Recent strides in machine learning (ML) research have led to the development of tools useful for research problems well beyond the realm for which they were designed. The value of these tools when applied to topics ranging from teaching robots how to throw to predicting the olfactory properties of molecules is now beginning to be realized. Inspired by advances such as these, we undertook the challenge of applying TensorFlow, a computing platform normally used for ML, to advance the understanding of fundamental physics.
Perhaps the biggest open problem in fundamental theoretical physics may be that our current understanding of quantum mechanics only includes three of the four fundamental forces — the electromagnetic, strong, and weak forces. There is currently no complete quantum theory that also includes the force of gravitation, while still matching experimental observations, i.e., an accurate model of quantum gravity.
One promising approach to a unified model that includes quantum gravity, which has survived many mathematical consistency checks, is called M-Theory, or "The Theory formerly known as Strings,” introduced in 1995 by Edward Witten. In the everyday world, we all experience four dimensions—three spatial dimensions (x, y, and z), plus time (t). M-Theory predicts that, at very short lengths, the Universe is described, instead, by eleven dimensions. But, as one can imagine, establishing the connection between the four-dimensional world that we observe and the 11-dimensional world predicted by M-theory is exceedingly difficult to solve analytically. In fact, it might require analytic manipulation of equations having more terms than there are electrons in the Universe.
This summer, we published an article in the Journal of High Energy Physics where we introduced novel ways to address such problems through creative use of ML technology. Using simplifications enabled by TensorFlow, we managed to bring the total number of known (stable or unstable) equilibrium solutions for one particular type of M-Theory spacetime geometries to 194, including a new and tachyon-free four-dimensional model universe. The geometries that we studied are special in that they are still (barely) accessible with exact calculations that do not require neglecting potentially important terms. We have also released a short instructive Google colab as well as a more powerful Python library for use in related research.
Applying TensorFlow to M-Theory
This work is predicated on a key observation that a mixed numerical and analytic approach can be more powerful than a purely analytical method. Instead of attempting to find analytic solutions with brute force, we use a numerical approach that leverages TensorFlow for the initial search for solutions to the model. This then yields hypotheses on which specific combinations can be tested and analyzed with stringent mathematical methods, ultimately proving the actual existence of a conjectured solution. This represents a novel methodology for making further progress in theoretical physics.
We hope that these results will be an important step in interpreting M-theory, and demonstrate how the research community can use new ML tools, such as TensorFlow, to approach other similarly complex problems. We are already applying the newly discovered methods in further theoretical physics research.
This research was conducted by Iulia M. Comşa, Moritz Firsching, and Thomas Fischbacher. Additional thanks go to Jyrki Alakuijala, Rahul Sukthankar, and Jay Yagnik for encouragement and support.