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Related Concept Videos

State Space Representation01:27

State Space Representation

178
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.
Consider an RLC circuit, a...
178
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Equation of State01:07

Equation of State

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The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
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Transfer Function to State Space01:23

Transfer Function to State Space

209
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
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Long-Term Memory01:18

Long-Term Memory

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Long-term memory is a relatively permanent type of memory, capable of storing vast amounts of information over extended periods. Its storage capacity is generally considered unlimited.
Long-term memory can be categorized into two primary types: explicit and implicit memory. Explicit memory, also known as declarative memory, involves the conscious recollection of information that we deliberately try to remember, recall, and articulate. This type of memory encompasses specific facts, events, and...
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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Data-Driven Learning of the Generalized Langevin Equation with State-Dependent Memory.

Pei Ge1, Zhongqiang Zhang2, Huan Lei1,3

  • 1Department of Computational Mathematics, Science, and Engineering, <a href="https://ror.org/05hs6h993">Michigan State University</a>, East Lansing, Michigan 48824, USA.

Physical Review Letters
|August 30, 2024
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Summary

We developed a new data-driven method for complex systems, capturing state-dependent memory beyond standard models. This approach improves predictions of molecular kinetics, like conformation changes.

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Area of Science:

  • Complex Systems Modeling
  • Computational Chemistry
  • Statistical Mechanics

Background:

  • Standard generalized Langevin equations (GLEs) with homogeneous kernels struggle to capture complex system dynamics.
  • Heterogeneous energy dissipation and state-dependent memory are often overlooked in reduced models.
  • Accurate molecular kinetics prediction requires models that account for these factors.

Purpose of the Study:

  • To develop a data-driven method for learning stochastic reduced models.
  • To incorporate state-dependent memory beyond the capabilities of standard GLEs.
  • To improve the prediction of molecular kinetics, including conformation relaxation and transition.

Main Methods:

  • A data-driven approach was employed to learn stochastic reduced models.
  • The method jointly learns state features and their non-Markovian coupling.
  • This allows for the natural encoding of heterogeneous energy dissipation.

Main Results:

  • The proposed model successfully captures state-dependent memory effects.
  • Numerical results highlight the limitations of standard GLEs with homogeneous kernels.
  • The importance of state-dependency in predicting molecular kinetics was demonstrated.

Conclusions:

  • The developed method offers a more accurate representation of complex systems.
  • State-dependent memory is crucial for understanding molecule kinetics.
  • This approach advances the modeling of conformation dynamics and transitions.