Are Neural Networks About to Reinvent Physics?

Can AI teach itself the laws of physics? Will classical computers soon be replaced by deep neural networks? Sure looks like it, if you’ve been following the news, which lately has been filled with headlines like, “A neural net solves the three-body problem 100 million times faster: Machine learning provides an entirely new way to tackle one of the classic problems of applied mathematics,” and “Who needs Copernicus if you have machine learning?”. The latter was described by another journalist, in an article called “AI Teaches Itself Laws of Physics,” as a “monumental moment in both AI and physics,” which “could be critical in solving quantum mechanics problems.”

Gary Marcus & Ernest Davis | NAUTILUS

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The trouble is, the authors have given no compelling reason to think that they could actually do this.

None of these claims is even close to being true. All derive from just two recent studies that use machine learning to explore different aspects of planetary motion. Both papers represent interesting attempts to do new things, but neither warrant the excitement. The exaggerated claims made in both papers, and the resulting hype surrounding these, are symptoms of a tendency among science journalists—and sometimes scientists themselves—to overstate the significance of new advances in AI and machine learning.

As always, when one sees large claims made for an AI system, the first question to ask is, “What does the system actually do?”

The Three-Body Problem

The three-body problem is the problem of predicting how three objects—typically planets or stars—move over time under mutual gravitational force. If there are only two bodies, then, as Newton proved, the behavior is simple: Each of the objects moves along a circle, an ellipse, or a hyperbola. But, as Newton and his successors also determined, when there are three or more bodies involved, the behaviors can become very strange and complex. There is no simple mathematical formula; and accurate prediction over extended periods of time becomes very difficult. Finding good ways to calculate solutions to the three-body problem and the n-body problem (the same problem, with more objects) has been a major challenge for computational physics for 300 years. The  slew of “AI that solves the three-body problem” articles were based on an article in arXiv entitled “Newton vs The Machine: Solving The Chaotic Three-Body Problem Using Deep Neural Networks.”

As is often the case, the technical article is less over the top than the popular ones, but, for a technical scientific article, this one is still pretty ambitious. It ends with the prediction that techniques developed for a narrow case should extend both to the general three-body problem and then ultimately to the four- and five-body problems and other chaotic systems, which could conceivably constitute a genuine revolution.

The trouble is, the authors have given no compelling reason to think that they could actually do this. In fact, they haven’t even engaged in the full breadth of the existing three-body problem. Instead, they focused only on a special case of the three-body problem, involving three particles of equal mass starting from specified positions with zero velocity.

Even here, they are entirely dependent on a conventional physics engine or simulator—which is to say no AI, no machine learning, just traditional numerical solution of the differential equations of motion—to generate the trajectories of motion over time from 10,000 different starting positions.

The media enthusiasm is sending the wrong impression, making it sound like any old problem can be solved with a neural network.

They then used this classically-derived database as input, to train the neural network. In testing the neural network on new examples, whose true solution was also calculated by the simulator, they found that the neural network could predict the later positions of the particles with reasonable accuracy, orders of magnitude faster than the conventional simulator.

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