From 331bb362fb91aeae35b631297503571fa2093fd8 Mon Sep 17 00:00:00 2001 From: Faezeh Habibi <155960330+Faezehabibi@users.noreply.github.com> Date: Mon, 9 Dec 2024 13:39:37 -0500 Subject: [PATCH 1/3] Update sindy.md --- docs/museum/sindy.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/museum/sindy.md b/docs/museum/sindy.md index c07ff654..e6315fc7 100644 --- a/docs/museum/sindy.md +++ b/docs/museum/sindy.md @@ -15,9 +15,10 @@ In this section, we teach, create, simulate, and visualize the Sparse Identifica 1. Learn how to discover the differential equation of a dynamical system using SINDy algorithm only by the system's stapshots. 2. Learn how to build polynomial libraries with arbitrary order out of the dataset. -3. Learn how to solve the sparse regression problem in 2 ways - - Iteratively finding the coefficient matrix by gradient descent. - - Iteratively performing the least squares (LSQ) method followed by thresholding-- Sequential Thresholding Least Square (STLSQ) for the given model. +3. Learn how to solve the sparse regression problem in various ways given SINDy's components. + - Sequential Thresholding Least Square (STLSQ) -- least squares (LSQ) method followed by thresholding iteratively. + - Iterative lasso regression. + The model **code** for this exhibit can be found [here](https://github.com/NACLab/ngc-museum/exhibits/sindy/sindy.py). @@ -107,8 +108,7 @@ This phase involves gathering the raw data points representing the system's stat ### 2.A: Making Library → $\mathbf{\Theta}_{(m \times p)}$ In this step, using the dataset collected in step 1, given the pre-defined function terms, we construct the dictionary of candidate predictors for system's differential equations. These functions form the columns of our library matrix $\mathbf{\Theta}(\mathbf{X})$ and $p$ is the number of candidate predictors. To identify the dynamical structure of the system this library of candidate functions appear in the regression problem to propose the model's structure that later the coefficient matrix will give weight to them according to the problem setup. Assuming sparse models for the system, by sparsification (LASSO or thresholding weigths) decide which structure best describe the system's behavior using predictors. -Given a set of time-series measurements of a dynamical system state variables ($\mathbf{X}_{(m \times n)}$) we construct: -Library of Candidate Functions: $\Theta(\mathbf{X}) = [\mathbf{1} \quad \mathbf{X} \quad \mathbf{X}^2 \quad \mathbf{X}^3 \quad \sin(\mathbf{X}) \quad \cos(\mathbf{X}) \quad ...]$ +Given a set of time-series measurements of a dynamical system state variables ($\mathbf{X}_{(m \times n)}$) we construct a library of candidate functions. For example: $\Theta(\mathbf{X}) = [\mathbf{1} \quad \mathbf{X} \quad \mathbf{X}^2 \quad \mathbf{X}^3 \quad ...]$

From 7979134c7b00387f48f6f7de4453553fffe26014 Mon Sep 17 00:00:00 2001 From: Faezeh Habibi <155960330+Faezehabibi@users.noreply.github.com> Date: Mon, 9 Dec 2024 13:43:19 -0500 Subject: [PATCH 2/3] Update sindy.md --- docs/museum/sindy.md | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/docs/museum/sindy.md b/docs/museum/sindy.md index e6315fc7..b55fc131 100644 --- a/docs/museum/sindy.md +++ b/docs/museum/sindy.md @@ -15,9 +15,8 @@ In this section, we teach, create, simulate, and visualize the Sparse Identifica 1. Learn how to discover the differential equation of a dynamical system using SINDy algorithm only by the system's stapshots. 2. Learn how to build polynomial libraries with arbitrary order out of the dataset. -3. Learn how to solve the sparse regression problem in various ways given SINDy's components. - - Sequential Thresholding Least Square (STLSQ) -- least squares (LSQ) method followed by thresholding iteratively. - - Iterative lasso regression. +3. Learn how to solve the sparse regression problem using the Sequential Thresholding Least Square (STLSQ) algorithm. + @@ -256,6 +255,9 @@ Solving LSQ with the sparse matrix $\mathbf{\Theta_s}$ and $\mathbf{W_s}$ and fi + + + + From 2e3a1f032b4736cea9d2efd92e11f5602c243cb6 Mon Sep 17 00:00:00 2001 From: Faezeh Habibi <155960330+Faezehabibi@users.noreply.github.com> Date: Mon, 16 Dec 2024 17:05:03 -0500 Subject: [PATCH 3/3] Add files via upload --- docs/images/museum/sindy/flow.png | Bin 173047 -> 173047 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/docs/images/museum/sindy/flow.png b/docs/images/museum/sindy/flow.png index b32dcd20bd8a1dd1b9eb32e67d25ca8ca5f9eabf..bb7e0a822a3a6eb622915031a093ea1a1071f6de 100644 GIT binary patch delta 28 kcmext_hxu%oDv*SpGy^v}xSbx`}b?CMMU#0KcXT&;S4c delta 28 kcmext_hxu9231#SR}bGJ2h@<-Nd+c6O-#=0I%{3s{jB1