🔬 materials science

Screening 39 billion protostructures for materials discovery

This paper presents a high-throughput computational screening of 39 billion protostructures that generates a curated dataset of 81 million locally relaxed crystal structures, including nearly 89,000 novel prototypes, to systematically map low-energy compositional-structural space for accelerated materials discovery.

Original authors: Abhijith S Parackal, Florian Trybel, Felix Andreas Faber, Rickard Armiento

Published 2026-01-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Abhijith S Parackal, Florian Trybel, Felix Andreas Faber, Rickard Armiento

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

Imagine you are trying to find the perfect recipe for a new type of cake. You know the basic ingredients (flour, sugar, eggs, etc.), but you don't know the exact amounts, the mixing order, or the baking temperature that will create the most delicious, stable cake.

In the world of materials science, scientists are doing the same thing, but instead of cakes, they are looking for new crystals (solid materials with a specific, repeating atomic pattern). The problem is that the number of possible "recipes" is so huge—trillions upon trillions—that checking them one by one is impossible.

This paper describes a new, super-fast method to sift through 39 billion potential crystal "recipes" to find the best ones. Here is how they did it, explained simply:

1. The Problem: A Needle in a Haystack

Traditionally, scientists have looked for new materials by taking known recipes and slightly tweaking them (like swapping sugar for honey). This is like only looking for new cake recipes in a cookbook you already own. You might find a variation, but you'll never invent a completely new type of cake because you're stuck in the "known" world.

The authors wanted to look at everything, including recipes that have never existed before. But the "haystack" of possibilities is too big to search manually.

2. The Solution: A Two-Step Filtering System

To solve this, the team built a two-step "funnel" to narrow down the 39 billion possibilities without checking every single one in detail.

Step 1: The "Rough Sketch" (The Protostructure)
Instead of drawing a full, detailed blueprint of a crystal, they first drew a "skeleton" or a "rough sketch."

The Analogy: Imagine you are looking for a house. Instead of checking the exact brick color, window size, and furniture layout for every possible house in the world, you first just look at the shape of the roof and the number of rooms.
The Science: They used a concept called a "protostructure." This describes a crystal only by its symmetry (how the atoms are arranged in a pattern) and which elements are used, ignoring the exact distances between atoms.
The Result: They generated 39 billion of these rough sketches.

Step 2: The "AI Scout" (Wren)
They couldn't check all 39 billion sketches in detail, so they used an Artificial Intelligence model named Wren.

The Analogy: Think of Wren as a super-fast scout who looks at your rough house sketches and instantly says, "This roof shape is unstable; it will collapse," or "This one looks promising."
The Action: Wren quickly predicted the energy (stability) of these sketches. It threw away the bad ones and kept only the 0.04% that looked like they might be stable. This reduced the list from 39 billion down to about 15 million.

Step 3: The "Detailed Build" (Concretization)
Now that they had 15 million promising sketches, they needed to turn them into real, detailed blueprints.

The Analogy: For the 15 million promising sketches, they now filled in the details: exact brick sizes, precise window placements, and specific furniture.
The Science: They used a mathematical technique called "Latin hypercube sampling" to generate millions of specific variations for each sketch. Then, they used another AI tool (called a Machine-Learned Interatomic Potential, or MLIP) to "relax" these structures. This means the AI simulated the atoms moving around until they found the most comfortable, low-energy position, like a person settling into a couch.
The Result: This process created 81 million fully detailed, optimized crystal structures.

3. The Treasure Hunt Results

After all this work, they found a massive treasure trove:

New Discoveries: They found 88,498 completely new types of crystal structures (prototypes) that have never been seen before in any database.
Stability: They identified 456,110 structures that are likely to be stable enough to be made in a lab (they are close to the "convex hull," which is the scientific term for the line between "stable" and "unstable").
Validation: To make sure their AI wasn't just guessing, they tested their method on three known chemical systems (Hf-Zn-N, Ti-Zn-N, and Zr-Zn-N). The method successfully "rediscovered" the known stable materials, proving it works.

4. Why This Matters

The authors created a massive, organized map of the "low-energy" landscape of materials.

The Map: They built 4,495 different "phase diagrams" (maps showing which materials are stable under which conditions).
The Pool: They now have a pool of 81 million candidates that other scientists can use to design new batteries, solar cells, or superconductors.

Summary

Think of this paper as building a massive, automated factory that can:

Imagine 39 billion possible house designs.
Use a smart AI to instantly reject the ones that would fall down.
Build detailed, stable models of the remaining 81 million houses.
Hand over the blueprints of 88,000 brand new house designs that no one has ever seen before, giving architects (materials scientists) a huge head start on building the future.

The paper does not claim these materials are already being used in products; it simply provides the list of candidates and the method to find them, ready for others to test and use.

Technical Summary: Screening 39 Billion Protostructures for Materials Discovery

Problem Statement
The field of crystal structure prediction (CSP) is central to materials discovery but faces a combinatorial bottleneck. The space of all possible materials is vast, making systematic, unbiased exploration difficult. Existing approaches largely rely on data from repositories like ICSD, AFLOW, and Materials Project, which are biased toward known structural prototypes (approximately 8,000 observed types). Methods that use generative AI or statistical priors derived from these databases inherit this bias, limiting their ability to discover structures vastly different from those already known. Furthermore, the full configurational space of a crystal with $N$ atoms involves $6+3N$ continuous degrees of freedom, rendering exhaustive enumeration computationally intractable for complex systems.

