From 96be9d3984c2a81d7cbc83eb37adc3d90b167608 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 14:45:05 +0800 Subject: [PATCH 01/35] neural_ode part added --- README.md | 71 ++++++++++++++++++ doc/imgs/nerual_ode_example.png | Bin 0 -> 55006 bytes pyrat/__pycache__/__init__.cpython-39.pyc | Bin 0 -> 264 bytes .../__pycache__/__init__.cpython-39.pyc | Bin 0 -> 497 bytes .../__pycache__/algorithm.cpython-39.pyc | Bin 0 -> 1324 bytes .../__pycache__/alk2011hscc.cpython-39.pyc | Bin 0 -> 6311 bytes .../althoff2013hscc.cpython-39.pyc | Bin 0 -> 5821 bytes .../__pycache__/asb2008cdc.cpython-39.pyc | Bin 0 -> 5877 bytes .../__pycache__/hscc2005.cpython-39.pyc | Bin 0 -> 1551 bytes .../__pycache__/scs2022.cpython-39.pyc | Bin 0 -> 6773 bytes .../__pycache__/xse2016cav.cpython-39.pyc | Bin 0 -> 5223 bytes .../__pycache__/__init__.cpython-39.pyc | Bin 0 -> 251 bytes .../__pycache__/__init__.cpython-39.pyc | Bin 0 -> 320 bytes 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100644 pyrat/util/visualization/__pycache__/__init__.cpython-39.pyc create mode 100644 pyrat/util/visualization/__pycache__/plot.cpython-39.pyc create mode 100644 pyrat/util/visualization/__pycache__/vis_2d.cpython-39.pyc create mode 100644 pyrat/util/visualization/__pycache__/vis_3d.cpython-39.pyc create mode 100644 test/algorithm/temp_test.py create mode 100644 test/algorithm/test_neural_ode.py diff --git a/README.md b/README.md index 5de1403..490b58a 100644 --- a/README.md +++ b/README.md @@ -138,6 +138,77 @@ plot(tp, [0, 1]) ## Computing Reachable Sets based on Boundary Analysis for Neural ODE +An example for computing the reachable sets of neural ODEs with the tool is also provided. Users can refer +to the example files provided and modify the neural network parameters to compute the reachable sets of other neural odes. Moreover, it is also enabled for users to modify the required caluculation parameters to +see the effect of using different settings for calculating reachable sets. + +For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function: + +$$ +w1 = [[0.2911133 , 0.12008807], + [-0.24582624, 0.23181419], + [-0.25797904, 0.21687193], + [-0.19282854, -0.2602416 ], + [ 0.26780415, -0.20697702], + [ 0.23462369, 0.2294843 ], + [ -0.2583547 , 0.21444395], + [ -0.04514714, 0.29514763], + [-0.15318371, -0.275755] , + [ 0.24873598, 0.21018365]] + +b1 = [0.0038677 , -0.00026365, -0.007168970, 0.02469357, 0.01338706, + 0.00856025, -0.00888401, 0.00516089, -0.00634514, -0.01914518] + +w2 = [[-0.58693904, -0.814841 , -0.8175157 , 0.97060364, 0.6908913 , + -0.92446184, -0.79249185, -1.1507587 , 1.2072723 , -0.7983982], + [1.1564877 , -0.8991244 , -1.0774536 , -0.6731967 , 1.0154784 , + 0.8984464 , -1.0766245 , -0.238209 , -0.5233613 , 0.8886671]] + +b2 = [-0.04129209, -0.01508532] +$$ + +```python +from pyrat.algorithm import ASB2008CDC +from pyrat.dynamic_system import NonLinSys +from pyrat.geometry import Zonotope, Interval, Geometry +from pyrat.model import * +from pyrat.util.visualization import plot +from pyrat.neural_ode.model_generate import neuralODE + + +# init neural ODE +system = NonLinSys(Model(neuralODE, [2,1])) + +# settings for the computation +options = ASB2008CDC.Options() +options.t_end = 8 +options.step = 0.02 +options.tensor_order = 2 +options.taylor_terms = 2 +options.r0 = [Zonotope([1.4, 2.4], np.diag([0.17, 0.06]))] +from pyrat.geometry.operation import boundary + +c = np.array([1.4, 2.4], dtype=float) +inf = c - [0.17, 0.06] +sup = c + [0.17, 0.06] +box = Interval(inf, sup) + +options.u = Zonotope.zero(1, 1) +options.u_trans = np.zeros(1) + +# settings for the using geometry +Zonotope.REDUCE_METHOD = Zonotope.REDUCE_METHOD.GIRARD +Zonotope.ORDER = 50 + +# reachable sets computation +ti, tp, _, _ = ASB2008CDC.reach(system, options) + +# visualize the results +plot(tp, [0, 1]) +``` + +![](doc/imgs/neural_ode_example.png) + ## Frequently Asked Questions and Troubleshooting ### the computation is slow diff --git a/doc/imgs/nerual_ode_example.png b/doc/imgs/nerual_ode_example.png new file mode 100644 index 0000000000000000000000000000000000000000..fe038e641eea387a2847c09010cf5ee83530fee0 GIT binary patch literal 55006 zcmd>lg;!MHA1xuE(u#B|-Q6IKQhosiW$2a~7@DCJ0f_;mTUw+9q-&5E8Ug8M2fz*I$?Rq04smdG5#bl(7v^QQ_wWEiqy+?= z|L+C-uI_dM+~Q2CKqC*p8gC(3Sfm!1FZMTuVh1d&NzE53iUvNJy9?f#*00m<4o4d6 zl?*rc`=qdyhrb3td+_0b$56#eeUDhV#n4VgL(_J8jU_zdYt%!WFOV<`>al0+BPS;w z!%6#cBL}g@!wCMJG<(k=>&e4sW%Z57w7(8 z-v%?tIo3a+{Qvs*kHPuZTEwo{|BZX&KK8|GCct>6r6d-YH1k*bYlfe-#DWktzMFuj(b0(-#mcMG zvG|Xp2J&NFvBv)lE!