Lecture 01

Summary

The video script discusses the importance of computation in modern research and problem-solving across various fields. It highlights how computers aid in solving complex problems, from plotting and solving differential equations to simulating nonlinear phenomena like turbulence and quantum systems. The script emphasizes the role of computation in understanding data, complementing real-world experiments, and visualizing complex phenomena in physics, biology, and engineering. It also touches on the relationship between theory, experiment, and computation, and the growing significance of data science and machine learning in today's research landscape.

Takeaways

• 🖥️ Learning computation is essential for both advanced research and basic tasks, offering tools that complement traditional methods.
• 🔍 Computational methods allow us to solve complex problems that lack analytical solutions, such as non-linear systems and multi-body problems.
• 📊 While computers can solve equations and create visualizations, true understanding comes from interpreting the results.
• 🌍 Computer simulations complement real experiments, especially in fields like fluid dynamics, astrophysics, and material science.
• 🚀 Computers are crucial for visualizing complex phenomena and conducting numerical experiments, particularly when physical experiments are impractical.
• 🔬 Computational methods have revolutionized many fields, from astrophysics to biology, enabling the study of previously unsolvable problems.
• 🤖 Machine learning and data science are emerging as key tools for prediction and analysis in science, engineering, and business.
• 🌧️ Data science focuses on using historical data to make predictions, unlike traditional computation, which is based on physical principles.
• 🚗 Simulations are vital in various industries, such as automotive design, climate forecasting, and drug development.
• 🔗 The relationship between theory, experiment, and computation forms a cycle of observation, prediction, validation, and model refinement.

Q & A

Why is learning computation important beyond just being fun?

Learning computation is crucial for advanced research and even basic work, as it allows for plotting, solving differential equations, and handling complex problems that analytical methods cannot solve.

What is the significance of computation in fields like classical mechanics, electronics, or mechanics?

In these fields, computation is used for tasks such as plotting and solving differential equations, which were traditionally done analytically but can now be addressed more efficiently using computational methods.

How has the advent of computational tools impacted the way we approach problems in physics?

Computational tools have enabled us to solve problems that previously had no analytical solutions, such as those involving helium atoms and nonlinear oscillations, by using numerical methods and simulations.

What are some examples of problems that require computational methods due to their complexity?

Examples include the study of large molecules, the simulation of liquid metals in the car industry, and the modeling of atmospheric conditions for weather and climate forecasts.

How do computer simulations complement real-world experiments?

Computer simulations act as numerical experiments that can provide insights into phenomena that are difficult to observe directly, such as flow profiles in metals or the behavior of complex systems like the atmosphere.

What is the role of visualization in computational methods?

Visualization, including 3D visualization, is crucial in computational methods as it helps in interpreting data and understanding the results of simulations, which is akin to interpreting the results of an experiment.

How are computational methods applied in astrophysics?

In astrophysics, computational methods are heavily used to simulate and study phenomena such as fluid flows, astrophysical flows, weather and climate forecasts, and the physics of turbulence in celestial bodies.

What are some applications of computational methods in the field of materials science?

Computational methods are used in materials science to understand the stable structures of molecules, their energy levels, and interactions, often employing tools like density function theory and quantum Monte Carlo.

How does the relationship between theory, experiment, and computation form a cycle in scientific research?

The cycle begins with observations, which lead to the development of theories that make predictions. These predictions are then tested through experiments or simulations, and the results either validate or refine the theory, leading to a continuous cycle of improvement.

What is the difference between computation and data science, particularly in the context of making forecasts?

Computation is based on simulating and forecasting based on underlying physical principles, while data science focuses on using data to make forecasts without necessarily relying on physical principles, often employing machine learning techniques.

How is machine learning, as part of data science, being applied in various industries?

Machine learning is being used in industries such as e-marketing, where companies like Amazon and Google analyze consumer patterns to optimize advertising and inventory management, and in areas like self-driving cars and language translation services.

Outlines

00:00

🤖 Importance and Applications of Computational Methods

This paragraph discusses the significance of learning computation, emphasizing its utility in both advanced research and basic tasks. It highlights how computational methods have become essential for solving complex problems in science and engineering, where traditional analytical tools fall short. The speaker recommends learning to plot and solve equations computationally, as it aids in understanding and remembering syntax. The paragraph also touches on the limitations of current analytical tools, which are primarily designed for linear problems, and the need for computational methods to tackle nonlinear problems, such as those involving helium atoms or nonlinear oscillations. The speaker also introduces the concept of computer simulations as numerical experiments that complement real-world experiments, providing insights into phenomena that are otherwise difficult to observe directly.

