Motivation

This is the big question motivating everything we will see in this course: How does the world work?

Depending on where you come from – your training and your interests – you probably have different answers to this question.

A physicist might tell me about quantum mechanics, general relativity, and the standard model of particle physics.
A biologist might tell me about the cell, the genome, and the brain.
A computer scientist might tell me about algorithms, data structures, and complexity theory.
A mathematician might tell me about the axioms of set theory, the Peano axioms, and the incompleteness theorems.
A philosopher might tell me about the nature of reality, the mind-body problem, and the problem of induction.

But what do all these answers have in common? They all develop and use models: representations, analogies, or abstractions of reality. Models are built out of words or numbers that we can manipulate, communicate, and use to make predictions. We’ve essentially come up with all these models by observing the world and finding patterns in it; using something we call intelligence: a power we like to brag about a little too much.

Historically, at first, we mainly relied on language to describe those patterns: like the sun comes out every day. But, not that long ago, we started using numbers to quantify those patterns. Then we started using equations to describe the relationships between those numbers. Finally, we started using computer algorithms to make predictions about those numbers.

We build representations of the world: using words, drawings, numbers, symbols, functions, equations, and algorithms etc. And we use those representations to understand (with some debate over what that means), and make predictions about how it behaves.

This is why the course is called: data-driven modeling in science and engineering. The course will expose you to the methods of building mathematical models in various fields of science and engineering; that many of you are probably already familiar with. So you will see many of the things you already know (linear algebra, differential equations, numerical methods, algorithms etc.) in a new context. That is, if you know those things. If not, you will learn them in this course.

But why data-driven?

Quantifying the world

You might have heard that “data is the new oil”. The world is changing fast, and everyone is disoriented, afraid of losing their jobs (which they probably should be). It feels as if the world is ending. And who’s the greatest culprit: intelligent machines. The world has changed:

In how we learn about it: through the internet, online courses and videos, etc.
In how we work: remote work, online meetings, emails, etc.
In how we entertain ourselves: online games, streaming, etc.
In how we shop: online shopping, online payments, etc.
In how we travel: online bookings, online check-ins, etc.
In how we define ourselves in it and interact with it: on the internet and through social media,
In how we build it: through artificial intelligence, robotics, and automation.
In how we build ourselves: through genetic engineering, synthetic biology, and brain-computer interfaces.

All of these are possible thanks to our ability to map the real-world we live in (you and me, and these tables) unto words and numbers that we can manipulate, communicate and process using computers. So what’s been happening in the past few centuries, at an exponentially accelerating rate, is essentially a revolution in the quantification of the world.

Data is the world quantified. And quantification is the first step to building models.

In a way, this is what Galileo Galilei figured out 5 centuries ago. He was sitting in mass staring at the chandelier that was swinging overhead; due to the wind coming in from the window. He started counting the number of oscillations of the chandeliers, while simultaneously having his fingers on his wrist to count his heartbeat pulses. He noticed that the number of swings per pulse was the same regardless of the amplitude of the swings. This led to his equation of motion for a pendulum. What he did then is find a way to ‘count’ the real-world, transform it into numbers, and then find a pattern, a mathematical analogy, that describes the relationship between those numbers.

To understand the world, you have to first quantify it. This is crucial to remember because as many of us are constantly immersed in abstract descriptions of the world - theories and representations - we forget that the those abstracts emerged from a concrete world that was somehow quantified, then modeled and abstracted.

So what’s data-driven?

A faster way to crunch numbers

In that respect, science has always been data-driven: we observe the world, we collect data, we build models, and we make predictions. But now we can do all of that at a much larger scale, and much faster, thanks to computers.

The course bridges traditional scientific modeling with modern data-driven modeling techniques. We will see advances and examples in artificial intelligence, machine learning as applied to scientific modeling. What is AI? And how do those methods work?

We’re going to cover a variety of data-driven methods that are used in science and engineering.
In short, you will learn how to become a modern scientist/engineer who knows how to take advantage of modern modeling techniques to solve a wide variety or problems.

A few big questions we are trying to answer

The big questions we face when we try to model the world: high-dimensional, nonlinear, multiscale, etc.
The big questions about intelligence: what is human intelligence? What is artificial intelligence? What is the relationship between the two?
Empirical laws: what is the relationship between the force and the length of the spring?