#e?QNbJlhTWP5-j{5pIC; zuJ>;oO8zueZ*?Xt0sqs_L}#QTqLRNp7c;$ZHi50=l8>c{o)XtKuej=2U;9)~t^Wg3 zwXuiix-Tl1tPs;)(;y<4JalVKnn{_A{rsG55Z;ItMcC(A@(yYMhd!Vx!0udqNz9MMWMO-+ 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-0.238209 , -0.5233613 , 0.8886671]] + + b2 = [-0.04129209, -0.01508532] + + act1 = "sigmoid" + + weight = [w1, w2] + bias = [b1,b2] + func_list =[act1] + + return weight, bias, func_list \ No newline at end of file diff --git a/pyrat/neural_ode/model_generate.py b/pyrat/neural_ode/model_generate.py new file mode 100644 index 0000000..480d24a --- /dev/null +++ b/pyrat/neural_ode/model_generate.py @@ -0,0 +1,40 @@ +from sympy import * +import sys +import numpy as np +import math +# import model_description as md +import pyrat.neural_ode.model_description as md + +def sigmoid(x): + return (1 / (1 + exp(-x))) + +def neuralODE (x, u): + weight, bias, func_list = md.get_param() + + layer_num = np.shape(bias)[0] + dim = np.shape(weight[0])[1] + + x = Matrix(x) + dxdt = [None] * dim + + for i in range(layer_num): + if (i < layer_num -1): + w = Matrix(weight[i]) + b = Matrix(bias[i]) + act_func = func_list[i] + if act_func == "tanh": + vecF = np.vectorize(tanh) + elif act_func == "sigmoid": + 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For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function: $$ -w1 = [[0.2911133 , 0.12008807], - [-0.24582624, 0.23181419], - [-0.25797904, 0.21687193], - [-0.19282854, -0.2602416 ], - [ 0.26780415, -0.20697702], - [ 0.23462369, 0.2294843 ], - [ -0.2583547 , 0.21444395], - [ -0.04514714, 0.29514763], - [-0.15318371, -0.275755] , - [ 0.24873598, 0.21018365]] - -b1 = [0.0038677 , -0.00026365, -0.007168970, 0.02469357, 0.01338706, - 0.00856025, -0.00888401, 0.00516089, -0.00634514, -0.01914518] - -w2 = [[-0.58693904, -0.814841 , -0.8175157 , 0.97060364, 0.6908913 , - -0.92446184, -0.79249185, -1.1507587 , 1.2072723 , -0.7983982], - [1.1564877 , -0.8991244 , -1.0774536 , -0.6731967 , 1.0154784 , - 0.8984464 , -1.0766245 , -0.238209 , -0.5233613 , 0.8886671]] - -b2 = [-0.04129209, -0.01508532] + \begin{equation} + w_1 = \left[ + \begin{array}{cc} + 0.2911133 & 0.12008807\\ + -0.24582624 & 0.23181419\\ + -0.25797904 & 0.21687193\\ + -0.19282854 & -0.2602416 \\ + 0.26780415 & -0.20697702\\ + 0.23462369 & 0.2294843 \\ + -0.2583547 & 0.21444395\\ + -0.04514714 & 0.29514763\\ + -0.15318371 & -0.275755 \\ + 0.24873598 & 0.21018365 + \end{array} + \right] + \end{equation} + +\begin{equation} + b_1 = \left[ + \begin{array}{ccccc} + 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ + 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 + \end{array} + \right] + \end{equation} + + +\begin{equation} + w_2 = \left[ + \begin{array}{ccccc} + -0.58693904& -0.814841 & -0.8175157& 0.97060364& 0.6908913\\ + -0.92446184& -0.79249185& -1.1507587& 1.2072723& -0.7983982\\ + 1.1564877& -0.8991244& -1.0774536& -0.6731967& 1.0154784\\ + 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 + \end{array} + \right] + \end{equation} + +\begin{equation} + b_2 = \left[ + \begin{array}{cc} + -0.04129209& -0.01508532 + \end{array} + \right] + \end{equation} $$ ```python diff --git a/doc/imgs/nerual_ode_example.png b/doc/imgs/neural_ode_example.png similarity index 100% rename from doc/imgs/nerual_ode_example.png rename to doc/imgs/neural_ode_example.png From 63c4f45ac994c3c188dbe6dfd9e2a45db8381d96 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:22:16 +0800 Subject: [PATCH 03/35] update --- README.md | 62 ++++++++++++++++++------------- test/algorithm/test_neural_ode.py | 15 +++----- 2 files changed, 43 insertions(+), 34 deletions(-) diff --git a/README.md b/README.md index 05c51a3..9076227 100644 --- a/README.md +++ b/README.md @@ -133,8 +133,10 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` +| With Boundary Analysis | Without Boundary Analysis | +| :-----------: | :-----------: | +| ![](doc/imgs/vanderpol_example.png) | ![](doc/imgs/vanderpol_example.png) | -![](doc/imgs/vanderpol_example.png) ## Computing Reachable Sets based on Boundary Analysis for Neural ODE @@ -145,7 +147,7 @@ see the effect of using different settings for calculating reachable sets. For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function: $$ - \begin{equation} + \begin{equation*} w_1 = \left[ \begin{array}{cc} 0.2911133 & 0.12008807\\ @@ -160,19 +162,11 @@ $$ 0.24873598 & 0.21018365 \end{array} \right] - \end{equation} - -\begin{equation} - b_1 = \left[ - \begin{array}{ccccc} - 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ - 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 - \end{array} - \right] - \end{equation} + \end{equation*} -\begin{equation} +\\ +\begin{equation*} w_2 = \left[ \begin{array}{ccccc} -0.58693904& -0.814841 & -0.8175157& 0.97060364& 0.6908913\\ @@ -181,15 +175,26 @@ $$ 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 \end{array} \right] - \end{equation} + \end{equation*} + +\\ +\begin{equation*} + b_1 = \left[ + \begin{array}{ccccc} + 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ + 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 + \end{array} + \right] + \end{equation*} -\begin{equation} +\\ +\begin{equation*} b_2 = \left[ \begin{array}{cc} -0.04129209& -0.01508532 \end{array} \right] - \end{equation} + \end{equation*} $$ ```python @@ -199,6 +204,7 @@ from pyrat.geometry import Zonotope, Interval, Geometry from pyrat.model import * from pyrat.util.visualization import plot from pyrat.neural_ode.model_generate import neuralODE +from pyrat.geometry.operation import boundary # init neural ODE @@ -206,17 +212,18 @@ system = NonLinSys(Model(neuralODE, [2,1])) # settings for the computation options = ASB2008CDC.Options() -options.t_end = 8 -options.step = 0.02 +options.t_end = 6 +options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 -options.r0 = [Zonotope([1.4, 2.4], np.diag([0.17, 0.06]))] -from pyrat.geometry.operation import boundary +Z = Zonotope([0.5, 0], np.diag([1, 0.5])) + +# Reachable sets computed with boundary analysis +# options.r0 = boundary(Z,1,Geometry.TYPE.ZONOTOPE) + +# Reachable sets computed without boundary analysis +options.r0 = [Z] -c = np.array([1.4, 2.4], dtype=float) -inf = c - [0.17, 0.06] -sup = c + [0.17, 0.06] -box = Interval(inf, sup) options.u = Zonotope.zero(1, 1) options.u_trans = np.zeros(1) @@ -231,8 +238,13 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` +|Time | With Boundary Analysis | Without Boundary Analysis | +| :-----------: | :-----------: | :-----------: | +|t=2s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) +|t=4s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) +|t=8s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) + -![](doc/imgs/neural_ode_example.png) ## Frequently Asked Questions and Troubleshooting diff --git a/test/algorithm/test_neural_ode.py b/test/algorithm/test_neural_ode.py index c50d4bd..b25b114 100644 --- a/test/algorithm/test_neural_ode.py +++ b/test/algorithm/test_neural_ode.py @@ -10,6 +10,7 @@ from pyrat.model import * from pyrat.util.visualization import plot from pyrat.neural_ode.model_generate import neuralODE +from pyrat.geometry.operation import boundary if __name__=="__main__": # init neural ODE @@ -17,18 +18,14 @@ # settings for the computation options = ASB2008CDC.Options() - options.t_end = 8 - options.step = 0.02 + options.t_end = 6 + options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 - options.r0 = [Zonotope([1.4, 2.4], np.diag([0.17, 0.06]))] - from pyrat.geometry.operation import boundary - - c = np.array([1.4, 2.4], dtype=float) - inf = c - [0.17, 0.06] - sup = c + [0.17, 0.06] - box = Interval(inf, sup) + Z = Zonotope([0.5, 0], np.diag([1, 0.5])) + # options.r0 = boundary(Z,1,Geometry.TYPE.ZONOTOPE) + options.r0 = [Z] options.u = Zonotope.zero(1, 1) options.u_trans = np.zeros(1) From ad061064abaaa9147ab80c978578a115f957d1ed Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:25:25 +0800 Subject: [PATCH 04/35] update --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 9076227..63b8b28 100644 --- a/README.md +++ b/README.md @@ -188,13 +188,13 @@ $$ \end{equation*} \\ -\begin{equation*} +\begin{align*} b_2 = \left[ \begin{array}{cc} -0.04129209& -0.01508532 \end{array} \right] - \end{equation*} + \end{align*} $$ ```python From 4d9dd27b0e7337c775e0fc4200b9cc978ba7ed6c Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:28:30 +0800 Subject: [PATCH 05/35] update --- README.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index 63b8b28..ed41bc2 100644 --- a/README.md +++ b/README.md @@ -188,13 +188,12 @@ $$ \end{equation*} \\ -\begin{align*} + b_2 = \left[ - \begin{array}{cc} +\begin{array}{cc} -0.04129209& -0.01508532 \end{array} - \right] - \end{align*} + \right] $$ ```python From 23937fe2ba75ba0b3e1ed48ad756e2e957c5b6f7 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:30:37 +0800 Subject: [PATCH 06/35] update --- README.md | 15 +++++---------- 1 file changed, 5 insertions(+), 10 deletions(-) diff --git a/README.md b/README.md index ed41bc2..4cb12a0 100644 --- a/README.md +++ b/README.md @@ -178,22 +178,17 @@ $$ \end{equation*} \\ -\begin{equation*} - b_1 = \left[ - \begin{array}{ccccc} + + b_1 = \begin{bmatrix} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 - \end{array} - \right] - \end{equation*} + \end{bmatrix} \\ - b_2 = \left[ -\begin{array}{cc} +b_2 = \begin{bmatrix} -0.04129209& -0.01508532 - \end{array} - \right] + \end{bmatrix} $$ ```python From 9798e9a09f00700169a6c24de50810900e9c27f7 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:31:12 +0800 Subject: [PATCH 07/35] update --- README.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/README.md b/README.md index 4cb12a0..bfc01a7 100644 --- a/README.md +++ b/README.md @@ -165,7 +165,7 @@ $$ \end{equation*} -\\ + \begin{equation*} w_2 = \left[ \begin{array}{ccccc} @@ -177,7 +177,6 @@ $$ \right] \end{equation*} -\\ b_1 = \begin{bmatrix} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ From 02d1d9a5c68198fd0181b619b3f91c20fc50be59 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:38:16 +0800 Subject: [PATCH 08/35] update --- README.md | 13 +++++++------ test/algorithm/test_neural_ode.py | 4 ++-- 2 files changed, 9 insertions(+), 8 deletions(-) diff --git a/README.md b/README.md index bfc01a7..df32f78 100644 --- a/README.md +++ b/README.md @@ -163,9 +163,8 @@ $$ \end{array} \right] \end{equation*} - - - +$$ +$$ \begin{equation*} w_2 = \left[ \begin{array}{ccccc} @@ -176,18 +175,20 @@ $$ \end{array} \right] \end{equation*} - - +$$ +$$ b_1 = \begin{bmatrix} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 \end{bmatrix} -\\ +$$ +$$ b_2 = \begin{bmatrix} -0.04129209& -0.01508532 \end{bmatrix} + $$ ```python diff --git a/test/algorithm/test_neural_ode.py b/test/algorithm/test_neural_ode.py index b25b114..dd6b95b 100644 --- a/test/algorithm/test_neural_ode.py +++ b/test/algorithm/test_neural_ode.py @@ -18,11 +18,11 @@ # settings for the computation options = ASB2008CDC.Options() - options.t_end = 6 + options.t_end = 1 options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 - Z = Zonotope([0.5, 0], np.diag([1, 0.5])) + Z = Zonotope([0.5, 0], np.diag([0.5, 0.5])) # options.r0 = boundary(Z,1,Geometry.TYPE.ZONOTOPE) options.r0 = [Z] From 30f1d518a0de994446491a1f44ca96fad85beca6 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:41:37 +0800 Subject: [PATCH 09/35] update --- README.md | 30 +++++++++++++++--------------- test/algorithm/test_neural_ode.py | 2 +- 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/README.md b/README.md index df32f78..5564603 100644 --- a/README.md +++ b/README.md @@ -147,9 +147,8 @@ see the effect of using different settings for calculating reachable sets. For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function: $$ - \begin{equation*} w_1 = \left[ - \begin{array}{cc} + \begin{align*} 0.2911133 & 0.12008807\\ -0.24582624 & 0.23181419\\ -0.25797904 & 0.21687193\\ @@ -160,35 +159,36 @@ $$ -0.04514714 & 0.29514763\\ -0.15318371 & -0.275755 \\ 0.24873598 & 0.21018365 - \end{array} + \end{align*} \right] - \end{equation*} $$ $$ -\begin{equation*} + w_2 = \left[ - \begin{array}{ccccc} + \begin{align*} -0.58693904& -0.814841 & -0.8175157& 0.97060364& 0.6908913\\ -0.92446184& -0.79249185& -1.1507587& 1.2072723& -0.7983982\\ 1.1564877& -0.8991244& -1.0774536& -0.6731967& 1.0154784\\ 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 - \end{array} - \right] - \end{equation*} + \end{align*} + \right] $$ $$ - b_1 = \begin{bmatrix} + b_1 = \left[ + \begin{align*} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 - \end{bmatrix} + \end{align*} + \right] $$ -$$ -b_2 = \begin{bmatrix} +$$ +b_2 = \left[ + \begin{align*} -0.04129209& -0.01508532 - \end{bmatrix} - + \end{align*} + \right] $$ ```python diff --git a/test/algorithm/test_neural_ode.py b/test/algorithm/test_neural_ode.py index dd6b95b..8a2e141 100644 --- a/test/algorithm/test_neural_ode.py +++ b/test/algorithm/test_neural_ode.py @@ -18,7 +18,7 @@ # settings for the computation options = ASB2008CDC.Options() - options.t_end = 1 + options.t_end = 2 options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 From 085378bd578e43edd8eca550363129e057170d29 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:42:21 +0800 Subject: [PATCH 10/35] update --- README.md | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index 5564603..025bbf0 100644 --- a/README.md +++ b/README.md @@ -161,8 +161,7 @@ $$ 0.24873598 & 0.21018365 \end{align*} \right] -$$ -$$ +\\ w_2 = \left[ \begin{align*} @@ -172,8 +171,7 @@ $$ 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 \end{align*} \right] -$$ -$$ +\\ b_1 = \left[ \begin{align*} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ @@ -181,9 +179,7 @@ $$ \end{align*} \right] -$$ - -$$ +\\ b_2 = \left[ \begin{align*} -0.04129209& -0.01508532 From 933fd97a688036158199cefd0e86eab975aee6a9 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 16:44:32 +0800 Subject: [PATCH 11/35] update --- README.md | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 025bbf0..d8e518e 100644 --- a/README.md +++ b/README.md @@ -161,8 +161,9 @@ $$ 0.24873598 & 0.21018365 \end{align*} \right] -\\ +$$ +$$ w_2 = \left[ \begin{align*} -0.58693904& -0.814841 & -0.8175157& 0.97060364& 0.6908913\\ @@ -171,15 +172,18 @@ $$ 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 \end{align*} \right] -\\ +$$ + +$$ b_1 = \left[ \begin{align*} 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 \end{align*} \right] +$$ -\\ +$$ b_2 = \left[ \begin{align*} -0.04129209& -0.01508532 From 1e7e43c606fe8fdef4123557660528feab8fd46e Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:06:17 +0800 Subject: [PATCH 12/35] update --- README.md | 35 +++++++++++++++--------------- doc/imgs/Neural_BA05.png | Bin 0 -> 339606 bytes doc/imgs/Neural_BA1.png | Bin 0 -> 302807 bytes doc/imgs/Neural_BA15.png | Bin 0 -> 435841 bytes doc/imgs/Neural_E05.png | Bin 0 -> 285888 bytes doc/imgs/Neural_E1.png | Bin 0 -> 375478 bytes doc/imgs/neural_ode_example.png | Bin 55006 -> 0 bytes test/algorithm/test_neural_ode.py | 10 ++++++--- 8 files changed, 25 insertions(+), 20 deletions(-) create mode 100644 doc/imgs/Neural_BA05.png create mode 100644 doc/imgs/Neural_BA1.png create mode 100644 doc/imgs/Neural_BA15.png create mode 100644 doc/imgs/Neural_E05.png create mode 100644 doc/imgs/Neural_E1.png delete mode 100644 doc/imgs/neural_ode_example.png diff --git a/README.md b/README.md index d8e518e..d9e305a 100644 --- a/README.md +++ b/README.md @@ -149,16 +149,16 @@ For example, consider a neural ODE with following parameters and $\textit{sigmoi $$ w_1 = \left[ \begin{align*} - 0.2911133 & 0.12008807\\ - -0.24582624 & 0.23181419\\ - -0.25797904 & 0.21687193\\ - -0.19282854 & -0.2602416 \\ - 0.26780415 & -0.20697702\\ - 0.23462369 & 0.2294843 \\ - -0.2583547 & 0.21444395\\ - -0.04514714 & 0.29514763\\ - -0.15318371 & -0.275755 \\ - 0.24873598 & 0.21018365 + 0.2911133 \quad & 0.12008807\\ + -0.24582624 \quad & 0.23181419\\ + -0.25797904 \quad & 0.21687193\\ + -0.19282854 \quad & -0.2602416 \\ + 0.26780415 \quad & -0.20697702\\ + 0.23462369\quad & 0.2294843 \\ + -0.2583547\quad & 0.21444395\\ + -0.04514714 \quad & 0.29514763\\ + -0.15318371 \quad & -0.275755 \\ + 0.24873598 \quad & 0.21018365 \end{align*} \right] $$ @@ -166,10 +166,10 @@ $$ $$ w_2 = \left[ \begin{align*} - -0.58693904& -0.814841 & -0.8175157& 0.97060364& 0.6908913\\ - -0.92446184& -0.79249185& -1.1507587& 1.2072723& -0.7983982\\ - 1.1564877& -0.8991244& -1.0774536& -0.6731967& 1.0154784\\ - 0.8984464& -1.0766245& -0.238209 & -0.5233613& 0.8886671 + -0.58693904 & -0.814841 & -0.8175157 & 0.97060364 & 0.6908913\\ + -0.92446184 & -0.79249185 & -1.1507587 & 1.2072723 & -0.7983982\\ + 1.1564877 & -0.8991244 & -1.0774536 & -0.6731967 & 1.0154784\\ + 0.8984464 & -1.0766245 & -0.238209 & -0.5233613 & 0.8886671 \end{align*} \right] $$ @@ -232,11 +232,12 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` + |Time | With Boundary Analysis | Without Boundary Analysis | | :-----------: | :-----------: | :-----------: | -|t=2s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) -|t=4s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) -|t=8s| ![](doc/imgs/neural_ode_example.png) |![](doc/imgs/neural_ode_example.png) +|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) | +|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) | +|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | diff --git a/doc/imgs/Neural_BA05.png b/doc/imgs/Neural_BA05.png new file mode 100644 index 0000000000000000000000000000000000000000..a8f0d2f95386ea8a521288cc61405914a83ccf88 GIT binary patch literal 339606 zcmeEt1yfy3x8}iJf;)lW!QEYgLvYvN?(VJuf;$9vcemiK2X}Wn=#cMy@2#n+n)w5B zPgS2SwfE}YtC#g!PlqeWNg%=F!2%^v4~b9kkiUfy+ru-AT#T z#L3mb;Rit0z{$?a*2&7;@UzPg2S;;T8y0#tdS=?sW=>9aj@%3k*8lwgy{&^O0}VT| z*as0fyKfqf004@?-v(AJP-G4O0{|pNg_PYgPG8+KjMcn1-n%ARw9Y!@AI6*}OQ&h^ z&f0@cyYJgl#@mU*7H@gF$G)GlZSp$fy2 z1fd#2940@*{XP4*>~#GG`1GIK!d5sBdp_XrDL6(r#KcAFw0XZgTC!vQd8f*3L6asC zUaQec=;Zf33D|BrBR~Jd($doCE9*aGA0_tYN|d5vV!+V^JE;c@KYi=;EBJo&!-xGJ z>g~0Oqdx`*2e}WXKYzSl%X?a?Oe6Vk-`n_eYn_)7R>EBeS)Px%#7`uRR?7k3Bf6g3 zx}IB`TAt6_TCPXF4jVI{t~5jnJmm{$x{g&et&jLaz`zFhLBJqi9?APY@m!t;|1;i$ z>j=cp4Vux?3?08vybnb-rmlu!2zO*{JWC^vBZdHvz~FM)0d6u{+#YiEK(%NTa&W$*-(z$Ju$pq?Ia_G3R~ zXYRpw`sAadBLj1D$q;?G|Ioj3&NzDkVQPSZO!zLlA=Xafyg@8?4>jQm7(QGBbbN?2jMtnm9OIXFLEc8q69r zGf(y$K)~nzfB5rAbfcpP2DU(l*vwm7?)khN!?h6*aN+y@{4t)RmpC@Te{TuPz=UPQgl4%i3>eq%%+c&QdsK zR!&z}wl%QPew41sZhs7y|LrOkVmL~T_-QKCZR2@;sOw4XJpzWv%`evHHowfI>1jFp zRl}weWa4wu=&ruTXr(#8L;xT|%Le*OHHm&tlQTz?zj!gJ%f z`Q>^PH2Dq^fM8@|>KRU;ZAw?%C{MsI8e62E-5^?e5N46WMr zA$eUVWbewq-^#b_#!Ejg4e<{a@!wHbcHFN-d)xmb^)*gq3(*!REbDct9OsD~ka0sEI!jRD!e zJ&>?R{SVQ9gzJN-~)8H&C{HQnKkhjq^hBj0OEU$la`Rsn1s zC&h!5SnpFKQ@+AwE1Uk&e|_O4Jksavr@5lXmh5LPA5gMy>JYJSM!HRFIPpsl@$T+$ zf+^qIgU`i7N=nM%3zzdT#_Q|r%VF%>Vd;)k!A$861qH<)V`luT_# ziONuPRFu_!kL|avJ=pIxo14S@*y|9Ec7yqQjt@Vv>ihn>G3D)bn@_y=-1Yvv-0A&X zdNyy7cm`}@;pQGm-*_=0@_o6wS(h)H&(o%_diwIO0bc0X2LE$$ zf4wOB_}!RVS)FQmD*j`jU^g*w1e2%>RCSsbDuFKS#Lr7Zhi7Md6}H|drDuyeu7m<_ zI|360$+{!59Bci0?{|8RTfx}Ze?Q=$y-LfbCAgrVU?N+oNX}cjO6(u28E2<=PFcOM zx%oL}r@YKXMqa+EETa5J#h(1zuDsh~+j{WD^8uf#<@mgsp7%QZH&jSSq049i_kRto zd&f4-=gteqy+k#K|M)1MkN*#A&XMuZ=(^#}!O(GwcH#5T)^)z4Zt1=qPPx?Xe)B$k zgZZyT-_fezVhs9QhS-X;}z zofR10-6iAWvXI2N3Rn0{I<&<0*{>Rn)N9g{?)BgV*XzX;Z$_xILgl*t>8Z<>lU%zubFmwmS zpn^Q25Dv(I7P^C@MVai2RLLR5!!45kicxV$PFm;JYgBw|8?K&5)FDXj5#_?`pDQPR zVW@Pj!#ZZ3G=~0b#}rPZdx`zaIf{}KLxG7rixF|2VeF@6JbkXiH?%nTl4UqKVAXfi zq%dfAcE^^Rx?ib={<9g|OvkjS=(Vwnb(#1Yh9T5)cJT)#N`v}tZLb;_{0Ovm5jz?C zWX{L8)045KzCxposixsdCIPcD(>cTB77W-Y2wBv~m9@}DWhn1Zs&^$jxH<-?fgkC^S+ZSw`W(jtx`ltb? zO;p_%+A9Afj?Li0Chrn*fnAM{G9Mz%2S03)ZzBYurtOV&7+i%|;Y82qcg_|)3ZtUm zKw&c82+53`sb`aWCPcx)S){_R;VRy0O;D3XUH#?cQ$yv@mpSta;Q2D5ds`r`R-ug1 ze5dy*h3#_+8ykg8uz9JvVE&`~!`;}d$pouAiRLDGohWcndk^`BxK@qPRCBD~Itv-w zow{BGyhk{t9cj)>RywR3L z)Uliow@FZY>Ie=r!VZOlq&U$>qd?J16gs2AXuJCl<3ZTH{jZ z2}lB+0_R1G%Umc~o)aUIZLK)XA1McB>Fsd}u7bG<3`6`>AOAXEttvFMW=BL<2Jl3c^zP^t3%BG*~ z#N`E8TKgg*qw4g3TBw|pM5%OLOnH2hNYp=kbpHbYXk$29x1@@hcp`-P6eiCX=)I-8 zeRWW?hij&4=c40JbFYuGhAfSaTB(dUx36 zyd@?#d&(dyMV0-EzP4-zf}I7D6Ji|9pz~!q(|AB{bJ8iPer}xFA!EO-MkyaO;a7M} zv2w%GWvtXfVSM%D>D{uQ)*`c!X3$AlX?bTfN!LtY5G38GO?z^NRcW0$#DQezI0aOm z^t#5wXrIzyC&{YHD!epDpyqq)umqTC7a5Lsr~4mqv@MUmaA~Ni8btNx!l_?34qtau z4ADeI*ujC}D5wDH*~}2=>3HX%bJQrG2@pFY?3AO*gzLd2$mOR7a>DGKq5_2qfE5k> ze))#Hm_}zK)})ptgIE=an&cZh6I|Y>)3x+ikuyxA8x~M0RJe@=iaB2tpfP9%KiQid z))SmGE3rL|25bCs4yz!q#VSkiyEZHv*2)rSxXv;n&mt-nMI1m%A{8O8EwfO)0BVxv zYt!TwplKk}4UDnU0k6|ywUfU@(KWzYkYrS9Vx=WPKtx!JnTPst{j;Qfi>o=qvUf*b zp>x`xu*w&HJbewC^htEP#wp|twN{3$^x?a|txG|d7b#nCMuBg_$YDG==iz=uwDJ9v z=kyqpAI~CaRD(d7yD0=~>alVhWyZ7GN2E!_*3|YT5gS*dL+a z8Zt0*ZvSU&Fo;XG?Uyok0F7uR>6q3FMSVbu3p8^io^@`L^(HrJz4i(ovw?%EWkv2e z{%WHL1$dSDpGG#U$QVrS1${apGhE$or4;agI9MwsL!|E55~^aMm_H#d_Dy^%TW92R zhk@>8&oy_YVZlX5kIPU;8i-7}9n%4$E3mI1F#`T7t|d^RRTvEgk zN{gI(H&rTYM!E8$67dVADr*+cD&>gC4wUu)BOo7M5@p|#o?o})E z%-wCrM2s)U19p#sAkF_zH_SRD@Hq!l_)Cx!0!8xYo!$bY@8%!@^8Z8%ZcyQ0BU!UN zgZArC(6hLt+BqX~eaKv=Cq64<=u*WvOEeoVyyp*m(gf>?W6Cn(tsFFWw-D?W$+sNFmAUBQEX!2(272gd>%uXAQF9zLgeQ zgJFOc2uVtJ3f(0w=9#+9ElRce+J{YyLZ2MoyNElrG5|AQbAz~2jAQ

