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Related Concept Videos

State Space Representation01:27

State Space Representation

347
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...
347
State Space to Transfer Function01:21

State Space to Transfer Function

391
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
391
Transfer Function to State Space01:23

Transfer Function to State Space

535
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 RLC...
535
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

237
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
237
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

876
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
876
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

160
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...
160

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Related Experiment Video

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Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models.

Mahdi Imani, Seyede Fatemeh Ghoreishi

    IEEE Transactions on Neural Networks and Learning Systems
    |April 5, 2021
    PubMed
    Summary

    This study introduces a novel two-stage Bayesian optimization (BO) framework for efficient inference in large-scale state-space models (SSMs). The method significantly reduces computational complexity, enabling accurate analysis of complex dynamical systems.

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    Area of Science:

    • Dynamical Systems and Control Theory
    • Computational Statistics and Machine Learning
    • Bioinformatics and Computational Biology

    Background:

    • State-space models (SSMs) are crucial for modeling dynamical systems across various scientific and engineering fields.
    • Current inference techniques for SSMs struggle with scalability, limiting their application to large, real-world problems.
    • Accurate model inference is essential for effective analysis, control, and decision-making in SSM-based systems.

    Purpose of the Study:

    • To develop a scalable and efficient Bayesian optimization (BO) framework for parameter inference in large-scale state-space models (SSMs).
    • To address the limitations of existing inference methods that are only applicable to small-scale systems.
    • To improve the accuracy and speed of inference for complex dynamical systems.

    Main Methods:

    • A two-stage Bayesian optimization (BO) framework is proposed for scalable SSM inference.
    • The framework reduces the high-dimensional parameter space to a lower-dimensional subspace using eigenvalue decomposition of gradient covariances.
    • Particle filtering approximates the inference function (log likelihood or log a posteriori) to guide the subspace identification.
    • A two-stage BO policy is employed, where the first stage in the reduced space informs the search in the original parameter space for the second stage.

    Main Results:

    • The proposed framework demonstrates significant improvements in both accuracy and speed for SSM inference.
    • Experiments show the effectiveness of the two-stage BO approach on various problems, including complex dynamical systems.
    • Successful application to real metagenomics data from a gut microbial community highlights its practical utility.

    Conclusions:

    • The developed two-stage Bayesian optimization framework offers a scalable and efficient solution for inference in large-scale state-space models.
    • This approach overcomes the limitations of traditional methods, enabling the analysis of complex systems previously intractable.
    • The framework's validated performance, including on real biological data, suggests broad applicability in diverse scientific domains.