Methodology
The authors propose a two-step, high-throughput framework designed to scale structure exploration by orders of magnitude while maintaining unbiased coverage of the configuration space.

Coarse-Grained Prescreening (Protostructures):
- Representation: The authors utilize "protostructures," a coarse-grained representation that specifies a crystal's space group, chemical elements, and the Wyckoff positions occupied by atoms, without defining explicit atomic coordinates or lattice parameters. This reduces the degrees of freedom significantly.
- Enumeration: They systematically enumerate all symmetry-distinct protostructures for binary and ternary compounds using elements from lithium to bromine (excluding noble gases). The enumeration is restricted to a structural complexity of five atoms in the asymmetric unit and a maximum of 64 atoms in the unit cell. This yields approximately 39 billion protostructures.
- Machine Learning Model (Wren): The Wren (Wyckoff Representation Network) model, a transformer-based architecture reimplemented using JAX for GPU acceleration, is used to predict the formation energy of these protostructures. The model is trained on the Alexandria database (PBE 3D dataset, ~4.5 million structures).
- Efficiency: The reimplemented Wren model achieves a 40-fold increase in inference throughput compared to previous GPU implementations, allowing the evaluation of millions of protostructures per second.
- Filtering: A convex hull of thermodynamic stability is constructed using Wren's predicted energies. Protostructures predicted to lie more than 100 meV/atom above the Alexandria convex hull are discarded. This stage retains approximately 15.7 million candidates (0.04% of the total).
Fine-Grained Exploration and Relaxation:
- Concretization: The retained protostructures are converted into explicit crystal structures. The degrees of freedom (lattice parameters and atomic coordinates within Wyckoff constraints) are sampled using Latin Hypercube Sampling (LHS). The number of samples is determined heuristically based on the number of degrees of freedom and atoms.
- Initial Volume Estimation: A linear regression model predicts effective atomic radii based on chemical identity and coordination to estimate initial unit cell volumes, avoiding unphysical starting geometries.
- Relaxation: The generated structures undergo symmetry-constrained geometry optimization using the MACE (Machine-learning Atomic Cluster Expansion) interatomic potential (MPA-0 version). This ensures the relaxation respects the original protostructure's symmetry.
- Validation: A secondary validation step uses the ORB neural network potential. Structures are retained only if MACE and ORB energy predictions agree within 100 meV/atom.
- Output: This stage produces 81 million locally relaxed crystal structures.

Key Results

Scale: The workflow screened 39 billion protostructures, resulting in a dataset of 81 million relaxed crystal structures.
Stability: Within the screened chemical space (Li–Br, binary/ternary, complexity $\le$ 5, unit cell $\le$ 64 atoms), the authors identified 456,110 structures with a decomposition enthalpy ( $H_d$ ) below 100 meV/atom relative to the convex hull.
Novelty: These structures span 91,295 unique crystal prototypes. Crucially, 88,498 of these prototypes are not present in existing databases (Alexandria or GNoME).
Validation:
- Known Systems: The method was validated on Hf-Zn-N, Ti-Zn-N, and Zr-Zn-N systems. It successfully rediscovered known phases and identified a missing ternary phase (Hf $_6$ Zn $_6$ N) that was omitted in a previous limited screening due to structure count caps.
- DFT Verification: High-throughput DFT calculations were performed on 2,303 new structures with $H_d \le 0$ . Of these, 631 remained below zero (on the convex hull), and the rest remained within 25 meV/atom of the hull.
- Error Analysis: The mean absolute error of the final MLIP predictions relative to DFT in Alexandria is 33 meV/atom. The error distribution shows a bias toward higher formation energies (false negatives), suggesting the methodology is conservative.

Significance and Claims
The paper claims to provide a systematic map of low-energy compositional-structural space and a large, structured pool of candidates for downstream property evaluation.

Overcoming Bias: By using protostructures and avoiding priors based on existing structural databases, the workflow overcomes the "structural prior" bias inherent in most current CSP methods, enabling the discovery of new prototypes in unexplored regions.
Scalability: The two-step approach (coarse-grained prescreening followed by fine-grained relaxation) successfully addresses the combinatorial explosion, making it feasible to screen tens of billions of candidates.
Diversity: The discovery of nearly 90,000 new prototypes represents a "true qualitative shift" in structural diversity for materials databases compared to previous efforts (e.g., Alexandria has ~8,449 prototypes under similar limits; GNoME has ~2,253).
Foundation for Future Work: The authors note that while the current screening is massive, the methodology provides a scalable foundation. They suggest that retraining the prescreening model with increased precision could further reduce the number of systems requiring expensive second-stage relaxation, potentially allowing for the screening of higher structural complexities across the periodic table.

The work does not claim to have experimentally synthesized these materials but positions the dataset as a resource for guiding future experimental and theoretical materials design.