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Updated: Jul 17, 2025
07:08
Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
Published on: July 14, 2015
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Local invertibility and sensitivity of atomic structure-feature mappings.
Sergey N Pozdnyakov1, Liwei Zhang2, Christoph Ortner2
1Laboratory of Computational Science and Modelling, Institute of Materials, Federal Institute of Technology (EPFL) CH-1015 Lausanne, Lausanne, 1015, Switzerland.
Open Research Europe
|August 30, 2023
Summary
Machine learning for atomic simulations requires understanding how atomic coordinates map to descriptors. This study reveals desirable symmetry-induced singularities and problematic spurious singularities in these mappings, offering tools to identify them.
Area of Science:
- Computational chemistry
- Materials science
- Machine learning
Background:
- Machine learning is increasingly used in atomic-scale simulations.
- Understanding the mathematical mapping from atomic coordinates to descriptors is crucial.
- Symmetric descriptors are essential for enforcing physical constraints in models.
Purpose of the Study:
- To analyze the sensitivity of the mapping between atomic coordinates and descriptors.
- To quantify this sensitivity using singular value decomposition (SVD) of the Jacobian.
- To identify sources of singularities in descriptor representations.
Main Methods:
- Singular value decomposition (SVD) of the Jacobian matrix.
- Analysis of mapping sensitivity to atomic displacements.
- Investigation across different atomic configurations and descriptor choices.
Main Results:
- Symmetry and smoothness create desirable null singular values in the mapping Jacobian.
- Spurious singularities arise from descriptor incompleteness, where distinct structures map to the same feature vector.
- Aggressive truncation of basis sets can introduce additional spurious singularities.
Conclusions:
- Constructing symmetric atomic representations involves subtle mathematical challenges.
- Singularities can be both physically desirable (enforcing symmetry) and problematic (due to incompleteness or truncation).
- Provides conceptual and numerical tools for identifying and analyzing singularities in atomic representations.
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