Machine learning discovers unexpected behavior in superlattices

As cell phones and other electronics get smaller and more powerful, dissipating heat becomes a vital issue. Prof. Xiulin Ruan's lab focuses on the nanoscale, where many principles of heat transfer are still unknown. Using machine learning, they have discovered that certain configurations of materials called "superlattices" conduct heat in unexpected ways.



“When we go down to the nanoscale, traditional heat transport theories start to break down, and new physics start developing,” said Prabudhya Chowdhury, Ph.D. student in mechanical engineering under Prof. Ruan.  "My research uses atomic simulations to understand how heat is transported across materials at such small scales.”

Specifically, Chowdhury studies superlattices, alternating layers of materials that can be as small as 0.5 nanometers thick.  His study focuses on silicon and germanium, elements often found in cell phones and other electronics.  Arranging these two different materials in a superlattice structure alters how heat travels through the system on the molecular level.

“A superlattice might be what we call periodic, meaning that each layer is the same fixed-length thickness, just alternating back and forth,” explained Chowdhury.  “In an aperiodic superlattice, the layers are all different random thicknesses.  We found that if we randomize the thickness, we generally go down in thermal conductivity, which was our target.”

But as their results show, the solution is not entirely that simple.  “You’d expect that as you go to more and more random structures, you’d get lower and lower thermal conductivity,” said Chowdhury.  "People believed this because there were an untrackable number of random structures, and no way to check them one by one."  To accelerate the speed of the search, their team (in collaboration with the Lockheed Martin Corporation and Oak Ridge National Laboratory) used a variant of machine learning called a genetic algorithm, in which computers mimic the natural selection process found in nature to consistently return better and better results.  “We could run a hundred simulations in parallel in just a few hours, and then feed that data back into the algorithm and get even better solutions, and then keep repeating that process.  This was only possible because of the high-performance computing cluster we have here at Purdue.  We found that moderate, instead of largest, randomness gives the best results. Such unexpected results were only made possible with the machine learning algorithm used."

Their research has been published in the journal Nano Energy.

Finding the ideal level of randomness of these superlattices is just the beginning of this research.  Right now, they are only able to focus on superlattices with two materials, with a smooth interface between them.  But the same process could apply to rough interfaces, or superlattices with three or more materials.  Moreover, the results of such simulations on various systems can then be validated by experimentalists using advanced nanoscale fabrication and measurement techniques.

Their end goal goes beyond just improving the performance of cell phones and electronics.  Chowdhury sees this fundamental research being used in thermoelectric generators, a technology that converts heat flux into electrical energy.  These devices have seen specialized use (in spacecraft, for example) but the technology is not yet developed enough to compete with current fossil fuel sources.  “There is big potential in thermoelectric generators as an alternative energy source,” said Chowdhury.  “If we can make these thermal conductivity systems efficient enough, there can be a push toward industrializing and commercializing them, which will only push the research even further.”

Chowdhury likes to quote a line from his professor, Xiulin Ruan: “Exceptions are how science is driven forward.  By discovering exceptions to theories that were widely accepted before, that is how we drive new knowledge forward. Machine learning has great potential to assist humans to accomplish this.”


This work was sponsored by the Defense Advanced Research Projects Agency (DARPA), with Dr. William Carter as the Program Manager.


Writer: Jared Pike, 765-496-0374,

Source: Xiulin Ruan, 765-494-5721,


Machine learning maximized Anderson localization of phonons in aperiodic superlattices
Prabudhya Roy Chowdhury, Colleen Reynolds, Adam Garrett, Tianli Feng, Shashishekar P. Adigab, Xiulin Ruan

Nanostructuring materials to achieve ultra-low lattice thermal conductivity has proven to be extremely attractive for numerous applications such as thermoelectric energy conversion. Anderson localization of phonons due to aperiodicity can reduce thermal conductivity in superlattices, but the lower limit of thermal conductivity remains elusive due to the prohibitively large design space. In this work, we demonstrate that an intuition-based manual search for aperiodic superlattice structures (random multilayers or RMLs) with the lowest thermal conductivity yields only a local minimum, while a genetic algorithm (GA) based approach can efficiently identify the globally minimum thermal conductivity by only exploring a small fraction of the design space. Our results show that this minimum value occurs at an average RML period that is, surprisingly, smaller than the period corresponding to the minimum SL thermal conductivity. Above this critical period, scattering of incoherent phonons at interfaces is less, whereas below this period, the room for randomization becomes less, thus putting more coherent phonons out of Anderson localization and causing increased thermal conductivity. Moreover, the lower limit of the thermal conductivity occurs at a moderate rather than maximum randomness of the layer thickness. Our machine learning approach demonstrates a general process of exploring an otherwise prohibitively large design space to gain non-intuitive physical insights.