動的システムの不確実なパラメータを再構築するためにストキャスティックニューラルネットワークを訓練するための新しいローカルタイムデコップルされた二乗ワッサータイン-2方法
Mingtao Xia1, Qijing Shen2, Philip K Maini3
1Department of Mathematics, University of Houston, Philip Guthrie Hoffman Hall, 3551 Cullen Blvd, Houston, TX, 77204, USA.
まとめ
この研究は,時間データを用いて動的システムの不確実なパラメータを推定する新しい方法を導入しています. この技術は,パラメータ分布を効果的に再構築し,モデルの精度を向上させます.
科学分野:
- 計算式数学
- ダイナミック・システム理論
- 機械学習
背景:
- ダイナミックなシステムにはしばしば予測が難しい不確実なパラメータが含まれます.
- これらのパラメータ分布を再構築することは,正確なシステムモデリングと予測に不可欠です.
- 既存の方法は,パラメータ空間の複雑さと次元性に苦労する可能性があります.
研究 の 目的:
- 動的システムにおけるパラメータ分布を再構築するための新しい方法を提案し分析する.
- 特定の損失関数で訓練されたストキャスティックニューラルネットワークの有効性を実証する.
- 様々なダイナミックなシステムでメソッドの性能を検証する.
主な方法:
- ローカル・タイム・デコップレッド・スクエア・ワセルスタイン-2メソッドの開発
- ストキャスティックニューラルネットワークモデルの適用
- 提案された損失関数を最小限に抑えることで ニューラルネットワークを訓練します
- 異なるダイナミックシステムからの数値的な例を用いた検証.
主要な成果:
- 提案されたローカル・タイム・デコップル・スクエア・ワースタータイン-2法は,パラメータ分布を効果的に再構築する.
- この損失関数で訓練された ストカスティックニューラルネットワークは 正確な近似値を提供します
- この方法は,多様なダイナミックなシステムで堅実な性能を示しています.
結論:
- 開発された方法は,ダイナミックシステムにおけるパラメータ推定のための強力なツールを提供します.
- このアプローチは,固有の不確実性を持つシステムの理解とモデリングを強化します.
- この発見は,ダイナミック・システム・モデリングに依存する分野に意味を持つ.
関連する概念動画
01:21Linear Approximation in Time Domain
124
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,...
124
01:23Linear time-invariant Systems
407
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...
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...
407
01:18Second Order systems II
171
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.
171
01:27State Space Representation
285
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...
285
01:24BIBO stability of continuous and discrete -time systems
512
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
512
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
710
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...
On...
710