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z`z#g%E-pT#{T;Z}IOYGhHuF7=peu@ixAU|g=Ckf8u{wKw-#1f+Z8`^pV+Z<&DB5Q^!?odG%ol+ky--FCZd_g~PhOmi%YJye8JrGV?m_K1NN z8M~YUuB-bcVt&8I7`V`G$)-({g#B$M0-GCo`~Q}Ot&ckkEF6D6V7EWf3LFpu2InzX z@z^8p>%Lpx`!sF)6wuWJpR_=2IFFk)9}Y0jDLSQjr~dz6nc_2s3~Qpd_cilbb*x^$ zZx(;;3ul`j51MQKJeE&CIZ3q#IGb@Em=R-2F1muR>ev$nZyRE5fq)wncw3Tx>bEyl Uzl$uFU%~(cp00i_>zopr0Dk)Q%K!iX diff --git a/test/algorithm/test_neural_ode.py b/test/algorithm/test_neural_ode.py index 8a2e141..e03ff67 100644 --- a/test/algorithm/test_neural_ode.py +++ b/test/algorithm/test_neural_ode.py @@ -18,14 +18,18 @@ # settings for the computation options = ASB2008CDC.Options() - options.t_end = 2 + options.t_end = 0.5 options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 Z = Zonotope([0.5, 0], np.diag([0.5, 0.5])) - # options.r0 = boundary(Z,1,Geometry.TYPE.ZONOTOPE) + + # Reachable sets computed with boundary analysis + options.r0 = boundary(Z,1,Geometry.TYPE.ZONOTOPE) + + # Reachable sets computed without boundary analysis + # options.r0 = [Z] - options.r0 = [Z] options.u = Zonotope.zero(1, 1) options.u_trans = np.zeros(1) From 3a50dc2641483e93412d102800562eb6df56ef60 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:07:37 +0800 Subject: [PATCH 13/35] update --- README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index d9e305a..d6f8442 100644 --- a/README.md +++ b/README.md @@ -166,10 +166,10 @@ $$ $$ w_2 = \left[ \begin{align*} - -0.58693904 & -0.814841 & -0.8175157 & 0.97060364 & 0.6908913\\ - -0.92446184 & -0.79249185 & -1.1507587 & 1.2072723 & -0.7983982\\ - 1.1564877 & -0.8991244 & -1.0774536 & -0.6731967 & 1.0154784\\ - 0.8984464 & -1.0766245 & -0.238209 & -0.5233613 & 0.8886671 + -0.58693904 \quad & -0.814841 \quad & -0.8175157 \quad & 0.97060364 \quad & 0.6908913\\ + -0.92446184 \quad & -0.79249185 \quad & -1.1507587 \quad & 1.2072723 \quad & -0.7983982\\ + 1.1564877 \quad & -0.8991244 \quad & -1.0774536 \quad & -0.6731967 \quad & 1.0154784\\ + 0.8984464 \quad & -1.0766245 \quad & -0.238209 \quad & -0.5233613 \quad & 0.8886671 \end{align*} \right] $$ @@ -177,8 +177,8 @@ $$ $$ b_1 = \left[ \begin{align*} - 0.0038677& -0.00026365& -0.007168970& 0.02469357& 0.01338706\\ - 0.00856025& -0.00888401& 0.00516089& -0.00634514& -0.01914518 + 0.0038677\quad & -0.00026365\quad & -0.007168970\quad & 0.02469357\quad & 0.01338706\\ + 0.00856025\quad & -0.00888401\quad & 0.00516089\quad & -0.00634514\quad & -0.01914518 \end{align*} \right] $$ @@ -186,7 +186,7 @@ $$ $$ b_2 = \left[ \begin{align*} - -0.04129209& -0.01508532 + -0.04129209\quad & -0.01508532 \end{align*} \right] $$ From 0aea7903be5aa79d1d73286436880e84d236c5cf Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:09:20 +0800 Subject: [PATCH 14/35] update --- README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index d6f8442..bf7922e 100644 --- a/README.md +++ b/README.md @@ -166,10 +166,10 @@ $$ $$ w_2 = \left[ \begin{align*} - -0.58693904 \quad & -0.814841 \quad & -0.8175157 \quad & 0.97060364 \quad & 0.6908913\\ - -0.92446184 \quad & -0.79249185 \quad & -1.1507587 \quad & 1.2072723 \quad & -0.7983982\\ - 1.1564877 \quad & -0.8991244 \quad & -1.0774536 \quad & -0.6731967 \quad & 1.0154784\\ - 0.8984464 \quad & -1.0766245 \quad & -0.238209 \quad & -0.5233613 \quad & 0.8886671 + -0.58693904 \quad & -0.814841 & -0.8175157 \quad & 0.97060364 & 0.6908913\\ + -0.92446184 \quad & -0.79249185 & -1.1507587 \quad & 1.2072723 & -0.7983982\\ + 1.1564877 \quad & -0.8991244 & -1.0774536 \quad & -0.6731967 & 1.0154784\\ + 0.8984464 \quad & -1.0766245 & -0.238209 \quad & -0.5233613 & 0.8886671 \end{align*} \right] $$ @@ -177,8 +177,8 @@ $$ $$ b_1 = \left[ \begin{align*} - 0.0038677\quad & -0.00026365\quad & -0.007168970\quad & 0.02469357\quad & 0.01338706\\ - 0.00856025\quad & -0.00888401\quad & 0.00516089\quad & -0.00634514\quad & -0.01914518 + 0.0038677\quad & -0.00026365 & -0.007168970\quad & 0.02469357 & 0.01338706\\ + 0.00856025\quad & -0.00888401& 0.00516089\quad & -0.00634514 & -0.01914518 \end{align*} \right] $$ @@ -186,7 +186,7 @@ $$ $$ b_2 = \left[ \begin{align*} - -0.04129209\quad & -0.01508532 + -0.04129209 \quad & -0.01508532 \end{align*} \right] $$ From d2dea1d0ee2586056ad5565901cae644cd6ef780 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:12:02 +0800 Subject: [PATCH 15/35] update --- README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index bf7922e..2011335 100644 --- a/README.md +++ b/README.md @@ -206,7 +206,7 @@ system = NonLinSys(Model(neuralODE, [2,1])) # settings for the computation options = ASB2008CDC.Options() -options.t_end = 6 +options.t_end = 1.5 options.step = 0.01 options.tensor_order = 2 options.taylor_terms = 2 @@ -232,6 +232,7 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` +In the following table, we show the reachable computed with boundary analysis and without boundary analysis on different time instance cases. |Time | With Boundary Analysis | Without Boundary Analysis | | :-----------: | :-----------: | :-----------: | From 7cdf081243ba40cd0072ee6fd049416e1d024573 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:17:26 +0800 Subject: [PATCH 16/35] update --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 2011335..6798ab1 100644 --- a/README.md +++ b/README.md @@ -236,9 +236,9 @@ In the following table, we show the reachable computed with boundary analysis an |Time | With Boundary Analysis | Without Boundary Analysis | | :-----------: | :-----------: | :-----------: | -|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) | -|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) | -|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | +|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) +|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) +|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ From f8d030a17f6c6dfe581beb64757f030bd16da698 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:18:16 +0800 Subject: [PATCH 17/35] update --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 6798ab1..2011335 100644 --- a/README.md +++ b/README.md @@ -236,9 +236,9 @@ In the following table, we show the reachable computed with boundary analysis an |Time | With Boundary Analysis | Without Boundary Analysis | | :-----------: | :-----------: | :-----------: | -|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) -|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) -|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ +|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) | +|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) | +|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | From a3063e56b55fdcc8b965d2192498a005c6f7c2a8 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:22:57 +0800 Subject: [PATCH 18/35] update --- README.md | 19 +++++++++++-------- 1 file changed, 11 insertions(+), 8 deletions(-) diff --git a/README.md b/README.md index 2011335..89838cb 100644 --- a/README.md +++ b/README.md @@ -133,9 +133,9 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` -| With Boundary Analysis | Without Boundary Analysis | -| :-----------: | :-----------: | -| ![](doc/imgs/vanderpol_example.png) | ![](doc/imgs/vanderpol_example.png) | +| With Boundary Analysis | Without Boundary Analysis | +| :---------------------------------: | :---------------------------------: | +| ![](doc/imgs/vanderpol_example.png) | ![](doc/imgs/vanderpol_example.png) | ## Computing Reachable Sets based on Boundary Analysis for Neural ODE @@ -234,12 +234,15 @@ plot(tp, [0, 1]) ``` In the following table, we show the reachable computed with boundary analysis and without boundary analysis on different time instance cases. -|Time | With Boundary Analysis | Without Boundary Analysis | -| :-----------: | :-----------: | :-----------: | -|t=0.5s| ![](doc/imgs/neural_BA05.png) |![](doc/imgs/neural_E05.png) | -|t=1s| ![](doc/imgs/neural_BA1.png) |![](doc/imgs/neural_E1.png) | -|t=1.5s| ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | +| Time | With Boundary Analysis | Without Boundary Analysis | +| :----: | :---------------------------: | :--------------------------: | +| t=0.5s | ![](doc/imgs/neural_BA05.png) | ![](doc/imgs/neural_E05.png) | +| t=1.0s | ![](doc/imgs/neural_BA1.png) | ![](doc/imgs/neural_E1.png) | +| t=1.5s | ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | +| Time | With Boundary Analysis | Without Boundary Analysis | +| :----: | :---------------------------------: | :---------------------------------: | +| t=0.5s | ![](doc/imgs/neural_BA05.png) | ![](doc/imgs/neural_E05.png) | ## Frequently Asked Questions and Troubleshooting From 8cb7dca33703dab32ee9470f875cab49b2d4fa66 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:26:15 +0800 Subject: [PATCH 19/35] update --- README.md | 7 ++----- 1 file changed, 2 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index 89838cb..c68372f 100644 --- a/README.md +++ b/README.md @@ -133,6 +133,7 @@ ti, tp, _, _ = ASB2008CDC.reach(system, options) # visualize the results plot(tp, [0, 1]) ``` + | With Boundary Analysis | Without Boundary Analysis | | :---------------------------------: | :---------------------------------: | | ![](doc/imgs/vanderpol_example.png) | ![](doc/imgs/vanderpol_example.png) | @@ -234,17 +235,13 @@ plot(tp, [0, 1]) ``` In the following table, we show the reachable computed with boundary analysis and without boundary analysis on different time instance cases. + | Time | With Boundary Analysis | Without Boundary Analysis | | :----: | :---------------------------: | :--------------------------: | | t=0.5s | ![](doc/imgs/neural_BA05.png) | ![](doc/imgs/neural_E05.png) | | t=1.0s | ![](doc/imgs/neural_BA1.png) | ![](doc/imgs/neural_E1.png) | | t=1.5s | ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | -| Time | With Boundary Analysis | Without Boundary Analysis | -| :----: | :---------------------------------: | :---------------------------------: | -| t=0.5s | ![](doc/imgs/neural_BA05.png) | ![](doc/imgs/neural_E05.png) | - - ## Frequently Asked Questions and Troubleshooting ### the computation is slow From 2db67c9e8303ff293a4a9f2617c4c7f357cc2426 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:27:58 +0800 Subject: [PATCH 20/35] update --- README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index c68372f..8088749 100644 --- a/README.md +++ b/README.md @@ -238,9 +238,9 @@ In the following table, we show the reachable computed with boundary analysis an | Time | With Boundary Analysis | Without Boundary Analysis | | :----: | :---------------------------: | :--------------------------: | -| t=0.5s | ![](doc/imgs/neural_BA05.png) | ![](doc/imgs/neural_E05.png) | -| t=1.0s | ![](doc/imgs/neural_BA1.png) | ![](doc/imgs/neural_E1.png) | -| t=1.5s | ![](doc/imgs/neural_BA15.png) | __Set Explosion Occured!