Jove
Visualize
お問い合わせ
JoVE
x logofacebook logolinkedin logoyoutube logo
JoVEについて
概要リーダーシップブログJoVEヘルプセンター
著者向け
出版プロセス編集委員会範囲と方針査読よくある質問投稿
図書館員向け
推薦の声購読アクセスリソース図書館諮問委員会よくある質問
研究
JoVE JournalMethods CollectionsJoVE Encyclopedia of Experimentsアーカイブ
教育
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab Manual教員リソースセンター教員サイト
利用規約
プライバシーポリシー
ポリシー

関連する概念動画

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

395
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....
395
Transfer Function to State Space01:23

Transfer Function to State Space

831
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...
831
Modeling with Differential Equations01:25

Modeling with Differential Equations

107
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
107
Separable Differential Equations01:20

Separable Differential Equations

125
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
125
Linear Differential Equations01:27

Linear Differential Equations

113
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
113
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

91
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
91

こちらも読む

関連記事

共著者、ジャーナル、引用グラフによってこの研究に関連する記事。

並び替え
Same author

Patterns of Sexual Behaviors and Sexual Partner Characteristics as Predictors of Perceived HIV Risk and HIV Status Among Adolescent Girls and Young Women in Kenya.

AIDS and behavior·2026
Same author

COVID-19 forecasting from U.S. wastewater surveillance data: A retrospective multi-model study (2022-2024).

Journal of theoretical biology·2026
Same author

Comparative study of Bayesian and frequentist methods for epidemic forecasting: Insights from simulated and historical data.

Statistical methods in medical research·2025
Same author

BayesianFitForecast: a user-friendly R toolbox for parameter estimation and forecasting with ordinary differential equations.

BMC medical informatics and decision making·2025
Same author

The impact of vaping behavior on functional changes within the subgingival microbiome.

Scientific reports·2025
Same author

Skin-adaptive focused flexible micromachined ultrasound transducers for wearable cardiovascular health monitoring.

Science advances·2025

関連する実験動画

Updated: May 3, 2026

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

11.5K

SmooNet:スムーズオペレータニューラルネットワークと機能微分方程式

Ruiyan Luo1, Xin Qi1

  • 1Department of Population Health Sciences, Georgia State University, USA.

Neural networks : the official journal of the International Neural Network Society
|February 17, 2026
PubMed
まとめ

スムースオペレータニューラルネットワーク (SmooNets) を使用した新しい機能微分方程式 (FDE) モデルを導入し,ダイナミックシステムにおけるメモリ効果をキャプチャします. このアプローチは,複雑なシステム行動のモデリングと予測のための柔軟で効率的な方法を提供します.

科学分野:

  • ダイナミック・システムと数学モデリング
  • コンピューティング神経科学と機械学習

背景:

  • 普通微分方程式 (ODE) は通常,動的システムをモデル化しますが,システムメモリを無視して過度に単純化することが多いです.
  • この制限は,固有のメモリ効果を持つシステムの正確なモデリングを妨げます.

研究 の 目的:

  • 動的システムにおけるメモリ効果をモデル化できる新しい機能微分方程式 (FDE) フレームワークを提案する.
  • FDE内の未知オペレータを近似するためのツールとして,スムースオペレータニューラルネットワーク (SmooNet) を導入する.

主な方法:

  • FDEのオペレータを近似するために,連続した隠された層 ("隠された文字列") を備えたスムートオペレータニューラルネットワーク (SmooNet) を開発しました.
  • SmooNetの構築と予測のための新しい移動窓の最適化戦略を実装しました.
  • SmooNetの普遍的な近似機能とソリューション収束のための理論的保証を確立しました.

主要な成果:

  • SmooNetは,FDEのフレームワーク内のオペレーターの普遍的な近接を示しました.
  • 大致的な神経FDEからの解は,元のFDEの解に均等に近いことが示されました.
  • 経験的研究は,動的システムの研究と予測のためのモデルの柔軟性と効率性を確認しました.
キーワード:
微分方程式の微分方程式とは機能的微分方程式とは機能的普遍的近似定理について移動窓は最小四角を統合した.滑らかなオペレーターニューラルネットワーク

さらに関連する動画

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

2.5K
Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.3K

関連する実験動画

Last Updated: May 3, 2026

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

11.5K
RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

2.5K
Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.3K

結論:

  • SmooNetsで提案されたFDEモデルは,メモリ効果を組み込むことで,ODEsの限界を効果的に解決しています.
  • SmooNetsは,複雑な動的システムをモデル化するための強力で理論的に根拠のある方法を提供します.
  • 開発されたフレームワークは,科学的予測と分析のための柔軟で効率的なツールを提供します.