Neil Gershenfeld

MAS 864

2023

When should you use MD? PD? FEM? DEM? MPM? LBM? LGA? PCA? ICA?

How can you represent beliefs? expectations? uncertainty?

How can you search with a model? Without a model?

How can you program 2 cores? 2000000 cores?

This course will answer these questions, and many more, with a survey of the range of levels of description for analytical, numerical, and data-driven mathematical modeling. The focus will be on understanding how these methods relate, and on how they can be implemented efficiently.

The schedule will be:

Contents | |

2/9: | Mathematical Computing, Benchmarking, Linear Algebra and Calculus |

2/16: | Ordinary Differential and Difference Equations |

Partial Differential Equations | |

2/23: | Random Systems |

Variational Principles | |

3/2: | Finite Differences: Ordinary Differential Equations |

3/9: | Finite Differences: Partial Differential Equations |

3/16: | Finite Elements |

3/23: | Discrete Elements |

3/30: | Spring Vacation |

Computational Geometry | |

4/6: | Function Fitting |

4/13: | Transforms |

Filtering and State Estimation | |

4/20: | Functions |

Density Estimation | |

4/27: | Search |

5/4: | Machine Learning Architectures |

5/11: | Constrained Optimization |

5/22: | Final Projects |

References |

Relevant background for each of these areas will be covered. The assignments will include problem sets, programming tasks, and a semester modeling project. The course is based on the text *The Nature of Mathematical Modeling*, with draft revisions for a second edition to be provided throughout the semester.