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1D Case - Figures 8a and 8c#
Investigation of the influence of
mesh resolution
the number of sampling points per element when computing the loss with the trapezoidal rule
The study has been done on fixed and r-adapted meshes.
#%% Libraries import
import sys
# sys.path.append("../neurom/")
from neurom.HiDeNN_PDE import MeshNN, NeuROM, MeshNN_2D, MeshNN_1D
# Import pre-processing functions
import neurom.src.Pre_processing as pre
# Import torch librairies
import torch
import torch.nn as nn
# Import Training funcitons
from neurom.src.Training import Training_1D_FEM_LBFGS
#Import post processing libraries
import neurom.Post.Plots as Pplot
import time
import os
import torch._dynamo as dynamo
mps_device = torch.device("mps")
from importlib import reload # Python 3.4+
import tomllib
import numpy as numpy
import argparse
* Executing job in Configuration/config_2D.toml
* WARNING: could not load tikzplotlib
# Load default configuration file (defines dimension, domain, boundary conditions, number of training iterations etc.)
Default_config_file = 'Configurations/config_1D.toml'
with open(Default_config_file, mode="rb") as f:
config = tomllib.load(f)
# Experiment setting: trapezoidal rule
# Tested variants: 6 mesh resolutions, 3 training sets, fixed and r-adaptive mesh
mesh_resolution = [10,21,41,80,160,324]
training_points = [10,20,30]
setting = ["fixed", "r-adaptive"]
config["solver"]["IntegralMethod"] = "Trapezoidal"
loss_u = numpy.zeros((len(setting),len(mesh_resolution), len(training_points)))
loss_grad = numpy.zeros((len(setting),len(mesh_resolution), len(training_points)))
for t in range(len(training_points)):
config["training"]["Points_per_element"] = training_points[t]
for se in range(len(setting)):
if setting[se] == "fixed":
config["solver"]["FrozenMesh"] = True
elif setting[se] == "r-adaptive":
config["solver"]["FrozenMesh"] = False
for res in range(len(mesh_resolution)):
config["interpolation"]["np"] = mesh_resolution[res]
# Load parameters
if config["interpolation"]["dimension"] == 1:
Mat = pre.Material( flag_lame = True, # If True should input lmbda and mu instead of E and nu
coef1 = config["material"]["E"], # Young Modulus
coef2 = config["geometry"]["A"] # Section area of the 1D bar
)
elif config["interpolation"]["dimension"] == 2:
try:
Mat = pre.Material( flag_lame = False, # If True should input lmbda and mu instead of E and nu
coef1 = config["material"]["E"], # Young Modulus
coef2 = config["material"]["nu"] # Poisson's ratio
)
except:
Mat = pre.Material( flag_lame = True, # If True should input lmbda and mu instead of E and nu
coef1 = config["material"]["lmbda"], # First Lame's coef
coef2 = config["material"]["mu"] # Second Lame's coef
)
MaxElemSize = pre.ElementSize(
dimension = config["interpolation"]["dimension"],
L = config["geometry"]["L"],
order = config["interpolation"]["order"],
np = config["interpolation"]["np"],
)
Excluded = []
Mesh_object = pre.Mesh(
config["geometry"]["Name"], # Create the mesh object
MaxElemSize,
config["interpolation"]["order"],
config["interpolation"]["dimension"]
)
Mesh_object.AddBorders(config["Borders"]["Borders"])
Mesh_object.AddBCs( # Include Boundary physical domains infos (BCs+volume)
config["geometry"]["Volume_element"],
Excluded,
config["DirichletDictionryList"]
)
Mesh_object.MeshGeo() # Mesh the .geo file if .msh does not exist
Mesh_object.ReadMesh()
# Vtk file not necessary if not using reference element implementation
if config["solver"]["IntegralMethod"] == "Gaussian_quad":
Mesh_object.ExportMeshVtk1D()
# Build the assembly weight matrix if needed
if config["interpolation"]["dimension"] ==1 and config["solver"]["IntegralMethod"] == "Trapezoidal":
Mesh_object.AssemblyMatrix()
if int(Mesh_object.dim) != int(Mesh_object.dimension):
raise ValueError("The dimension of the provided geometry does not match the job dimension")
if config["solver"]["TrainingStrategy"]=="Integral":
