Impact of Scientific Computing on Science and Society

✍ Scribed by Pekka Neittaanmäki, Marja-Leena Rantalainen

• Publisher: Springer-ECCOMAS
• Year: 2023
• Tongue: English
• Leaves: 451
• Series: Computational Methods in Applied Sciences, 58
• Category: Library

✦ Synopsis

This book analyzes the impact of scientific computing in science and society over the coming decades. It presents advanced methods that can provide new possibilities to solve scientific problems and study important phenomena in society. The chapters cover Scientific computing as the third paradigm of science as well as the impact of scientific computing on natural sciences, environmental science, economics, social science, humanistic science, medicine, and engineering. Moreover, the book investigates scientific computing in high performance computing, quantum computing, and artificial intelligence environment and what it will be like in the 2030s and 2040s.

✦ Table of Contents

Foreword
Preface
Contents
Contributors
Mathematical and Numerical Modeling
On Extreme Computational Complexity of the Einstein Equations
1 Historical Facts of Importance
2 Exterior and Interior Schwarzschild Solution
3 Einstein Equations of General Relativity
4 Explicit Form of the First Einstein Equation
5 Computational Complexity of the Einstein Equations
6 Concluding Remarks
References
Systematic Imposition of Partial Differential Equations in Boundary Value Problems
1 Introduction
2 Formal Sum of p-Forms
3 Differential Operator for General Fields
3.1 Hodge Operator and Wedge Product
3.2 Action
3.3 Differential Operator in Space-time
3.4 Differential Operator in Space and Time
4 Instantiation of Particular Models
4.1 Electromagnetism
4.2 Schrödinger Equation
4.3 Elasticity
4.4 Yang-Mills Equation
5 Approximations in Finite Dimensional Spaces
6 Conclusions
References
Curiously Empty Intersection of Proof Engineering and Computational Sciences
1 Introduction
2 Unfit for Computational Sciences?
3 Closer Investigation
3.1 Architecture of Interactive Theorem Provers
3.2 Theoretical Background
3.3 Role of Elaboration
3.4 Proof Engineering by Example
4 Unexploited Opportunities?
4.1 Reasons to Get Excited
4.2 Reasons to Remain Skeptical
5 Conclusions
References
Challenges for Mantle Convection Simulations at the Exa-Scale: Numerics, Algorithmics and Software
1 Introduction
2 Geophysics
2.1 Significance and Physics of Mantle Convection
2.2 Challenges and Future Directions
3 Mathematics
3.1 Basic Components of Finite Element Simulations
3.2 Two-Scale Surrogate
3.3 All-at-Once Multigrid Method
4 High Performance Computing
4.1 Grand Challenge Problems
4.2 Scalability Taken Seriously
4.3 Asymptotically Optimal Not Necessarily Good Enough
4.4 With Matrix-Free Multigrid Methods Towards Extreme Scale
4.5 Quest for Textbook Efficiency
5 Conclusions
References
Remarks on the Radiative Transfer Equations for Climatology
1 Introduction
2 Radiative Transfer Equations for a Stratified Atmosphere
3 Effect of Absorption Coefficient on Atmospheric Temperature
4 Unaffected Sunlight?
5 Earth Albedo
6 General Statement About Earth Albedo
6.1 Energy Type Estimate for the Grey Problem
6.2 Frequency Dependent Case
7 Calculus of Variations for the ν-dependent Case
7.1 Support of the Conjecture
7.2 Numerical Simulations
References
Simulation and Its Use in Additive Manufacturing
1 General Background
2 Additive Manufacturing in 3D Printing
2.1 L-PBF and DED Techniques
2.2 DfAM
3 Incorporation of Simulation in DfAM
3.1 Simulation Process
3.2 Different Simulation Approaches
4 State-of-the-Art in AM Simulation
5 Speculations About the Future Usability of the Simulation
References
A Posteriori Error Estimates for Domain Decomposition Methods
1 Introduction
2 Fully Guaranteed a Posteriori Error Estimates
3 Domain Decomposition Methods for the Basic Elliptic Problem
3.1 Problem Formulation
3.2 Schwarz Alternating Method
4 Guaranteed Bounds of Errors
4.1 A Posteriori Error Estimate Adapted to DDM
4.2 Computation of Admissible Flux Fields
5 Numerical Evidence
References
Optimization and Control
Multi-criteria Problems and Incompleteness of Information in Structural Optimization
1 Introduction
2 Prototype Problem
3 Multi-criteria Optimization of a Beam with a Crack System
4 Optimization of Shell with Uncertainties in Damage Characteristics
5 Conclusion
References
Stability in Discrete Games with Perturbed Payoffs
1 Introduction
2 Basic Definitions and Notations
3 Auxiliary Lemma and Statements
4 Main Result
5 Other Results
6 Conclusion
References
Optimal Control Problems in Nonsmooth Solid and Fluid Mechanics: Computational Aspects
1 Introduction
2 Identification of the Slip Bound in the Stokes System with Nonsmooth Slip Conditions
3 Optimal Surface Coating Governed by the Stokes System with Threshold Slip Boundary Conditions
4 Conclusions
References
Optimal Control Approaches in Shape Optimization
