🔬 materials science

Correcting DFT formation energies towards experimental accuracy using foundational MLIPs and latent-feature delta-learning

This paper presents the experimentally focused MC3D database and demonstrates that combining foundational machine learning interatomic potentials with latent-feature delta-learning significantly corrects DFT formation energies, reducing errors to experimental uncertainty levels while preserving relative phase stability.

Original authors: Timo Reents, Marnik Bercx, Giovanni Pizzi

Published 2026-07-21

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Timo Reents, Marnik Bercx, Giovanni Pizzi

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 a chef trying to invent a new, delicious recipe for a cake. You have a massive cookbook of thousands of existing recipes, but they were all written by a chef who uses a very old, slightly inaccurate measuring cup. Sometimes the cake comes out perfect, but other times it's too salty or too dry because the cup doesn't measure ingredients quite right. In the world of materials science, scientists are the chefs, and the "recipes" are crystal structures of new materials they want to discover. The "ingredients" are atoms like oxygen, iron, or carbon. The "old measuring cup" is a computer simulation method called Density Functional Theory (DFT), specifically a version known as GGA. It's incredibly fast and has helped build huge libraries of potential materials, but it has a known flaw: it often guesses the "stability" of a material wrong, making it think a material is stable when it would actually fall apart in the real world.

To fix this, scientists usually try to manually tweak the numbers, like adding a pinch of salt to every recipe to compensate for the bad cup. This is called an "empirical correction." It helps, but it's a bit of a guess-and-check game. Recently, a new generation of "smart" computer models, called foundational Machine Learning Interatomic Potentials (MLIPs), has arrived. Think of these as AI chefs who have tasted millions of cakes and learned the true flavor of ingredients without needing a measuring cup at all. The big question is: Can we use these AI chefs to fix the old, inaccurate recipes without having to re-cook every single cake from scratch?

This paper, titled "Correcting DFT formation energies towards experimental accuracy using foundational MLIPs and latent-feature delta-learning," takes a deep dive into exactly that. The authors, working with the Materials Cloud three-dimensional crystals database (MC3D), first checked if their new database of "recipes" matched up with two other famous databases (Materials Project and OQMD). They found that while the raw computer numbers were very similar, the differences usually came from how different teams tried to manually fix the errors.

The real magic happens next. The authors tested a specific AI model called PET-OMATPES, which was trained on a more advanced level of physics (called r2SCAN) that is known to be more accurate but much slower to run. They used this AI to look at the old, fast GGA recipes and predict what the formation energy should be. The result was a massive improvement: the AI reduced the average error by more than 40% compared to the old method, all without running a single new, slow simulation. It was like having the AI chef instantly tell you, "Hey, if you used the right cup, this cake would actually be this sweet."

But the authors didn't stop there. They wanted to get even closer to the truth. They trained a second, simpler machine learning model to learn the tiny "leftover" mistakes that the AI chef still made. To do this, they used something called "latent features." Imagine the AI chef doesn't just give you a number; it also gives you a secret code that describes the shape and texture of the cake in a way a human can't see. The authors used this secret code to teach their second model how to fix the final, tiny errors.

The result is a two-step process that brings the computer predictions down to an error of less than 50 meV/atom. To put that in perspective, that's a level of accuracy so high it's almost indistinguishable from the uncertainty in real-world experiments themselves. The paper suggests that this method is superior to the old manual "pinch of salt" corrections (known as FERE) because it fixes the errors more consistently and, crucially, doesn't accidentally ruin the "stability ranking" of the materials. In other words, it makes the predictions more accurate without confusing which materials are actually stable and which are not. The authors conclude that by combining the speed of old methods with the brainpower of these new foundational AI models, we can finally trust our computer-generated recipes much more than before.

Technical Summary: Correcting DFT Formation Energies towards Experimental Accuracy using Foundational MLIPs and Latent-Feature Delta-Learning

Problem Statement
High-throughput computational materials discovery relies heavily on databases of formation energies calculated via Density Functional Theory (DFT). While these databases (e.g., Materials Project, OQMD) enable the screening of thermodynamic stability, the standard Generalized Gradient Approximation (GGA) functionals (PBE, PBEsol) exhibit systematic inaccuracies when compared to experimental formation enthalpies. These errors, often exceeding 150 meV/atom, stem from issues such as the overbinding of diatomic gases and the poor description of localized electrons. Although meta-GGA functionals (e.g., r2SCAN) offer improved accuracy, their widespread adoption in high-throughput workflows is hindered by computational costs and a lack of verified pseudopotentials. Furthermore, existing empirical correction schemes (e.g., FERE) introduce non-smoothness and additional uncertainty, which can be detrimental when training machine learning (ML) models. The challenge is to improve the agreement between DFT-calculated formation energies and experimental data without requiring the re-computation of entire databases at higher theoretical levels, while ensuring that corrections do not arbitrarily distort relative phase stability.