match config["solver"]["IntegralMethod"]:
case "Gaussian_quad":
Model_FEM = MeshNN_1D(Mesh_object, config["interpolation"]["n_integr_points"])
case "Trapezoidal":
Model_FEM = MeshNN(Mesh_object)
if config["solver"]["TrainingStrategy"]=="Mixed":
if config["solver"]["IntegralMethod"] == "Gaussian_quad":
Model_FEM = MeshNN_1D(Mesh_object, config["interpolation"]["n_integr_points"])
Model_test = MeshNN_1D(Mesh_object, config["interpolation"]["n_integr_points"])
Model_test.Freeze_Mesh()
# Default setting
Model_FEM.Freeze_Mesh()
Model_FEM.UnFreeze_FEM()
if not config["solver"]["FrozenMesh"]:
Model_FEM.UnFreeze_Mesh()
if config["solver"]["TrainingStrategy"]=="Mixed":
Model_FEM = Training_1D_FEM_LBFGS(Model_FEM, config, Mat, Model_test)
else:
Model_FEM = Training_1D_FEM_LBFGS(Model_FEM, config, Mat)
l2_loss, l2_loss_grad = Pplot.Normalized_error_1D(Model_FEM,config,Mat)
loss_u[se,res, t] = l2_loss
loss_grad[se,res, t] = l2_loss_grad
_ _ ____ ___ __ __
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| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.013471980208606512
loss_decrease = 1.0134719802086065
epoch = 2
loss = -0.013471980208606512
loss_decrease = 0.0
epoch = 3
loss = -0.013471980208606512
loss_decrease = 0.0
epoch = 4
loss = -0.013471980208606512
loss_decrease = 0.0
epoch = 5
loss = -0.013471980208606512
loss_decrease = 0.0
epoch = 6
loss = -0.013471980208606512
loss_decrease = 0.0
* Final training loss: -1.3472e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.026277009039676592
loss_decrease = 1.0262770090396767
epoch = 2
loss = -0.02638806789739027
loss_decrease = 0.00422646495063372
epoch = 3
loss = -0.02638806789739027
loss_decrease = 0.0
epoch = 4
loss = -0.02638806789739027
loss_decrease = 0.0
epoch = 5
loss = -0.02638806789739027
loss_decrease = 0.0
epoch = 6
loss = -0.02638806789739027
loss_decrease = 0.0
epoch = 7
loss = -0.02638806789739027
loss_decrease = 0.0
* Final training loss: -2.6388e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.29382898522387113
loss_decrease = 0.7061710147761289
epoch = 2
loss = -0.029891531117842502
loss_decrease = 1.1017310497637522
epoch = 3
loss = -0.029929934800869515
loss_decrease = 0.0012847680125722732
epoch = 4
loss = -0.029929934800869515
loss_decrease = 0.0
epoch = 5
loss = -0.029929934800869515
loss_decrease = 0.0
epoch = 6
loss = -0.029929934800869515
loss_decrease = 0.0
epoch = 7
loss = -0.029929934800869515
loss_decrease = 0.0
epoch = 8
loss = -0.029929934800869515
loss_decrease = 0.0
* Final training loss: -2.993e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 0.6227918382287809
loss_decrease = 0.3772081617712191
epoch = 2
loss = 0.30879616056450904
loss_decrease = 0.5041743619461603
epoch = 3
loss = -0.030197060299426523
loss_decrease = 1.0977896235634
epoch = 4
loss = -0.03103276235466195
loss_decrease = 0.027674947393846114
epoch = 5
loss = -0.03107986842142716
loss_decrease = 0.0015179462990387955
epoch = 6
loss = -0.03107986842142716
loss_decrease = 0.0
epoch = 7
loss = -0.03107986842142716
loss_decrease = 0.0
epoch = 8
loss = -0.03107986842142716
loss_decrease = 0.0
epoch = 9
loss = -0.03107986842142716
loss_decrease = 0.0
epoch = 10
loss = -0.03107986842142716
loss_decrease = 0.0
* Final training loss: -3.108e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.290760703574934
loss_decrease = -0.290760703574934
epoch = 2
loss = 0.6493008386707275
loss_decrease = 0.4969626539819486
epoch = 3
loss = 0.43675250071413485
loss_decrease = 0.32734955092885665
epoch = 4
loss = 0.31665659575935734
loss_decrease = 0.27497473914495846
epoch = 5
loss = -0.02840862835415424
loss_decrease = 1.0897143111326295
epoch = 6
loss = -0.030461244865180412
loss_decrease = 0.07225327761120208
epoch = 7
loss = -0.03105069333797396
loss_decrease = 0.01935076768537889
epoch = 8
loss = -0.03133508475807802
loss_decrease = 0.009158939448101255
epoch = 9
loss = -0.031397476207245464
loss_decrease = 0.0019911051669122127
