Simple equations predict hydrogen storage in porous materials
The new approach found two physical traits—void fraction and pore volume—predict metal-organic framework performance without using supercomputers.
Experts
Alauddin Ahmed
A new set of simple equations can fast-track the search for metal-organic frameworks (MOFs), a Nobel-Prize-winning class of nanoporous materials that are promising candidates for clean hydrogen energy storage. With millions of possible MOFs to choose from, the formulas accurately predict how much usable hydrogen each porous crystal can hold, according to a new University of Michigan study.
With molecules in general containing 80-90% empty space, just one gram of a MOF has an internal surface area as big as a football field. Hydrogen molecules cling to their porous surface, but small variations in the crystal’s structure impact how the hydrogen interacts with the material.
Using a few physical properties of a potential MOF, researchers can now—without using a supercomputer or machine learning—estimate how much hydrogen can be stored under real-world conditions.
“By enforcing the right physics from the beginning, we show that you can match black-box machine-learning performance with models that are fully transparent. The combination of accuracy, interpretability, and deployability is what sets this approach apart,” said Alauddin Ahmed, research faculty of mechanical engineering at U-M and author of the study in PRX Energy.
The optimal MOF would store hydrogen with high weight efficiency and space efficiency. While the U.S. Department of Energy set targets for a 5.5% capacity by weight and 40 grams of hydrogen per liter under real-world conditions, no material has yet reached both benchmarks simultaneously.
Simple, explainable models
Previously, researchers relied on complex computer simulations that are accurate but computationally expensive and time consuming. More recently, machine learning models have sped up the search process, but they don’t explain the underlying physics.
To improve transparency, the researchers combined symbolic regression with other advanced algorithms to sift through billions of mathematical possibilities to find the simplest algebraic equations that predict performance as accurately as a complex simulation.
“I care deeply about interpretability. In safety-critical and mission-critical applications, people need to understand why a model is making a prediction, not just whether it is accurate on a test set,” said Ahmed.
The study curated a database of 88,400 MOFs detailing seven key crystal properties. Each entry also includes a prediction of storage capacity under a real-word operating range—between 100 and 5 bar at 77 kelvin.
The team used their algorithm to search for mathematical relationships between crystal properties and hydrogen storage capacity within this large dataset. To ensure the math was widely applicable, they validated the equations against a superdatabase of 600,000 MOFs pulled from open-source repositories previously reported by the author.
Pore space drives hydrogen uptake
Just one or two physical traits drove the vast majority of variation in usable hydrogen capacity across the MOFs. Void fraction—the ratio of empty space inside the crystal to crystal volume—can alone predict a MOF’s space efficiency. Void fraction plus pore volume predicts weight efficiency. Additional factors only added marginal gains to the predictions.
“We expected these features to matter, but we did not expect simple, constrained equations to match the accuracy of complex machine-learning models so closely,” said Ahmed.
Because the final models are fast, interpretable and essentially cost free, they can be integrated directly into automated systems that design and screen new hydrogen storage materials.
“More broadly, this work shows that physics-informed symbolic regression can be a practical bridge between large-scale simulations and real-world design. If we can replicate this success across other classes of energy materials, we will have a powerful new way to turn data into insight and, ultimately, into better technologies,” said Ahmed.
Computational resources and services were provided in part by Advanced Research Computing—Technology Services (ARC-TS), a division of Information and Technology Services (ITS) at the University of Michigan.
This research was funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy (DE-EE0007046) and by the University of Michigan Graham Sustainability Institute.