Machine Learning For Physicists- Machine learning (ML) is a field that is growing quickly, has many application areas, and has room for new ideas. The goal of this summary is to give scientists a simple introduction to the main ideas and tools in machine learning. The bias-variance tradeoff, gradient descent, regularization, overfitting, and generalization are some of the more basic ideas that are covered. More complicated supervised and unsupervised learning problems are then brought up.

Some of the topics discussed are variational methods, energy-based models like MaxEnt models and Restricted Boltzmann Machines, group models, neural networks, deep learning, clustering, and data visualization. The review emphasizes the clear connections between statistical physics and machine learning.

This study is unique in that it uses Python Jupyter notebooks. It introduces readers to modern machine learning and statistical packages through datasets like the Ising Model and Monte Carlo models of supersymmetric proton-proton collisions.

Code for “Machine Learning for Physicists

These resources go into great depth about the code used in the course. On the 2023 website, notebooks marked as “new” replace older versions, but older versions are kept for reference. The official website for the 2020 course and the more current website for the 2023 course both have slides, videos of lectures and tutorials, and summaries of what was taught in lectures.

All the code on this website (except for code by other people, like tSNE and MNIST, which is always clearly marked) was licensed under Attribution-ShareAlike 4.0 International (CC BY-SA 4.0). It used to be available under the terms of the MIT license. You can choose which license to use.

These sites are useful for anyone who wants to learn about modern machine learning methods like deep neural networks from a physics point of view. There are slides, movies, and code summaries that help break down complicated ideas and make them easier to use in real life.

Machine Learning For Physicists Key points

Physics-informed machine learning, or PIML, is a way to combine neural networks or kernel-based regression approaches to make mathematical physics models easier to use in situations with a lot of data, uncertainty, and dimensions.

Neural networks trained in physics are very good at solving ill-posed and inverse problems. By adding domain decomposition, they can be used on very large problems. These neural networks are helpful for adding real ideas to models for machine learning.

Some ideas for future research in this area are to create equivariant neural network architectures with built-in physical constraints, look into new intrinsic variables and representations, and use operator regression. These are all ways to make physics-based machine-learning models work better and faster.

Physics-informed machine learning background

Walter Pitts, a logician and cognitive psychologist, and Warren McCulloch, an American neurophysiologist, wrote a paper in 1943 that tried to map out how people think and make decisions scientifically. They gave us a way to talk about how the brain works in general terms and showed that simple parts linked together in a neural network can have a lot of computing power. The exact date that machine learning was created is unknown, but its past is often told through a number of important events.

Alan Turing, an English mathematician, said that the question of whether machines can think is “too meaningless” to be talked about. He came up with the “Turing Test” seven years later, in 1950, to see if a computer is really smart. Turing thought it was more important to see how well a digital computer could do in a game he called “The Imitation Game.” In this game, a human interrogator must tell the difference between a computer and a human subject within a certain amount of time by looking at how they answer different questions. “Thinking” computer’s success was measured by how likely it was to be mistaken for a person.

In the later part of that decade, in 1957, Frank Rosenblatt created the perceptron, the first neural network for computers that worked like the brain. After two years, Arthur Samuel made the first computer tool to help people learn, which was a game called “checkers.” The IBM computer used in this experiment got better at what it did as it played more, which showed that it had learned.

Strengths and limitations of physics-informed machine learning

One great thing about physics-based machine learning is how fast it works: it can produce results in milliseconds. The flow structure of the neural network makes the result of a new sample very useful. When the training works, the estimates are amazingly right.

The technology has some problems, however. Getting enough samples could be too expensive in some situations, and experts will only be able to train the technology well with enough data.

We may have millions of pictures of cats and dogs to train our systems, but let us say we know less about chemistry.

Also, self-driving cars make split-second choices based on billions of samples. However, in high-stakes situations, even a lot of samples might not be enough to eliminate all the possible deaths.

For self-driving cars to be safe, they need a huge amount of training data. It would be great if billions of hours of real driving video were fed into the system, but this is more challenging to do than it sounds because some events, like accidents or finding things on the side of the road, only happen sometimes.

Future applications of physics-informed machine learning

Personalized medicine could greatly benefit from using machine learning based on physics and from making new chemicals and materials.

Imagine having a tool that could make sure that a patient’s medication or drug therapy fits their needs based on their medical background and what their family has been through.

In the new field of personalized medicine, a person’s genetic profile is used to help make decisions about how to avoid illness, diagnose it, and treat it.

Scientists have found that many of the differences in how people respond to drugs are genetic. They have also found that things like age, nutrition, health, exposure to the environment, and other treatments can affect how well drugs work.

Neural networks that have been properly trained can find problems that a person would miss on their own, and physics-based machine learning could help by taking into account things that no one doctor or even a group of doctors might find.

These kinds of networks can do that because they can see connections between variables that are too complicated for a person to see. You can make this feature even better by teaching neural networks how to use counterfactual thinking.

It has a huge potential to improve experiment design: Researchers can tell machines what kind of study to do to reach a certain goal. Because these machines often make tests that no person could have thought of, they end up being better.

Can a physicist learn machine learning?

Physics majors are well suited as Machine Learning Educators due to their analytical and quantitative skills honed through rigorous training in complex problem-solving, mathematics, and statistics. Their experience in research and data modeling is beneficial for teaching practical aspects of machine learning.

This chance can be found in machine learning, a branch of artificial intelligence (AI) that is growing very quickly. A system called “machine learning” is one in which an algorithm or set of algorithms learns from data and changes based on that data. This is a lot like bringing physics to the real world. It is possible that machine learning is the best way to make sense of data that needs to be organized better or for which we need to know all the rules.