Methodology
The authors introduce a multi-stage approach to refine formation energies for the Materials Cloud three-dimensional crystals database (MC3D), focusing on experimentally known compounds.

Database Validation: The study first establishes the thermodynamic stability data for MC3D (using PBE and PBEsol functionals within Quantum ESPRESSO) and validates it against established databases (Materials Project and OQMD) and experimental references. This includes an analysis of inter-database discrepancies arising from different computational parameters and empirical correction schemes.
Foundational MLIP Zero-Shot Correction: Instead of re-running DFT calculations with meta-GGA functionals, the authors employ a foundational Machine Learning Interatomic Potential (fMLIP), specifically PET-OMATPES, trained on r2SCAN-level data. They evaluate the "zero-shot" formation energies of this model on geometries relaxed at the GGA (PBE/PBEsol) level. They also test the effect of performing structural relaxations directly with the fMLIP.
Delta-Learning with Latent Features: To further reduce errors, the authors train classical ML models (Random Forest, Kernel Ridge Regression, and Gaussian Process Regression) in a delta-learning framework. These models predict the residual difference between the calculated formation energy (either GGA or fMLIP-estimated) and experimental values.
- Features: The models utilize two types of input features: (i) purely compositional features (Magpie) and (ii) latent features (LFs) extracted from the intermediate layers of the PET-OMATPES fMLIP. The LFs are hypothesized to encode structural information and correction-relevant patterns learned from millions of crystal structures.
- Regularization: The study systematically investigates the impact of regularization (specifically in Kernel Ridge Regression) on the trade-off between minimizing the Mean Absolute Error (MAE) of formation energies and preserving the relative phase stability (measured by the "stability flip rate").

Key Results

Database Consistency: Pure DFT formation energies across MC3D, Materials Project, and OQMD show high agreement (Median Absolute Difference ~15–18 meV/atom). Discrepancies in corrected values are largely driven by differing empirical correction schemes, particularly regarding oxygen-containing compounds.
fMLIP Zero-Shot Performance: The PET-OMATPES model, evaluated at the r2SCAN level on GGA-relaxed geometries, reduces the MAE relative to experiment by more than 40% compared to pure GGA. For PBEsol-relaxed structures, the bias vanishes entirely (ME ≈ 0 meV/atom), and the MAE drops to ~85 meV/atom. Structural relaxations performed directly by the fMLIP yield results comparable to DFT relaxations, with slightly better volume agreement with experimental structures.
Delta-Learning Improvements: Training classical ML models on the residuals significantly improves accuracy. Using the latent features of the fMLIP, the best models (KRR and GPR) achieve a MAE of approximately 50 meV/atom (specifically 49–52 meV/atom), a value comparable to the inherent uncertainty of experimental data itself.
Latent Features vs. Compositional Features: Contrary to previous findings that compositional features are superior for corrections, this study demonstrates that latent features simultaneously reduce the prediction error and lower the stability flip rate.
Regularization and Stability: Careful tuning of regularization parameters (e.g., $\alpha = 0.1$ in KRR) allows for a balance where the MAE is minimized while the stability flip rate (the fraction of materials changing stability classification) is kept low (below 10% for strict thresholds, converging to ~3–4% for standard 25 meV/atom windows). The learned corrections are shown to be non-random and physically motivated, as they largely align with the stability changes already introduced by the underlying fMLIP.
Comparison with FERE: The proposed ML approach outperforms established FERE corrections. While FERE methods can degrade predictions for a significant portion of compounds (up to 32% for FERE-all), the ML approach degrades fewer compounds and limits the magnitude of degradation for those cases.

Significance and Claims
The paper claims to extend the established practice of pairing PBEsol geometries with meta-GGA energies into the era of foundational MLIPs. The primary contribution is demonstrating that fMLIPs can serve as superior estimators of formation energies relative to experiment without requiring additional DFT calculations. Furthermore, the work establishes that the latent features of these foundational models are a powerful resource for downstream ML corrections, offering a pathway to achieve experimental-level accuracy (MAE < 50 meV/atom) while maintaining the integrity of relative phase stability. The authors position this two-step approach (zero-shot fMLIP evaluation followed by delta-learning) as a robust method for correcting existing GGA databases, validated against both experimental data and established empirical correction schemes.

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