In the quest to understand the hidden forces shaping our world, physicists and materials scientists often find themselves battling with immense mathematical complexity. Every interaction inside a material—from the way heat moves through it, to how it expands when warmed, to the sudden transformations it undergoes at critical temperatures—is governed by the strange and intricate laws of quantum mechanics.
Yet, decoding these laws is no easy feat. For decades, scientists have relied on painstaking supercomputer calculations to simulate quantum interactions, often requiring days or weeks of computational time. Now, researchers at the California Institute of Technology (Caltech) have unveiled a breakthrough: an artificial intelligence (AI)–driven method that makes these calculations thousands of times faster while preserving accuracy.
This innovation could open the door to a new era of materials discovery, where encyclopedic knowledge of quantum interactions is not just a dream but a practical reality.
The Quantum Dance of Phonons
To understand the significance of this breakthrough, it helps to picture the tiny stage where it plays out. Inside every solid material, atoms are not rigidly fixed but vibrate constantly, like dancers in an intricate, invisible ballet. These vibrations, called phonons, are quantum mechanical particles of sound and heat.
Phonons are not just a curiosity—they are central to how materials behave. They determine how heat flows, why metals expand when heated, and why some materials undergo dramatic transformations known as phase transitions. In advanced technologies, from semiconductors to superconductors, phonons often hold the key to performance and functionality.
But there’s a challenge. Phonons interact with each other in extraordinarily complex ways. When two or more phonons collide or merge, the interactions can be represented mathematically by high-dimensional objects called tensors. As the number of phonons increases, these tensors explode in complexity, quickly overwhelming even the fastest computers.
As Marco Bernardi, Caltech professor of applied physics, physics, and materials science, puts it: “The calculations for four-phonon interactions are a nightmare. For complex materials, this task would involve weekslong calculations. Now we can do them in 10 seconds.”
Harnessing the Power of AI
Bernardi and his graduate student, Yao Luo (MS ’24), set out to tackle this computational bottleneck. Their earlier work introduced mathematical shortcuts to simplify electron-phonon calculations using a method called singular value decomposition (SVD). But the case of phonon–phonon interactions was even tougher.
Inspired by advances in machine learning, the team developed a new approach that treats phonon tensors not as insurmountable obstacles but as patterns waiting to be uncovered. They employed a method known as CANDECOMP/PARAFAC tensor decomposition, a technique that breaks down giant tensors into simpler building blocks.
But adapting this method to the quantum world was no trivial task. The phonon problem comes with strict physical symmetries, and the AI needed to learn within those constraints. The researchers designed a neural network capable of identifying the most essential features of these tensors while discarding redundant information.
By training the AI on supercomputers equipped with GPUs, they taught it to compress the impossibly large tensors into highly efficient forms. Remarkably, only a handful of terms are needed to accurately capture the full quantum behavior.
The result? A reduction in computational time by factors of 1,000 to 10,000, transforming calculations that once required days into results delivered in seconds.
Why This Matters
The implications of this breakthrough extend far beyond efficiency. By unlocking the ability to compute phonon interactions at lightning speed, scientists can now explore vast libraries of materials with unprecedented depth.
High-throughput materials discovery—where thousands of candidate compounds are screened to identify the most promising for technologies like thermoelectrics, superconductors, or quantum computers—depends on rapid, accurate calculations. With this AI-based method, researchers can finally perform such screening for thermal physics and heat transport, domains previously too computationally demanding to explore at scale.
In practical terms, this could accelerate the search for better materials to manage heat in electronics, design efficient energy systems, or build the next generation of quantum devices.
A Vision for the Future
Bernardi’s ambitions reach even further. While the current focus is on phonon interactions, the same approach could be generalized to compress and learn all quantum interactions in materials, including those involving electrons, excitons, magnons, and beyond.
“My vision right now is to compress all different types of quantum interactions and high-order processes in materials with similar techniques,” Bernardi says. “The key will be to bypass the formation of large tensors altogether and to learn the interactions directly in compressed form.”
Such a future would mean physicists are no longer held back by computational barriers. Instead, they could access a near-complete map of how particles behave in real materials—an encyclopedia of quantum behavior that could revolutionize physics, chemistry, and engineering.
The Team Behind the Breakthrough
The study, titled “Tensor Learning and Compression of N-phonon Interactions” and published in Physical Review Letters, is the product of a collaborative effort. Alongside Bernardi and Luo, contributors include Dhruv Mangtani, who worked on the project as a SURF student; Shiyu Peng, a postdoctoral scholar; and Caltech graduate students Jia Yao (MS ’25) and Sergei Kliavinek.
Together, they have demonstrated not only a novel computational technique but also a new way of thinking about the relationship between physics and AI: not as separate fields, but as partners in discovery.
The Human Side of a Quantum Revolution
Beyond the technical details lies a story of perseverance and imagination. Scientists have long struggled with the seemingly impossible complexity of quantum interactions. Where traditional methods hit a wall, Bernardi and his team saw opportunity. They combined physics, mathematics, and artificial intelligence to create a bridge over that wall, showing once again the power of human curiosity when paired with modern technology.
At its heart, this research is about more than tensors or algorithms. It’s about unlocking the secrets of matter itself, about daring to ask how far we can go in decoding the universe’s rules. And with AI as a new ally, that quest may be moving into its most exciting chapter yet.
More information: Yao Luo et al, Tensor Learning and Compression of N-Phonon Interactions, Physical Review Letters (2025). DOI: 10.1103/nmgj-yq1g link.aps.org/doi/10.1103/nmgj-yq1g. On arXiv: DOI: 10.48550/arxiv.2503.05913
