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Beyond Numerical Hessians: Higher-Order Derivatives for Machine Learning Interatomic Potentials via Automatic

Nils Gönnheimer1,2, Karsten Reuter2, Johannes T Margraf1,2

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Automatic differentiation (AD) enhances machine learning interatomic potentials (MLIPs) by enabling efficient and accurate Hessian matrix calculations. This accelerates high-throughput predictions of material properties like heat capacity, crucial for gas adsorption studies.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Machine Learning

Background:

  • Machine learning interatomic potentials (MLIPs) offer speed and accuracy improvements over traditional methods.
  • Calculating Hessian matrices for large systems using finite differences is computationally expensive and can be imprecise.
  • Analytical second-order derivatives are often not implemented in existing MLIPs.

Purpose of the Study:

  • To implement automatic differentiation (AD) for efficient and accurate calculation of Hessian matrices in MLIPs.
  • To integrate AD-based second-order derivatives into the MACE equivariant graph neural network architecture.
  • To demonstrate the utility of AD-enhanced MLIPs for high-throughput property prediction.

Main Methods:

  • Implementation of AD-based second-order derivative calculations for MACE.
  • Application of the MACE-MP-0 foundation model for high-throughput heat capacity prediction of porous materials.
  • Comparison of AD-based methods with finite-difference approaches and first-principles calculations.

Main Results:

  • AD significantly improves the efficiency and accuracy of Hessian matrix calculations.
  • High-throughput prediction of heat capacities for porous materials is enabled with high accuracy.
  • Foundation models with analytical Hessians achieve zero-shot accuracy comparable to bespoke ML models.

Conclusions:

  • AD provides a robust and efficient method for calculating second-order derivatives in MLIPs.
  • This advancement facilitates accurate prediction of material properties relevant to gas adsorption.
  • The study highlights the potential of foundation models and analytical Hessians for materials discovery and analysis.