1 Introduction
2 Distributed Penalization of the State System
2.1 Dirichlet Conditions
2.2 Neumann Conditions
3 Hamiltonian Approach in Dimension Two
References
Optimal Factor Taxation with Credibility
1 Introduction
2 Households and Public Sector
3 Production and Investment
4 Non-Credible Public Policy
5 Savers
6 Government
7 Policy Rules
8 Conclusions and Extensions
8.1 Endogenous Fertility
8.2 Endogenous Mortality
References
Transformative Direction of R&D into Neo Open Innovation
1 Introduction
2 Development of the Digital Economy
2.1 R&D-Driven Growth
2.2 Dilemma Between R&D Expansion and Declining Productivity
3 Neo Open Innovation
3.1 Self-Propagating Function
3.2 Spinoff to Uncaptured GDP
3.3 Soft Innovation Resources
3.4 Concept of Neo Open Innovation
4 Conclusion
References
On Tetrahedral and Square Pyramidal Numbers
1 Introduction
2 Main Theorem
3 Proof of the Main Theorem
3.1 Proof with Even n
3.2 Proof with Odd n
4 Weird Numbers
References
AI and Applications in Health Care
Randomized Constructive Neural Network Based on Regularized Minimum Error Entropy
1 Introduction
2 Incremental Extreme Learning Machine
3 Proposed Method
3.1 Problem Formulation
3.2 Problem Solving
4 Experimental Results
4.1 Comparison of RMSE-MEE-RCNN with IELM
4.2 Comparison of RMSE-MEE-RCNN with ELM, B-ELM And MLP-MEE
5 Conclusion
References
On the Role of Taylor's Formula in Machine Learning
1 Introduction
2 Methods
2.1 Basic Formulations
2.2 Taylor's Formula
2.3 Autoencoder Inspired by Taylor's Formula
2.4 Feature Selection Method Based on Taylor's Formula
3 Computational Experiments
3.1 Experimental Setting
3.2 Additive Autoencoder Inspired by Taylor's Formula
3.3 Feature Selection for a Distance-Based Classifier
4 Conclusions
References
Computational Methods in Spectral Imaging
1 Introduction
2 Noise Reduction
3 Model-Based Analysis
4 Machine Learning
5 Applications
6 Concluding Remarks
References
Method for Radiance Approximation of Hyperspectral Data Using Deep Neural Network
1 Introduction
2 Methods
2.1 Dataset and Network Architecture
2.2 Training
3 Results
4 Discussion
4.1 Findings
4.2 Related Work
5 Conclusions
References
Directional Wavelet Packets for Image Processing
1 Introduction
2 Quasi-analytic Directional Wavelet Packets
2.1 Properties of qWPs
2.2 Implementation Scheme for 2D qWP Transforms
2.3 Summary of 2D qWPs
3 Numerical Examples
3.1 Image Denoising
3.2 Image Inpainting
4 Discussion
References
Trends in Scientific Computing
Fifty Years of High-Performance Computing in Finland
1 Introduction
2 History
2.1 From Centralized Systems to Computing Ecosystem
2.2 Development of CSC
2.3 Towards the European HPC Ecosystem
3 Future Developments
3.1 Prerequisites for Success
3.2 LUMI in Kajaani
3.3 ELIXIR and National Nodes
3.4 LUMI's Eco-efficiency
4 Conclusions
Quantum Scientific Computing
1 Introduction
2 Quantum Computing in a Nutshell
3 Quantum Algorithms for Scientific Computing
3.1 Quantum Linear Solver Algorithms
3.2 Hybrid Quantum-Classical Algorithms
3.3 Quantum Algorithms for Partial Differential Equations
4 Opportunities for Scientific Quantum Computing
References
Quantum Computing at IQM
1 Introduction to Quantum Technology
2 Overview of Quantum Computing
2.1 History of Quantum Computing
2.2 Differences Between Quantum and Classical Computing
3 Basics of Quantum Computing Theory
3.1 Qubit
3.2 Quantum Information Processing
3.3 Quantum Algorithms
4 Quantum Computing at IQM
4.1 IQM Technology
4.2 Co-design Quantum Computers and Their Components
5 Future Outlook at IQM
References
Contribution of Scientific Computing in European Research and Innovation for Greening Aviation
1 Introduction
2 Technologies to Reduce Aircraft Drag
2.1 Drag Reduction by Laminar Flow and Flow Control
2.2 High Lift Design for Transonic Wings
2.3 Research on Shock Wave Boundary Layer Interaction
3 Aeroacoustic Research to Reduce Aircraft Noise
3.1 Low-Noise Technologies for Propulsion Systems
3.2 Airframe Noise Reduction Research
4 Computational and Numerical Methods in Aeronautics
4.1 Development of Reynolds Averaged Navier-Stokes (RANS) Flow Solvers
4.2 Numerical Methods for Industrial Needs
5 European Scientific Networks in Flow Physics and Design Methods
6 Conclusions
References
Thirty Years of Progress in Single/Multi-disciplinary Design Optimization with Evolutionary Algorithms and Game Strategies in Aeronautics and Civil Engineering
1 Introduction and Motivation
2 Methods of Design Optimization
2.1 Evolutionary Methods Genetic Algorithms and Evolutionary Algorithms
2.2 Multi-objective Optimization and Game Theory
2.3 Advanced Methods and Tools for EAs
3 Progress of the Use of Optimization Methods in Aeronautical Engineering Design
3.1 Period 1994–2004
3.2 Period 2004–2014
3.3 Period 2014–2022
4 Applications to Civil Engineering Design
5 Conclusions and Perspectives
References