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Potential Energy00:52

Potential Energy

The energy stored by a structure and location of matter in space is called potential energy. For instance, raising a kettlebell changes its spatial location and increases its potential energy. Similarly, a stretched rubber band contains potential energy which, under certain conditions, can be converted into other forms of energy, such as kinetic energy.
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Methods in PES-Learn: Direct-Fit Machine Learning of Born-Oppenheimer Potential Energy Surfaces.

Ian T Beck1, Justin M Turney1, Henry F Schaefer1

  • 1Department of Chemistry, Center for Computational Quantum Chemistry, University of Georgia, Athens, GA 30602, USA.

Molecules (Basel, Switzerland)
|January 10, 2026
PubMed
Summary
This summary is machine-generated.

PES-Learn 1.0 is a new open-source software for building machine learning models of molecular potential energy surfaces (PESs). It introduces kernel ridge regression and enhanced Python API for easier PES construction and gradient prediction.

Keywords:
kernel ridge regressionmachine learningneural networkspotential energy surface

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Area of Science:

  • Computational chemistry
  • Machine learning
  • Materials science

Background:

  • Developing accurate molecular potential energy surfaces (PESs) is crucial for simulating chemical processes.
  • Traditional methods for PES construction can be computationally expensive and time-consuming.
  • Automating the construction of PESs using machine learning offers a promising alternative.

Purpose of the Study:

  • To present PES-Learn version 1.0, an open-source software package for automated construction of semi-global molecular potential energy surfaces (PESs).
  • To introduce and evaluate kernel ridge regression (KRR) as a new machine learning method within PES-Learn.
  • To enhance PES-Learn's interoperability and demonstrate its performance through benchmarking.

Main Methods:

  • Release of PES-Learn version 1.0 with a new Python API for improved interoperability with QCSchema.
  • Implementation and evaluation of kernel ridge regression (KRR) for PES construction.
  • Benchmarking of all available machine learning methods in PES-Learn using benzene and ethanol datasets from the rMD17 database.
  • Assessment of fitting performance, timings, and gradient prediction capabilities using neural network models.

Main Results:

  • PES-Learn 1.0 facilitates automated construction of semi-global PESs with enhanced interoperability.
  • Kernel ridge regression (KRR) demonstrates effective capabilities for modeling select semi-global PESs.
  • Benchmarking shows PES-Learn's performance in fitting accuracy and computational efficiency for benzene and ethanol.
  • Neural network models successfully predict gradients for ethanol and benzene.

Conclusions:

  • PES-Learn 1.0 provides a robust and user-friendly platform for machine learning-based PES construction.
  • The inclusion of KRR expands the methodological options for PES modeling.
  • The software demonstrates strong performance and potential for broader adoption in computational chemistry research.
  • PES-Learn is an active project encouraging community contributions for future development.