Los Alamos THOR Framework Uses Tensor Networks to Solve a Century-Old Physics Problem 400 Times Faster Than Supercomputer Simulations
Los Alamos and University of New Mexico researchers built THOR, an open-source tensor network framework that computes configurational integrals for crystalline solids 400 times faster than molecular dynamics simulations.
Predicting how atoms behave inside a material under heat and pressure is one of the foundational problems of statistical physics. The mathematics that governs those predictions, known as the configurational integral, has been understood in principle since the early twentieth century. In practice, evaluating the integral directly has been considered computationally impossible: the number of dimensions scales with the number of atoms in the system, and classical integration techniques would require more time than the age of the universe to process even a modest crystal.
For decades, scientists have relied on approximation methods such as Monte Carlo sampling and molecular dynamics simulations. These approaches work, but they demand enormous computational resources, often requiring weeks of supercomputer time to produce results for a single material under a single set of conditions.
A team at Los Alamos National Laboratory and the University of New Mexico has now demonstrated a fundamentally different approach. Their framework, called THOR (Tensors for High-dimensional Object Representation), uses tensor network algorithms to compress the high-dimensional configurational integral into a sequence of manageable smaller calculations, producing results that match state-of-the-art simulations but more than 400 times faster.
How tensor train decomposition sidesteps the curse of dimensionality
The core obstacle in computing configurational integrals is what mathematicians call the curse of dimensionality. A crystal with even a few hundred atoms generates an integral over thousands of dimensions. Evaluating it directly by sampling points across all those dimensions is infeasible because the number of required samples grows exponentially with the number of dimensions.
THOR circumvents this barrier through a technique called tensor train cross interpolation. Rather than attempting to evaluate the full high-dimensional integral at once, the method represents the integrand as a high-dimensional tensor and decomposes it into a chain of smaller, connected matrices. The algorithm identifies the most important structural features of the crystal and samples only those, dramatically reducing the computational load while preserving accuracy.
The framework also incorporates automatic detection of crystallographic symmetries. When atoms occupy equivalent positions in a crystal lattice, the symmetry reduces the effective number of independent variables that need to be computed, further compressing the problem.
Validated across three materials under extreme conditions
The research team, led by Los Alamos senior AI scientist Boian Alexandrov with lead author Duc Truong, tested THOR on three materials that present distinct computational challenges: copper, crystalline argon under extreme pressure in the gigapascal range, and tin undergoing a solid-to-solid phase transition between its alpha and beta crystalline forms.
In each case, THOR reproduced the internal energy and pressure-temperature curves generated by conventional molecular dynamics simulations. The tin phase transition calculation, which involves tracking how the material transforms between two distinct crystal structures as temperature changes, is particularly demanding for traditional methods because it requires sampling configurations near the boundary where both phases coexist.
The framework completed all three sets of calculations in seconds rather than the thousands of hours that molecular dynamics would typically require. Alexandrov described the result as replacing “century-old simulations and approximations of configurational integral with a first-principles calculation,” according to a University of New Mexico report on the research.
Why configurational integrals matter beyond the laboratory
Configurational integrals are not merely academic exercises. They underpin the prediction of thermodynamic properties such as free energy, entropy, and phase stability, quantities that determine whether a material will maintain its structure under the temperatures and pressures encountered in real-world applications. Aerospace engineering, semiconductor fabrication, and nuclear energy all depend on accurate phase diagrams to select materials that will perform reliably under extreme conditions.
Traditionally, generating a complete phase diagram for a single material has required running separate molecular dynamics simulations at each combination of temperature and pressure, a process that can consume months of supercomputer time. THOR’s speed advantage could compress that timeline from months to hours, enabling researchers to screen candidate materials far more rapidly.
Open-source availability and broader implications
The THOR framework is available on GitHub under an open-source license, hosted by Los Alamos National Laboratory. The research was published in Physical Review Materials, with co-authors including Benjamin Nebgen, Derek DeSantis, and Dimiter Petsev of the University of New Mexico’s Department of Chemical and Biological Engineering.
The work arrives as tensor network methods are gaining traction beyond their origins in quantum physics. Originally developed to simulate quantum many-body systems, tensor networks have in recent years been applied to machine learning, signal processing, and now classical statistical mechanics. THOR represents one of the most concrete demonstrations that these mathematical tools can deliver practical speedups in problems that have resisted efficient solution for a century.
Whether the approach can scale to amorphous or disordered materials, where the symmetry advantages that THOR exploits are absent, remains an open question. The researchers have identified extending the framework to non-crystalline systems as a priority for future work.