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@@ -8,13 +8,13 @@ Sparse identification of nonlinear dynamics (SINDy) algorithm is a method that a
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## Examples:
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### Lorenz Equations
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Lorenz equation is a set of ordinary differential equations famous for having chaotic behavior. We will use the Lorenz equations to demonstrate the noise robustness of NSS-SINDy. Moreover, it is also used to test the performance of NSS-SINDy under different data usage.
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Lorenz equation is a set of ordinary differential equations famous for having chaotic behavior. We will use the Lorenz equations to demonstrate the noise robustness of modified-SINDy. Moreover, it is also used to test the performance of modified-SINDy under different data usage.
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### Van der Pol Oscillator
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The Van der Pol oscillator is used to demonstrate that NSS-SINDy can tackle different types of noise distributions. Moreover, we show that NSS-SINDy can identify the non-zero mean noise added to the signal.
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The Van der Pol oscillator is used to demonstrate that modified-SINDy can tackle different types of noise distributions. Moreover, we show that modified-SINDy can identify the non-zero mean noise added to the signal.
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### Duffing and Cubic Oscillator
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Duffing and Cubic oscillators are used to test the effectiveness of NSS-SINDy under different noise levels.
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Duffing and Cubic oscillators are used to test the effectiveness of modified-SINDy under different noise levels.
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### Lotka-Volterra Equations
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The Lotka-Volterra equations are usually used to describe the dynamics of the predator-prey system. We will show that NSS-SINDy can identify the models of Lotka-Volterra equations given noisy measurement data.
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The Lotka-Volterra equations are usually used to describe the dynamics of the predator-prey system. We will show that modified-SINDy can identify the models of Lotka-Volterra equations given noisy measurement data.
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