05:01

🌐 Simulations and Visualizations in Various Fields

The second paragraph delves into the practical applications of computer simulations and visualizations across different fields. It starts by discussing the use of simulations to study phenomena that are not easily observable, such as the flow of liquid metals, which cannot be directly viewed with lasers. The speaker then moves on to discuss the importance of simulations in understanding atmospheric conditions, rainwater formation, and the use of 3D visualization for interpreting data. The paragraph also highlights the power of computers in simulating complex physical and biological phenomena, with examples from astrophysics, turbulence, and quantum systems. The speaker mentions the use of computational methods in understanding materials, nonlinear physics, and health-related issues, such as blood flow and drug design. The paragraph concludes by emphasizing the role of simulations in complementing real experiments and the importance of understanding the data and visualizations they produce.

10:05

🔬 The Interplay Between Theory, Experiment, and Computation

This paragraph explores the relationship between theory, experiment, and computation in the context of scientific discovery and understanding. The speaker describes a cyclical process where observations lead to the development of theories, which in turn make predictions that can be validated through further observations or experiments. The paragraph underscores the importance of predictability in a theory and the iterative process of refining models based on new observations. It also touches on the limitations of existing theories and the role of computer simulations in addressing these limitations, as seen in the study of phenomena like dark matter, dark energy, and fusion. The speaker also introduces the concept of data science, which, unlike computation, relies on data patterns rather than underlying physical principles for making predictions, and highlights its applications in various fields, including e-marketing and machine learning.

15:05

🚀 The Evolution of Scientific Inquiry and the Rise of Data Science

The final paragraph discusses the evolution of scientific inquiry, focusing on the shift from experiment-dominated fields to those where simulations play a significant role. It provides examples of how certain scientific areas, such as the study of superconductors and aerodynamics, have incorporated simulations to augment experimental data. The speaker also discusses the limitations of theories in explaining all observations, necessitating the use of simulations to better understand complex phenomena. The paragraph then contrasts computation, which is based on physical principles, with data science, which relies on data patterns to make predictions. The speaker concludes by emphasizing the growing importance of data science in both scientific research and business applications, such as e-marketing and machine learning, and acknowledges the shift towards data-driven approaches in various industries.

Keywords

💡Computation

Computation refers to the process of performing mathematical calculations, especially using a computer. In the context of the video, computation is essential for both advanced research and basic work, highlighting its utility in solving complex problems that cannot be addressed analytically. For instance, the script mentions using computation for solving differential equations and plotting in various scientific fields.

💡Analytical Computation

Analytical computation is the traditional method of solving mathematical problems using direct mathematical formulas and theorems. The video script contrasts this with modern computational methods, explaining that while analytical solutions were once the only way to solve problems like the hydrogen atom, today's complex problems often require computational approaches.

💡Nonlinear Problems

Nonlinear problems are those that involve variables whose relationship is not directly proportional, leading to more complex dynamics than linear problems. The script emphasizes that most available analytical tools are designed for linear problems, but for nonlinear problems like the helium atom or nonlinear oscillations, no analytical solutions exist, necessitating computational methods.

💡Perturbative Methods

Perturbative methods are mathematical techniques used to approximate solutions to complex problems by making small changes or perturbations to a known solution. The video mentions that these methods are used in both quantum mechanics and classical mechanics, but their coverage in courses has decreased due to the ease of computation.

💡Computer Simulations

Computer simulations are virtual models that replicate real-world conditions and allow for the observation of outcomes that would be difficult or impossible to achieve in physical experiments. The script describes simulations as numerical experiments that complement real experiments, providing insights into phenomena like liquid metal flow or atmospheric conditions.

💡Visualization

Visualization in the context of the video refers to the graphical representation of data or simulation results, which can be particularly useful in understanding complex phenomena. The script mentions 3D visualization as a powerful tool that allows researchers to see and interpret data more effectively.

💡Quantum Systems

Quantum systems are physical systems governed by the principles of quantum mechanics, which differ significantly from classical mechanics. The script discusses the use of computational methods like density functional theory and quantum Monte Carlo to understand the properties and interactions of molecules in quantum systems.

