Symbolic Ensemble Learning Enables Discovery of Fast Accurate Physics-Based Interatomic Potentials

Abstract

Machine learning has transformed materials simulation by delivering force fields with ab initio accuracy, yet bridging the gap between high-dimensional regression and physical interpretability remains a grand challenge. Conventional analytical potentials offer transparency but often fail to capture the complexity of far-from-ground state regimes. Here, we introduce a hybrid symbolic-neural framework that unifies the interpretability of the Embedded Atom Method (EAM) with the adaptability of data-driven learning. Using Equation Learner Neural Networks (EqNNs) trained on density functional theory (DFT) data, we obtain interpretable models for aluminum through three distinct training protocols: random initialization trained via Monte Carlo Tree Search (MCTS) and gradient descent, and two transfer-learning strategies initialized from a copper potential - one employing MCTS followed by gradient descent, and the other using gradient descent only. We find that while all three resulting symbolic models achieve sub-10 meV/atom accuracy, they occupy distinct local minima in the functional landscape, exhibiting complementary trade-offs across phonon dispersion, surface energetics, and elastic response. By integrating these diverse functional forms through a weighted symbolic ensemble, we derive a composite potential that surpasses the fidelity of its constituent models. The resulting ensemble effectively mitigates individual biases, delivering superior consistency with DFT benchmarks across equation-of-state curvature, phonon spectra, and melting dynamics. This approach demonstrates that combining transfer learning with ensemble symbolic regression yields compact, transparent potentials capable of robust prediction across equilibrium and non-equilibrium states.

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Cite

BibTeX RIS

BibTeX

@misc{varughese2026symbolic,
  title = {{Symbolic Ensemble Learning Enables Discovery of Fast Accurate Physics-Based Interatomic Potentials}},
  author = {Bilvin Varughese and Aditya Koneru and Adil Muhammad and Troy D. Loeffler and Sukriti Manna and Jan Michael Y. Carrillo and Orcun Yildiz and Thomas Peterka and Subramanian K. R. S. Sankaranarayanan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16526},
  eprint = {2609.16526},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16526},
  note = {CC BY-NC-SA 4.0},
}

RIS

TY  - UNPB
TI  - Symbolic Ensemble Learning Enables Discovery of Fast Accurate Physics-Based Interatomic Potentials
AU  - Bilvin Varughese
AU  - Aditya Koneru
AU  - Adil Muhammad
AU  - Troy D. Loeffler
AU  - Sukriti Manna
AU  - Jan Michael Y. Carrillo
AU  - Orcun Yildiz
AU  - Thomas Peterka
AU  - Subramanian K. R. S. Sankaranarayanan
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16526
UR  - https://arxiv.org/abs/2609.16526
AB  - Machine learning has transformed materials simulation by delivering force fields with ab initio accuracy, yet bridging the gap between high-dimensional regression and physical interpretability remains a grand challenge. Conventional analytical potentials offer transparency but often fail to capture the complexity of far-from-ground state regimes. Here, we introduce a hybrid symbolic-neural framework that unifies the interpretability of the Embedded Atom Method (EAM) with the adaptability of data-driven learning. Using Equation Learner Neural Networks (EqNNs) trained on density functional theory (DFT) data, we obtain interpretable models for aluminum through three distinct training protocols: random initialization trained via Monte Carlo Tree Search (MCTS) and gradient descent, and two transfer-learning strategies initialized from a copper potential - one employing MCTS followed by gradient descent, and the other using gradient descent only. We find that while all three resulting symbolic models achieve sub-10 meV/atom accuracy, they occupy distinct local minima in the functional landscape, exhibiting complementary trade-offs across phonon dispersion, surface energetics, and elastic response. By integrating these diverse functional forms through a weighted symbolic ensemble, we derive a composite potential that surpasses the fidelity of its constituent models. The resulting ensemble effectively mitigates individual biases, delivering superior consistency with DFT benchmarks across equation-of-state curvature, phonon spectra, and melting dynamics. This approach demonstrates that combining transfer learning with ensemble symbolic regression yields compact, transparent potentials capable of robust prediction across equilibrium and non-equilibrium states.
ER  -

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