Related Experiment Video
Updated: Jun 9, 2025
13:19
The Use of Chemostats in Microbial Systems Biology
Published on: October 14, 2013
30.8K
Benchmarking methods for computing local sensitivities in ordinary differential equation models at dynamic and steady
Polina Lakrisenko1,2, Dilan Pathirana3, Daniel Weindl1,3
1Computational Health Center, Helmholtz Zentrum München Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany.
Plos One
|October 23, 2024
Summary
Choosing the right methods for computing steady-state sensitivities is crucial for dynamic models. Combining numerical integration for steady states with tailored methods for sensitivities offers the most robust and efficient approach.
Area of Science:
- Computational modeling
- Systems biology
- Parameter estimation
Background:
- Estimating dynamic model parameters is computationally intensive.
- Steady-state computations are often required for model simulations.
- Selecting efficient methods for steady-state and gradient computation is unclear.
Purpose of the Study:
- To evaluate method pairs for computing steady-state and sensitivities.
- To identify robust and computationally efficient methods.
- To guide modelers in method selection.
Main Methods:
- Explored six method pairs for steady-state and sensitivity computation.
- Used numerical integration and Newton's method for steady states.
- Employed numerical integration and tailored methods for sensitivity analysis.
Main Results:
- All method pairs yielded accurate steady-state and gradient values.
- Method pairs combining numerical integration (steady-state) and tailored methods (sensitivities) were most robust and efficient.
- Newton's method for steady-state offered speedups but risked simulation failures.
Conclusions:
- No single method pair is universally best for computing steady-state sensitivities.
- Guidance is provided for selecting appropriate methods based on specific modeling problems.
- Optimizing computational efficiency and robustness in dynamic model analysis is achievable.
Related Concept Videos
01:18Second Order systems II
91
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
91
01:21Linear Approximation in Time Domain
66
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
66
01:26Linear Approximation in Frequency Domain
86
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
86
01:27State Space Representation
166
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...
Consider an RLC circuit, a...
166
01:20Relation between Mathematical Equations and Block Diagrams
170
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
170
01:24Transient and Steady-state Response
157
In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
157