🔬 materials science

Agentic Global Optimization of Site-Disordered Crystalline Materials

This paper introduces an agentic global optimization framework that utilizes surrogate models to efficiently identify the lowest-energy atomic orderings in site-disordered crystalline materials, demonstrating superior accuracy and a 4.3-fold reduction in computational cost compared to traditional search methods across diverse crystal structures.

Original authors: Martin Hoffmann Petersen, Zekun Ren, Kedar Hippalgaonkar

Published 2026-11-02

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CC BY 4.0

Original authors: Martin Hoffmann Petersen, Zekun Ren, Kedar Hippalgaonkar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Crystals are the ordered building blocks of the solid world, from the salt in a shaker to the silicon in a computer chip. In an ideal crystal, atoms sit in a perfect, repeating pattern, like soldiers in a formation. However, the materials that power our modern world are rarely perfect. Scientists often deliberately mix different types of atoms into the same spot in the pattern to change how the material conducts electricity or stores energy. This mixing creates a state called disorder, where the specific arrangement of atoms is not fixed but varies from place to place. The problem for researchers is that even a small amount of mixing creates a staggering number of possible arrangements. To understand how a material will actually behave, scientists must find the single arrangement that is the most stable and lowest in energy. Traditionally, finding this perfect arrangement has been like searching for a needle in a haystack by checking every single possibility one by one, a process that is slow, expensive, and often impossible for complex materials.

A team of researchers has now developed a smarter way to solve this puzzle, treating the search for the best atomic arrangement as a problem of intelligent decision-making rather than brute-force calculation. Instead of blindly testing random combinations, they created a computer system that learns as it goes. This system builds a mental map of the energy landscape based on the few arrangements it has already tested. With each new test, the system decides which arrangement to check next by balancing three goals: looking for a better version of the best arrangement it has found so far, exploring areas where it is unsure about the energy, and trying something completely new to avoid getting stuck in a local dead end. This approach, which the authors call an "agentic" search, allows the computer to act like a seasoned explorer who knows when to follow a promising trail and when to venture into the unknown.

The researchers tested this method against three older, more traditional ways of searching: a random walk that picks arrangements by chance, a statistical method that accepts worse options occasionally to escape local traps, and a genetic algorithm that mimics evolution by mixing and mutating good arrangements. They ran these tests on fourteen different crystal structures, ranging from simple metal alloys to complex compounds used in batteries. For every single test case, the researchers knew the true answer beforehand because they had calculated every possible arrangement for these specific systems. The results were striking. The new intelligent search found the perfect, lowest-energy arrangement in 94 percent of its attempts, whereas the traditional methods succeeded less than 56 percent of the time. More importantly, the intelligent search was far more efficient. On average, it needed only a fraction of the computer time to find the answer. The best version of the new method, which uses a specific type of statistical model, required about four times fewer calculations than the best traditional method to reach the same result.

One of the most compelling tests involved a material called Na2/3FePO4, which is relevant for battery technology. This material is particularly difficult because it has two types of disorder happening at once: some spots are missing sodium atoms, and the iron atoms in other spots have different electrical charges. These two problems are linked, meaning a change in one affects the other. The researchers applied their intelligent search to this complex system, encoding the electrical charge information directly into the model. Despite the massive number of possible arrangements—estimated at hundreds of billions before simplification—the system successfully recovered the exact atomic ordering that scientists have observed in real experiments. It found this correct structure in just 75 attempts, a number that would be impossible to reach by checking every possibility.

The study demonstrates that the key to solving these difficult material science problems is not just having faster computers, but having smarter ways to choose what to calculate. By using a model that learns from its own history, the researchers showed that it is possible to navigate vast, complex landscapes of atomic possibilities with remarkable speed and accuracy. While the method is not a magic bullet that solves every problem instantly, it provides a reliable and efficient tool for discovering the hidden structures that determine how materials work. The researchers found that a specific statistical approach, known as Bayesian ridge regression, was the most consistent performer, succeeding in every single run across all the different materials they tested. This suggests that for scientists trying to design new materials, the future lies in adaptive search strategies that can learn and evolve alongside the data they collect.

