Table of Contents
Foreword vii
Preface ix
Acknowledgements xiii
Chapter 1. The World in Equations 1
1.1. Numerical modeling 3
1.1.1. Modeling 3
1.1.2. Understanding, designing, forecasting, optimizing 4
1.2. Putting the world into equations: example of mechanics 5
1.2.1. Construction of classical mechanical models 5
1.2.2. Emergence of quantum mechanics 23
1.3. Solving an equation 34
1.3.1. Finding a mathematical formula 34
1.3.2. Calculating using a computer 38
Chapter 2. Simulation Practice 49
2.1. Validating a simulation 50
2.1.1. Demonstrating a theorem 50
2.1.2. Confronting points of view… 51
2.1.3. Relying on experience 54
2.1.4. Changing point of view 57
2.2. Maturity of a technique 61
2.3. Practice, practice, practice... 63
2.3.1. The engineer’s palette 63
2.3.2. Complementary philosophies 68
2.3.3. Users with different needs 70
Chapter 3. A Global Technique 77
3.1. A very generalized technique 78
3.2. A strategic technique 80
3.3. Hercules of the calculation 85
3.3.1. High-performance computing 85
3.3.2. Stroke to computing power 88
Chapter 4. The Data World 101
4.1. Big data 102
4.2. Data and networks 104
4.3. Learning from data 115
4.4. Biological and digital brains 121
4.4.1. Biological neurons 123
4.4.2. Digital neural networks 129
4.5. Are humans overwhelmed by machines? 137
4.5.1. All-round machine victories 137
4.5.2. A war of intelligence? 139
4.5.3. Science fiction 140
4.5.4. Science without fiction 142
4.5.5. Complementarity of intelligence 145
4.5.6. Complexity and robustness 150
4.5.7. Imitation game 151
4.5.8. Priority to the law! 153
4.5.9. More human than human? 155
Conclusion 159
Glossary of Terms 171
References 201
Index 237