__ | +| t=0.5s | ![](doc/imgs/Neural_BA05.png) | ![](doc/imgs/Neural_E05.png) | +| t=1.0s | ![](doc/imgs/Neural_BA1.png) | ![](doc/imgs/Neural_E1.png) | +| t=1.5s | ![](doc/imgs/Neural_BA15.png) | Set Explosion Occured! | ## Frequently Asked Questions and Troubleshooting From 21515a80ee92b832a81ff442c59f0176f2492ab5 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:28:51 +0800 Subject: [PATCH 21/35] update --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 8088749..d0dd4b6 100644 --- a/README.md +++ b/README.md @@ -240,7 +240,7 @@ In the following table, we show the reachable computed with boundary analysis an | :----: | :---------------------------: | :--------------------------: | | t=0.5s | ![](doc/imgs/Neural_BA05.png) | ![](doc/imgs/Neural_E05.png) | | t=1.0s | ![](doc/imgs/Neural_BA1.png) | ![](doc/imgs/Neural_E1.png) | -| t=1.5s | ![](doc/imgs/Neural_BA15.png) | Set Explosion Occured! | +| t=1.5s | ![](doc/imgs/Neural_BA15.png) | __Set Explosion Occured!__ | ## Frequently Asked Questions and Troubleshooting From 5e52fee52713caaf1f09de0156ad02b2dec73d90 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:35:23 +0800 Subject: [PATCH 22/35] update --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index d0dd4b6..cfd0e94 100644 --- a/README.md +++ b/README.md @@ -145,7 +145,7 @@ An example for computing the reachable sets of neural ODEs with the tool is also to the example files provided and modify the neural network parameters to compute the reachable sets of other neural odes. Moreover, it is also enabled for users to modify the required caluculation parameters to see the effect of using different settings for calculating reachable sets. -For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function: +For example, consider a neural ODE with following parameters and $\textit{sigmoid}$ activation function, also evaluated in 'Manzanas Lopez, D., Musau, P., Hamilton, N. P., & Johnson, T. T. Reachability analysis of a general class of neural ordinary differential equations. In Formal Modeling and Analysis of Timed Systems: 20th International Conference, FORMATS 2022, Warsaw, Poland, September 13–15, 2022, Proceedings (pp. 258-277).': $$ w_1 = \left[ From 9e87fd1beb12b78f8de080b9f268514022f3e40d Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:42:32 +0800 Subject: [PATCH 23/35] update --- README.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/README.md b/README.md index cfd0e94..bfa9e62 100644 --- a/README.md +++ b/README.md @@ -281,6 +281,14 @@ it is inevitable that the range of +### RuntimeWarning: divide by zero encountered in true_divide + +-This warning may be reported on the paltforms with Windows operating system. It does not affect the running of the tool and it can be eliminiated with +```python + nnumpy.seterr(divide='ignore',invalid='ignore') +``` +in the decalration. + > Feel free to contact [dingjianqiang0x@gmail.com](mailto:dingjianqiang0x@gmail.com) if you find any > issues or bugs in this code, or you struggle to run it in any way. From aecf7a49a5839e1d046be506564bcc4a321874d5 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:43:03 +0800 Subject: [PATCH 24/35] update --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index bfa9e62..c4380e5 100644 --- a/README.md +++ b/README.md @@ -285,7 +285,7 @@ it is inevitable that the range of -This warning may be reported on the paltforms with Windows operating system. It does not affect the running of the tool and it can be eliminiated with ```python - nnumpy.seterr(divide='ignore',invalid='ignore') + numpy.seterr(divide='ignore',invalid='ignore') ``` in the decalration. From 34ebaae62c434d393938754d5751f6bec9b50fb5 Mon Sep 17 00:00:00 2001 From: LeungCAC <1265610755@qq.com> Date: Thu, 16 Feb 2023 19:46:40 +0800 Subject: [PATCH 25/35] update --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index c4380e5..601d5d6 100644 --- a/README.md +++ b/README.md @@ -244,7 +244,7 @@ In the following table, we show the reachable computed with boundary analysis an ## Frequently Asked Questions and Troubleshooting -### the computation is slow +### The computation is slow - The tool supports two modes of computation for reachable sets, one is to compute the reachable set of evolved states @@ -264,7 +264,7 @@ In the following table, we show the reachable computed with boundary analysis an reachable states at a suitable time consumption. -### controlling the wrapping effect +### Controlling the wrapping effect YramQ$g<5=_lGqnySLA6!;%tEXby>QD~K3IFtnPjPVGCCTuMAA&Z}0bvU#Nysdt)P8SPK9GT)Xg_fh!Ar|~xB{{hzf 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