Technical Summary: Agentic Global Optimization of Site-Disordered Crystalline Materials

Problem Statement
Site-disordered crystalline materials, where multiple elements partially occupy the same atomic site, present a significant challenge for atomistic simulation. Because partial occupancy prevents a straightforward description of the electronic configuration at Wyckoff sites, simulations cannot proceed without first resolving an explicit atomic ordering. The number of possible orderings grows combinatorially with supercell size, making the identification of the global-minimum energy ordering a costly combinatorial search problem. Traditional approaches like cluster expansion (CE) and special quasirandom structures (SQS) are valuable for capturing phase transitions but are not designed as general search procedures for locating a single globally optimal ordering. Furthermore, while Machine Learning Interatomic Potentials (MLIPs) have accelerated energy evaluations, they remain a computational bottleneck for large disordered systems, necessitating optimization algorithms that minimize the number of required energy evaluations.

Methodology
The authors propose an "agentic" search framework where an autonomous loop plans, acts, and updates its strategy based on observed outcomes. Instead of relying on fixed sampling policies, the agentic approach fits a surrogate model to previously evaluated configurations and selects subsequent candidates by balancing three factors: exploitation (current best estimate), uncertainty (estimate reliability), and novelty (diversity relative to explored configurations).

The study implements and benchmarks four agentic surrogate models within a shared framework:

ExtraTrees ensemble: A random forest variant using extremely randomized trees.
Bayesian ridge regression: A linear model with an isotropic Gaussian coefficient prior.
Sparse ARD (Automatic Relevance Determination) regression: A linear model with separate prior precisions for coefficients, employing a pruning mechanism.
ALiEGNN-inspired graph ensemble: A compact graph neural network ensemble trained from scratch on bootstrap samples of the run history.

These are compared against three traditional global optimization baselines:

Random walk: Generates candidates via random swaps without energy-directed proposals.
Markov chain Monte Carlo (MCMC): Uses a fixed acceptance probability for uphill moves ( $P_{acc} = 0.3$ for $\Delta E > 0$ ).
Genetic Algorithm (GA): Uses roulette-wheel selection, crossover, and mutation on a population of 20 structures.

All methods utilize the same energy evaluator (TensorNet-MATPES-PBE-v2) and are constrained to a maximum budget of 200 energy evaluations per system. The benchmark spans 14 test cases across 12 distinct crystal structures, with ground truth established by exhaustive enumeration of all symmetry-inequivalent configurations.

Key Results

Success Rate: The agentic surrogates successfully locate the global minimum in 94.3% of runs (264 out of 280), compared to 55.2% for traditional methods (116 out of 210).
Efficiency: The agentic surrogates require significantly fewer evaluations. The best agentic surrogate (Bayesian ridge regression) achieves a median 4.3-fold reduction in evaluations relative to the best traditional method (Genetic Algorithm).
Surrogate Performance:
- Bayesian Ridge Regression: Emerges as the most robust and consistent method, reaching the global minimum in all 70 runs with the fewest average evaluations (19.5 ± 11.1). It outperforms the GA in every single system tested.
- Sparse ARD: Is the fastest method in 8 of the 14 systems but shows higher variability and lower robustness in others.
- ExtraTrees and ALiEGNN: Perform well but generally require more evaluations and show greater variability than Bayesian ridge.
Statistical Significance: A one-sided paired Wilcoxon signed-rank test confirms that Bayesian ridge regression requires significantly fewer evaluations than the GA ( $p = 6.1 \times 10^{-5}$ ).
Complex Systems Application: The framework was applied to $\text{Na}_{2/3}\text{FePO}_4$ , a system with coupled Na/vacancy configurational disorder and $\text{Fe}^{2+}/\text{Fe}^{3+}$ charge disorder. By embedding charge states into the surrogate representation and using a charge-encoded MLIP, the Bayesian ridge search recovered the experimentally reported ordering within 75 evaluations, despite a configuration space of approximately $5 \times 10^{11}$ .

Significance and Claims
The paper claims that treating site-disorder resolution as an agentic global optimization problem, guided by a surrogate model fitted to the search's own history, substantially outperforms classical fixed-policy strategies. The authors assert that the efficiency of global optimization depends less on the cost of individual evaluations and more on the intelligence of how evaluations are chosen. The adaptive nature of the agentic framework makes it particularly well-suited for complex systems with multiple coupled disordered sublattices, which are increasingly difficult to resolve with traditional methods. The study establishes agentic surrogate-guided search as a reliable and efficient alternative for materials discovery, with Bayesian ridge regression recommended as the default surrogate for chemically diverse systems.

Technical Summary: Agentic Global Optimization of Site-Disordered Crystalline Materials

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