💡Nonlinear Physics

Nonlinear physics deals with systems in which the response to input is not directly proportional to the input, leading to complex behaviors. The video script cites blood flow in the heart and the study of turbulence as examples where nonlinear physics plays a crucial role in understanding and simulating these phenomena.

💡Machine Learning

Machine learning is a subset of artificial intelligence that enables computers to learn from and make predictions based on data. The script touches on machine learning's applications in various fields, such as self-driving cars, e-marketing, and Google translation, highlighting its importance in modern research and industry.

💡Data Science

Data science is an interdisciplinary field that uses scientific methods, processes, and algorithms to extract knowledge and insights from data. The video differentiates data science from computation by emphasizing its focus on data-driven predictions rather than simulations based on underlying physical principles.

💡Lattice Quantum Chromodynamics

Lattice quantum chromodynamics (QCD) is a computational approach to studying the strong force in particle physics by discretizing spacetime into a lattice. The script mentions its use in simulating phenomena like fusion and understanding complex physics that cannot be easily analyzed through traditional theoretical frameworks.

Highlights

Computation is essential for both advanced research and basic work, including solving differential equations and plotting.

Computational tools are indispensable for fields like classical mechanics, electronics, and quantum mechanics.

Analytical computation is limited to simple problems like the hydrogen atom; computers allow for solving more complex systems.

Learning to plot and solve equations computationally aids in syntax retention and better understanding of concepts.

Most current analytical tools are designed for linear problems, making computation crucial for tackling nonlinear issues.

Beyond simple harmonic oscillators and the hydrogen atom, analytical solutions are unavailable, necessitating computational methods.

Computational methods, such as perturbative methods, are supplementary to analytical tools for complex problems.

The availability of computers has reduced the need for complicated mathematical methods, simplifying problem-solving.

Computer simulations are akin to numerical experiments, requiring model development and interpretation of results.

Visualization through computers, such as 3D visualization, aids in better understanding and interpretation of data.

Real-world applications of computation include weather forecasting, fluid dynamics in vehicles, and astrophysics.

In astrophysics, computation is heavily utilized for simulating phenomena around stars, black holes, and galaxies.

Computational tools like density functional theory and quantum Monte Carlo are used for understanding quantum systems.

Nonlinear physics and health research, including blood flow and drug design, benefit significantly from computational methods.

Machine learning, a subset of data science, leverages data for predictions without relying heavily on underlying physical principles.

The relationship between theory, experiment, and computation forms a cycle, with each aspect informing and validating the others.

Data science, including machine learning, is distinct from computation, focusing on data-driven forecasts rather than physical simulations.

The transcript highlights the importance of computation across various scientific disciplines and its role in solving complex, real-world problems.

Transcripts

Okay, so one question is, why do we learn computation?

Is it advantageous or is it just for fun now?

Okay, of course it is for fun.

But he's also very useful right now for advanced research, for even basic work, we need to

computing right now.

So the so just to tell you that you may be doing other courses like classical mechanics,

electronics or mechanics.

So you can use plotting some solving differential equation.

Earlier, we used to do this analytical computation only know so hydrogen atom.

He do solve analytically.

Now, we can also solve it on a computer.

And we can look at the results.

So I would say strongly recommend that once you learn few things like plotting, solving

equations, you should use it.

And that's where you also kind of learn this keep remembering the syntax.

And it makes you even better and you can connect things and okay.

Anyway, so for advanced research, we should keep in mind that the problems at present

in science and engineering both are quite complex.

And so present available analytical tools don't work.

Most of the tools developed are for linear problems, the linear PDE linear ODE, linear

algebra, so they don't work for nonlinear problems.

So then we need to basically what are the problems we solve?

linear oscillator, simple harmonic oscillator, which is linear problem and hydrogen atom.

Solved both in classical mechanics and quantum mechanics, okay, so in physics, you may know

this, or every student would have fair idea about these two problems.

But beyond it, we have simply no analytical solution.

So, for helium atom, there's no solution.

Okay, as soon as you put nonlinear oscillations, then there's no analytical solution.

So, the idea is that you go for either mathematical tools like perturbative methods, and quantum

mechanics, you've seen that there's a perturbative methods.

Classical mechanics too has this method, but normally we don't cover it in courses now.

One reason why we don't cover it because computations have become very easy in the sense because

computers are available.

They're good programming languages, you can do things very easily.

So why do extremely complicated math, you simply get the result by solving those equations.

