Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Classification of Systems-II

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

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....

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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,...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

State Space Representation

State Space Representation

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...

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Publisher Correction: Multiomics characterization of an alcohol-induced hepatocellular carcinoma mouse model.

Lab animal·2026

Same author

Multiomics characterization of an alcohol-induced hepatocellular carcinoma mouse model.

Lab animal·2026

Same author

Is sublobar resection a valid option for radiologically pure-solid clinical stage IA non-small cell lung cancer?: insights from real-world data and current status.

Lung cancer (Amsterdam, Netherlands)·2026

Same author

Lobe-Specific Variability in Postoperative Pulmonary Function in Lung Cancer Patients: A Longitudinal Analysis and Comparison With Traditional Predictive Models.

Respirology (Carlton, Vic.)·2025

Same author

VQ-FedDiff: Federated Learning Algorithm of Diffusion Models With Client-Specific Vector-Quantized Conditioning.

IEEE transactions on pattern analysis and machine intelligence·2025

Same author

Deep Learning-Based Landmark Detection Model for Multiple Foot Deformity Classification: A Dual-Center Study.

Yonsei medical journal·2025

Search research articles

Related Experiment Video

Updated: Oct 5, 2025

Designing and Implementing Nervous System Simulations on LEGO Robots

Designing and Implementing Nervous System Simulations on LEGO Robots

Published on: May 25, 2013

Learning Polymorphic Neural ODEs With Time-Evolving Mixture.

Tehrim Yoon, Sumin Shin, Eunho Yang

IEEE Transactions on Pattern Analysis and Machine Intelligence

|January 25, 2022

Summary

This summary is machine-generated.

Stacking Neural Ordinary Differential Equations (NODE) blocks improves performance by overcoming representational limits. A novel training method using time-evolving mixture weights further enhances NODE capabilities.

Related Experiment Videos

Last Updated: Oct 5, 2025

Designing and Implementing Nervous System Simulations on LEGO Robots

Designing and Implementing Nervous System Simulations on LEGO Robots

Published on: May 25, 2013

Area of Science:

Artificial Intelligence
Machine Learning
Deep Learning

Background:

Neural Ordinary Differential Equations (NODE) model deep residual networks as continuous structures.
Standard NODEs face representational limits, hindering performance saturation as layer depth increases.

Purpose of the Study:

To enhance the performance of Neural ODEs by addressing their representational limitations.
To introduce a novel training methodology for improved NODE efficacy.

Main Methods:

Implementing stacked Neural ODE blocks to increase representational capacity.
Developing a time-evolving mixture weight strategy for training multiple ODE functions.
Utilizing a separate neural ODE to manage the evolving mixture weights.

Main Results:

Stacked Neural ODEs demonstrate improved performance compared to vanilla NODEs.
The proposed training method, incorporating time-evolving mixture weights, further enhances performance.
The approach is compatible with existing advancements in Neural ODEs.

Conclusions:

Stacking Neural ODE blocks is an effective strategy to overcome performance saturation.
The novel training approach offers a more efficient method for training Neural ODEs.
This work provides a versatile framework for advancing Neural ODE research.