushu University)
16:30-16:45
Concluding Remarks
Daisuke Sakurai (Kyushu University)Abstracts-----------Fiber Topology Meets Applications: Where We are Heading
Daisuke Sakurai (Kyushu University)
In differential topology, the study of the topology of fibers, known as fiber topology,extends the Morse theory, of functions, to that of maps. This establishes a thoroughexploration of topological transitions of inverse images. It has been proven powerfulfor understanding todayʼs data whose size and complexity are overwhelming. To
aid
the interaction among mathematics, computation, and applications, we havelaunched this research gathering "Fiber Topology Meets Applications". This opening
talk presents a general introduction to fiber topology, from the speaker's standpointof computer science, and presents recent collaboration around him. Although eachparticipant works on his own mission in his area, we have found a few fruitful
directions that have mutual benefits to our rather diverse variety of disciplines. Key
topics include topological analysis in high-performance computing and specialized
treatments of discrete geometry in theoretical backgrounds of computation.

Why Topology is Necessary at Exascale - And Why It's Not Easy
Hamish Carr (University of Leeds)
As computation scales to exabyte levels, humans are increasingly unable
to process the data directly. In a realistic assessment, a human might meaningfully
perceive 10 GB of data in a lifetime, which requires billion-fold data reduction
without information loss. As a result, techniques like computational topology, withmathematically well-founded approaches, become increasingly necessary toanalyse and display (i.e. visualise) extreme data sets. However, much of themathematics on which these methods are based is either linearly defined orcouched in serial metaphors. As a result, one of the major challenges to exascale
comprehension is now the ability to scale computational topology to massive hybrid
systems using both shared-memory and distributed parallelism. This talk will
therefore give an overview of the basic ideas behind computational topology at
scale, and illustrate recent approaches to scalability.

Modeling Semiconductor Epitaxy For Next Generation Power Device
Application

Yoshihiro Kangawa (Kyushu University)
Gallium nitride semiconductor (GaN) is attractive material for next generation
power device. A vertical GaN power device with a blocking voltage beyond 1200V
is necessary for high-power modules in hybrid vehicles and electric vehicles. To
develop such devices, it is indispensable to reduce carrier concentration in drift
layer less than 1E+16 cm^­3. That is, it is indispensable to control unintentional
doping during thin film growth. In the present work, we model elementary growth
processes in GaN MOVPE (Metalorganic Vapor Phase Epitaxy) such as (1) vapor
phase reaction, (2) surface reaction and (3) solid-phase diffusion during growth.
In this presentation, we discuss how to control unintentional doping in GaN MOVPE
from the theoretical viewpoint.

Data Parallel Hypersweeps for In Situ Topological Analysis
Petar Hristov (University of Leeds), Gunther Weber (Lawrence Berkeley National
Laboratory and University of California, Davis), Hamish Carr (University of Leeds),
Oliver Rübel (Lawrence Berkeley National Laboratory) and James Ahrens (LosAlamos National Laboratory)
The contour tree is a tool for understanding the topological structure of a scalar
field. Recent work has built efficient contour tree algorithms for shared memory
parallel computation, driven by the need to analyze large data sets in situ while thesimulation is run- ning. Unfortunately, methods for using the contour tree forpractical data analysis are still primarily serial, including single isocontour extraction,
branch decomposition and simplification. We report data parallel methods for thesetasks using a data structure called the hyperstructure and a novel general purpose
approach called a hyper-sweep. We implement and integrate these methods witha Cinema database that stores features as depth images and with a web serverthat reconstructs the features for direct visualization.

Design of Multimodal Test Problems in Multiobjective Optimization Using
Fiber Topology
Speakers: Reiya Hagiwara (Kyushu University), Takahiro Yamamoto (TokyoGakugei University), Naoki Hamada (KLab Inc.), Daisuke Sakurai (KyushuUniversity)
In industry, product designers often face a multiobjective optimization problem that
requires to optimize multiple conflicting objective functions, such as cost andperformance, simultaneously. In academia, researchers develop methods forsolving multiobjective optimization problems based on performance comparison onartificial test problems. While multiobjective optimization problems that appear inreal-world applications are often "multimodal", the definition of multimodality inmulti-objective optimization was not well-established, and multimodal test
problems supported by theory were not well developed. In this talk, we present a
method for designing test problems that enable us to control their multimodality
using fiber topology.