Okay, so this one reason I mean, okay, so this is also for simple things, as well as

for complex things, like, I want to understand large molecules, then I use computational

methods.

Now, so computer simulations are like numerical experiments.

So it is basically experiment and you need to do more work for making models.

So understanding is not coming from computer.

So please keep in mind that computers are only helping us solve those equations.

But to understand, you need to understand the solution, you need to understand the data,

understand the plot.

So computer can plot it, but then you have to see what those plot means.

So it's like experiment.

So I'm going to say a little bit more a little bit later.

So we make made models on based on numerical results.

Often simulations or computer experiments complement the real experiment.

So the example I can give you is we can work with liquid metals.

Okay, so liquid metals like mercury or molten iron.

So for example, in car industry, we have, we work with molten materials.

So you can do experiments with them, I mean apply magnetic field to see the flow, what

happens to the flow, at what temperature it starts boiling.

That's one but if you want to look at the flow profile, metals you can't really see

through lasers because the laser cannot go through the metals.

It will go through air and water but not through metals.

Then simulations become very handy.

Okay, we can do experiments on parts of the atmosphere, not all of the atmosphere.

So for all of atmosphere, if you want to do it, then we need computer simulations.

Sometimes even for like, given system like rainwater formation, we complement both experiments

and simulation.

So we need to do both.

Okay, so also computers give very, it gives you an avenue for visualization.

Now we can do 3D visualization.

So it's really very nice to be able to see what the data is telling us.

So this way, we need to do both real experiment as well as computer experiments.

And computers have become very powerful.

At present, we can really simulate very, very complex physical phenomena or biological phenomena.

So many unsolved problems are being solved using computers right now.

So there are some examples which I gave you is I'm giving right now is turbulence and

computational astrophysics.

Okay, there are many, many more.

I mean, in biology, there are tons of them in engineering also.

So there are huge amount of things which remain unsolved, which we are able to solve now using

computers.

So just let's go through applications in physics.

Okay, I mean, there are much more than what I'm going to show you in the slides, but it

will give a fair idea where computers are heavily used.

So flows with something which I work on.

So flow all around us, fluid flows, astrophysical flows.

So weather and climate forecast, this is one place where without computers we can't do

anything.

So that's one, you understand when you simulate the whole weather system and forecast for

rain temperature, climate forecast is for 100 years and so on.

Now flows around automobiles, aeroplanes, space vehicles, rockets, oil exploration.

So we are looking for oil inside the earth, but you simulate, of course, you can get some

data from the from within the earth, but there's a lot of simulations are done.

Physics of turbulence, we can simulate turbulent flows, flows in and around stars, black holes,

galaxies, planets.

Yeah, so in astrophysics is heavily used.

Quantum turbulence is one interesting example where in quantum systems, there is turbulence,

like superfluid is an example where you see turbulence.

So that comes under quantum turbulence.

So I will not get into that well, there's one example which I'm going to give you when

I cover Schrodinger equation, but people are using computers for solving these systems.

Now materials and quantum systems.

So all kinds of materials, beat, polymers, large molecules, you know, or strong materials,

like for aeroplanes, we want strong and light materials, drugs, we want medicines.

So for these a tool used is the density function theory often, and also quantum Monte Carlo.

So these are tools, we will not cover it in this course, but you may be hearing these

words.

So these are the tools which are used for simulating quantum systems or understanding

quantum systems.

So they give you an idea what is the stable structure among the molecules?

What are the energy levels of the molecule, how the molecules interact with each other,

all that is done using this.

Now nonlinear physics and health.

So here also the nonlinear physics flows is important thing.

Also health, like blood flow is an important problem in heart how the blood is flowing.

If it in evolution for in Covid times it is very critical, a drug design, understanding

the brain.

So there are projects now going on in universities, where people are trying to simulate full 10

power 11 neurons, okay, and how they are firing and they're trying to process images, memory,

memory is a big problem in brain, how do you remember things?

Image processing, so all that is being done right now.

So social network, everybody's aware of the computer networks, biological networks.

So this is an important topic of research.

Human body, like I said, would heart, digestive system, you can simulate them and you can

get some insights.

Earthquake, this is one more place where there's one challenge how to predict earthquake and

there are work going on in the direction.

Now machine learning has become very important area of research at present.

So we'll not do machine learning in our course, but examples are, everybody knows about self

driving cars.

These are using machine learning.