“Rather than building an algorithm or a model from a clear description of desired behavior,” says Chris Rowen, vice president of engineering for Collaboration AI at Cisco. “Machine learning is basically a system in which we provide a set of examples that define the desired behavior of the system.”

As Rowen said, let us say you need a computer that can tell the difference between a dog and a cat. You do not have to try to figure out what makes a dog a dog or a cat a cat using algorithms. Instead, you can use machine learning to train a general system with lots of pictures of dogs and cats. The system takes these inputs and figures out what traits of dogs and cats are important. Then, it comes up with an algorithm that can tell the difference between these two groups of inputs across a wide range of picture types.

How machine learning is used in physics?

ML has been used in processing satellite data in atmospheric physics [10], in weather forecasts [11], pre- dicting the behaviour of systems of many particles [6], discovering functional materials [12] and generating new organic molecules [13].

Cross-validation makes it less important to use just one training-test split, which might be off because of the randomness in the data. It gives a more accurate picture of how well the model works. The end measure of performance is usually found by taking the average of the results from all k runs. Cross-validation lowers variance by training and testing the model on different groups of the data. This gives a more accurate picture of how well the model will work on new data.

Overfitting can also be avoided with regularization methods such as L1 (Lasso) and L2 (Ridge) regression [22]. During model training, these methods add a punishment term to the loss function. This makes the coefficients smaller, which discourages making the model too complicated. Early stopping, dropout in neural networks, feature selection and dimensionality reduction, ensemble methods, and data augmentation are some other ways to stop overfitting. Data augmentation involves

• changing the existing data in ways like rotation,
• scaling, or
• flipping to make it look like it is bigger.

When overfitting is fixed, machine learning models can work better, be more reliable, and make more accurate predictions in the real world.

Researchers have used supervised learning methods to guess the Higgs boson’s mass, sort particles in particle physics experiments, and guess the weather and climate. In physics, supervised learning methods are mostly used to solve problems with regression and predicting time series [6]. 

Is machine learning important for physics?

Overview. Machine Learning (ML) is quickly providing new powerful tools for physicists and chemists to extract essential information from large amounts of data, either from experiments or simulations.

Data power the world we live in. Every time you walk past a security camera, tweet, buy something, or binge-watch something, that information is added to the data environment. You already know this, and you also know how important info is. However, you might not know that scientists and astronomers can use machine learning to make a big difference in the world thanks to all this data and improvements in semiconductor computing devices.

Machine learning is what makes photo filters, self-driving cars, online fraud detection programs, and language translation software work. It is a way to make sense of data that combines physics and astronomy skills, job possibilities, and the power to change the world. It powers cutting-edge studies to find and treat diseases, predict extreme weather, and other big problems that society has to deal with.

What is the relationship between physics and machine learning?

At the theoretical level, physics and machine learning are connected by the notion of scales. In both physics and machine learning, the problems we are attacking, be they image classification in machine learning, or the study of many body systems in physics, involve very large-scale phenomena.

A big area of study in machine learning is making artificial neural networks, which are computer programs that work like the brain. Our understanding of quantum mechanics grows every year, even though the models we use now are very general and basic. In the last ten years, we have made much progress toward building artificial neural networks that can describe quantum states and solve quantum many-body problems.

The Ising model is a well-known example of how machine learning is helping us learn more about quantum states. In the model, a magnet is in a ferromagnetic state below a critical temperature, where each atom in a grid has a specific spin direction. Above the critical temperature, the atoms are in a paramagnetic state, where the spin directions are random. Carrasquilla and Melko used Monte Carlo simulations to study machine learning that can quickly tell if a magnet is ferromagnetic or paramagnetic. They also found that the program could correctly predict the critical temperature for different lattices that had not been seen before.

What is physics aware machine learning?

Physics-aware machine learning (ML) combines classical, physics-based modeling approaches with ML methods to improve the generalization capabilities, interpretability, robustness, reliability and efficiency of ML methods in engineering applications.

Most of the time, first principles are used to model physical processes. In classical mechanics, Newton’s second rule, for example, talks about how an object moves when a force acts on it. Even though these equations give us useful information about physics, it can take a long time to solve high-fidelity models. On the other hand, low-fidelity models are made easier to understand. 

Data-driven methods have come up as flexible options that are also cheaper to run on computers. New developments in machine learning have made it possible to use data to model, recreate, and predict how physical systems will behave. These models are fine with making assumptions that are too simple, and more data can help them show how complicated the systems they are based on really are. Not so great about these models is that they are often “black boxes” that are tough to understand. 

Also, the data that is collected might need to be fixed by noise or hard to get because it costs a lot. We can use the huge amount of information we have in domain-specific physics in these situations. Physics-aware machine learning is a middle ground between methods that are based on first principles and those that are based on data. By adding knowledge about physics, machine learning models are pushed to find solutions that make sense physically and are not affected by errors in the data.

In the same month, PNNL made progress in differential equations, which are important in engineering for tasks like modeling and controlling industrial systems, where safety and performance are crucial.

In July 2020, PNNL released a neural network method based on physics that estimates the state and parameters of subsurface fluids with fewer data. This made subsurface modeling even better. This kind of research can help with things like cleaning up the Hanford Site in Washington state, which used to be a nuclear power plant but is no longer used.

At the same time, the lab showed a new way to train physics-based neural networks that take into account imperfect data. A group of scientists devised a way to use probability theory to help physics-based neural networks understand how noisy measurements affect determining a system’s state and identifying it in a number of different tasks. This can be especially helpful when using data from the real world, which always has some noise in it.