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In practical electrical applications, the concept of time-varying instantaneous power is not frequently utilized. Instead, focus shifts to the more practical quantity known as average power. Average power is determined by integrating the instantaneous power over a specified time period and subsequently dividing it by that duration.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Ab initio machine learning of phase space averages.

Jan Weinreich1, Dominik Lemm1, Guido Falk von Rudorff1

  • 1Faculty of Physics, University of Vienna, Kolingasse 14-16, AT-1090 Wien, Austria.

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|July 15, 2022
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We introduce ab initio machine learning (AIML) to predict molecular properties, bypassing traditional simulations. This approach accelerates the exploration of chemical compound space for material and biochemical applications.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Biochemistry

Background:

  • Equilibrium structures are crucial for material properties and biochemical functions.
  • Conventional methods like molecular dynamics (MD) and Monte Carlo (MC) simulations are used to determine these structures.
  • These simulations can be computationally intensive and time-consuming.

Purpose of the Study:

  • To develop a machine learning approach for predicting phase space averages, which represent equilibrium structures.
  • To enable a general machine learning pathway for obtaining ensemble properties across diverse chemical compounds.
  • To accelerate the exploration of chemical compound space for material and biochemical applications.

Main Methods:

  • Developed an ab initio machine learning (AIML) model that does not require bond topologies.
  • Trained the AIML model on hundreds of MD trajectories to predict Boltzmann averaged structures.
  • Used AIML output to train machine learning models for predicting free energies of solvation.

Main Results:

  • AIML successfully predicts Boltzmann averaged structures.
  • Machine learning models trained on AIML output achieve competitive prediction errors (MAE ~0.8 kcal/mol) for solvation free energies.
  • The AIML approach bypasses the need for traditional MD or MC simulations for phase space sampling.

Conclusions:

  • AIML offers a significantly accelerated pathway for exploring ensemble properties and chemical compound space.
  • This method enables rapid prediction of material properties and biochemical functions.
  • AIML provides a Pareto-efficient approach for solvation free energy predictions in terms of accuracy and computational time.