So it basically, it collects data while driving, then it learns and it becomes better and better

drivers.

E marketing, like Amazon is using shopping pattern, and then trying for advertising,

their inventory management and so on.

Google translation.

So the right now the captions in YouTube for any movie if you see, so all they are automatic

from speech to text.

That's machine learning, French to English or vice versa.

So that's all based on machine learning.

So it's, well, this would be N here.

So machine learning is a big thing in science and engineering.

Defense is important.

You can see for aircraft designs, image processing, terrain mapping and so on.

Economics, of course, banking, stock market, okay.

Complex physics, again, so flows is something which I wanted to say, they are complex anyway.

What are other complex systems?

In inverse, you see dark matter, dark energy, inverse.

Fusion is one more example, but I mean, all complex things which we don't understand is

complex physics.

A brain, brain is a complex system.

Okay.

Fusion is a colliding of two nuclei in the fuse and they generate energy.

So that's why the fusion is important.

So in nuclei, so the simulated using lattice quantum chromodynamics, the lattice QCD.

So these are all being worked out in computers.

So in particle physics is accelerator simulations.

So basically, you collect all the data, analyze it.

So when any scattering of two particles, they generate a huge amount of data and we need

to use computers for analyzing the data.

It's all automated.

So now, so you may ask, what is the relationship between theory, experiment and computation?

N is missing here.

So this is a cycle.

So we observe certain physical observation.

So observation could be by experiment or by looking at by naked eye or a telescope.

So experiment doesn't mean that you do it in your lab.

Experiment could also be just observing a phenomena.

In astrophysics, we normally don't do the experiment, but you observe.

In biology also, you basically observe things or do computer simulation.

So you can also do computer simulation and observe how things are evolving.

That's another experiment.

Now, given the observation, you construct a theory that explains observation and make

a prediction.

So it makes a prediction.

So for example, Newton's laws, it made predictions about the orbital motion of the planets, how

the planets, I mean, there are some three body interaction, tidal motion, all these

are predictions and they were found to be reasonably good with the observation.

So prediction and observations go hand in hand and that's how we validate a theory.

So there must be predictability in a theory.

So once you predict, then you validate it.

If the experiment can result in predictions match, then theory is good.

Otherwise, you make a new model.

This model is no good.

It doesn't explain the observation, all the observation.

So you make another model.

So you go on like this and you try to better the model.

But sometimes the model was good for 100 years, but then suddenly some observations come either

by experiment or now computer simulation and it turns out that this theory is not able

to explain the observations.

So it happened for Newton's laws, Newton's framework of mechanics.

So Einstein's new relativity came or quantum mechanics came.

So these new things came because those models were not good enough to explain the observation.

So some examples I can give you.

So superconductor is where experiments were there, which happened many years back, last

century, early last century.

So here experiment was dominant.

Now of course simulations are done for new superconductors.

Aeroplane is the place where both experiment and simulations are roughly 50-50.

There are some simulation experiments.

Whether an inverse is essentially more simulations.

So you can see that which part is dominated by numerical simulations.

There are theories, but I mean we need to do much more than, well theories are not powerful

enough to capture the observations.

There are, I mean they said there are theory for stars, but they are not good enough.

They cannot explain the magnetic field or they cannot explain the various phenomena

we observe on X-ray emission and so on.

So we need to simulate, there is no other option.

Theories are very limited.

They have very limited predictions.

Now so there is new thing called data science.

Now right machine learning is part of data science.

So what is the difference between computation and data science?

Though we are focusing on computation in this course, but we should know the difference.

So computer science is simulate and forecast based on underlying physical principles.

So one example is why predicts occurrence of rain.

So that rain occurrence can be done by simulating the velocity field, humidity, temperature

and making a forecast.

Now but you start with physical principle.

Now in data science, the idea is that you use the data to make a forecast.

So you collect 100 years of data of temperature, humidity, wind patterns and see whether it

led to rain and not rain.

And from that pattern of the data, you see whether tomorrow there will be rain.

So that is basically data, not much, well basically you don't worry too much about physical

principles, just based on data and data model.

So this is done for fog prediction, rainfall predictions.

So both these things are being used.

Now data science is being heavily employed for science as well as for business.

E-marketing is like Amazon, Google they are using heavily by seeing my search pattern,

marketing pattern, shopping pattern, they give advertising like yeah so e-marketing

is hugely using machine learning.

So these are just based on data.

Thank You.