Eco-efficient Flight Trajectory Exploration by Using the Chemistry-climate
Model EMAC
Hiroshi Yamashita and Bastian Kern (German Aerospace Center)
The climate impact of aviation emissions is a topic studied intensively due to its
importance for a sustainable society. Climate-optimized routing of aircraft aims atminimizing climate impact. However, in reality, current routing models in the airline
industry tends to optimize the financial cost of operation with little considerationon the environmental sustainability. To support governments and airlines in findinga practical solution to this trade-off between the financial and environmental costs,
a product for the calculation of multi-objective flight trajectory optimizations isdeveloped at our team. In this study, the flight trajectory optimization is carriedout of flights from New York (JFK) to Paris (CDG) over the North Atlantic by using
the chemistry-climate model EMAC with the air traffic submodel AirTraf. The
compromise solutions in terms of the Pareto front or, more precisely, thenondominated front are analyzed. The talk also introduces the EMAC model in its
first part.

Elimination of B_2 Singularities
Takahiro Yamamoto (Tokyo Gakugei University)
A smooth stable map of a compact manifold with boundary into a surface withoutboundary admits singularities which consists of folds, cusps, boundary folds,
boundary cusps and B2 singularities. In this talk, we give a set of local moves fora smooth stable map of a compact manifold with boundary into a surface withoutboundary and study the following question. Given a compact surface withboundary M, and a smooth stable map f of M into the plane R^2, can f be deformed
to a smooth stable map g so that g has no B2 singularities.

Simplifying Indefinite Fibrations on 4-manifolds
Osamu Saeki (Kyushu University)

A broken Lefschetz fibration (BLF, for short) is a smooth map of a closed oriented
4-manifold onto a closed surface whose singularities consist of Lefschetz criticalpoints together with indefinite folds. Such a class of maps was first introduced by
Auroux-Donaldson-Katzarkov (2005) in relation to near-symplectic structures. In
this talk, we give a set of explicit moves for BLFs, and give an elementary andconstructive proof to the fact that any map into the 2-sphere is homotopic to a BLF
with embedded singular set image. We also show how to realize any given nullhomologous 1-dimensional submanifold with prescribed local models for its
components as the round locus of a BLF. These algorithms allow us to give a purely
topological and constructive proof of a theorem of Auroux-Donaldson-Katzarkov onthe existence of broken Lefschetz pencils with embedded round image onnear-symplectic 4-manifolds. We moreover establish a correspondence between
BLFs and Gay-Kirby trisections of 4-manifolds, and show the existence of simplified
trisections on all 4-manifolds.
This is a joint work with R. Inanc Baykur (University of Massachusetts).

An Efficient Triangulation for Extruded Spatiotemporal Prism Meshes
Akito Fujii, Kenji Ono and Daisuke Sakurai (Kyushu University)
It is common to run simulations on a spatial mesh with an associated (spatial)
triangulation. We consider the problem of re-triangulating space-time mesh that
conforms to the pre-defined spatial triangulation. The problem originates incomputer graphics where shell maps were concerned about 3D geometry. Today
the general dimensionality, and especially 4D, has become relevant for online (akain-situ) analysis, in which a diagnostic program component examines the simulated
physical fields. As the analysis is especially important for visualizing big data fromscientific computation, providing a spatiotemporal triangulation equipped with thevery fine temporal resolution thanks to in-situ opens the door to a new variety ofdiagnoses. This article proposes an instant combinatorial triangulation, which is\emph{implicit} in the sense that the triangles can be determined on-the-fly andlocally for an arbitrary sub-complex of the space-time. In other words, thealgorithm does not have to iterate over all the vertices to determine the triangles
and is thus efficient in a range of scenarios.
Our algorithm is also scalable in distributed memory machines, on which simulators
would run. We assume a static spatial triangulation, which is rather simplistic yetfound in today's simulations, including atmospheric simulations run in academia
and even at meteorological agencies. For such a static triangulation we extrude
them along the time axis, which gives us a prism mesh, and further re-triangulatethem to get the spatiotemporal triangulation.
Being combinatorial, implementations of the algorithm do not require arbitrary
precision arithmetic. Our algorithm is easy to implement, inserts no additionalvertex, is memory efficient, works for arbitrary dimension and is parameter free.