epoch = 10
loss = -0.031397788754922946
loss_decrease = 9.954547792919148e-06
epoch = 11
loss = -0.031397788754922946
loss_decrease = 0.0
epoch = 12
loss = -0.031397788754922946
loss_decrease = 0.0
epoch = 13
loss = -0.031397788754922946
loss_decrease = 0.0
epoch = 14
loss = -0.031397788754922946
loss_decrease = 0.0
epoch = 15
loss = -0.031397788754922946
loss_decrease = 0.0
* Final training loss: -3.1398e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 2.748125204951951
loss_decrease = -1.748125204951951
epoch = 2
loss = 1.3741057390135196
loss_decrease = 0.4999843032852119
epoch = 3
loss = 0.8877273862848661
loss_decrease = 0.3539599165620457
epoch = 4
loss = 0.6697213131100449
loss_decrease = 0.2455777263864477
epoch = 5
loss = 0.5364212517570859
loss_decrease = 0.19903810546799172
epoch = 6
loss = 0.44582236937656733
loss_decrease = 0.16889502808428167
epoch = 7
loss = 0.3701450358802082
loss_decrease = 0.16974772621253933
epoch = 8
loss = 0.3212641943100091
loss_decrease = 0.13205861711466707
epoch = 9
loss = 0.2570062648805385
loss_decrease = 0.20001584542429224
epoch = 10
loss = -0.028671090696792585
loss_decrease = 1.1115579447455082
epoch = 11
loss = -0.030105200798891833
loss_decrease = 0.0500193772628148
epoch = 12
loss = -0.03055156714347434
loss_decrease = 0.014826884815162424
epoch = 13
loss = -0.030901681755986773
loss_decrease = 0.011459792254461091
epoch = 14
loss = -0.031139344394027053
loss_decrease = 0.0076909289247416475
epoch = 15
loss = -0.031291663103639664
loss_decrease = 0.004891519477263851
epoch = 16
loss = -0.031425570478071214
loss_decrease = 0.004279330695464873
epoch = 17
loss = -0.03146535473768743
loss_decrease = 0.0012659836881554764
epoch = 18
loss = -0.03148162314687937
loss_decrease = 0.0005170260855966684
epoch = 19
loss = -0.03148240189327521
loss_decrease = 2.4736538907399078e-05
epoch = 20
loss = -0.03148242917742829
loss_decrease = 8.66647759857328e-07
epoch = 21
loss = -0.03148242992242362
loss_decrease = 2.36638453804245e-08
epoch = 22
loss = -0.03148243049242144
loss_decrease = 1.810526764235192e-08
epoch = 23
loss = -0.03148243121216179
loss_decrease = 2.286165138442186e-08
epoch = 24
loss = -0.03148243121216179
loss_decrease = 0.0
epoch = 25
loss = -0.03148243121216179
loss_decrease = 0.0
* Final training loss: -3.1482e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.019001305289668015
loss_decrease = 1.019001305289668
epoch = 2
loss = -0.021647487351436574
loss_decrease = 0.13926317278884123
epoch = 3
loss = -0.021925963637317962
loss_decrease = 0.012864138981141728
epoch = 4
loss = -0.021925968109557055
loss_decrease = 2.0397001321910004e-07
epoch = 5
loss = -0.02192596814364243
loss_decrease = 1.5545664046548572e-09
epoch = 6
loss = -0.02192596816247409
loss_decrease = 8.588748191605143e-10
epoch = 7
loss = -0.021925968189333987
loss_decrease = 1.2250266922118818e-09
epoch = 8
loss = -0.021925968189333987
loss_decrease = 0.0
epoch = 9
loss = -0.021925968189333987
loss_decrease = 0.0
* Final training loss: -2.1926e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.02656985401348947
loss_decrease = 1.0265698540134895
epoch = 2
loss = -0.026676602829094623
loss_decrease = 0.004017666621388169
epoch = 3
loss = -0.026676625873327822
loss_decrease = 8.638368740717215e-07
epoch = 4
loss = -0.026676626499851926
loss_decrease = 2.3485882600217137e-08
epoch = 5
loss = -0.026676626505202267
loss_decrease = 2.005629046646088e-10
epoch = 6
loss = -0.026676626510552606
loss_decrease = 2.0056277456869765e-10
epoch = 7
loss = -0.02667662651590293
loss_decrease = 2.0056225430572957e-10
epoch = 8
loss = -0.026676626521253265
loss_decrease = 2.0056264443256126e-10
* Final training loss: -2.6677e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.31220338129613834
loss_decrease = 0.6877966187038617
epoch = 2
loss = -0.029893603772666137
loss_decrease = 1.09575041643867
epoch = 3
loss = -0.030324860857347105
loss_decrease = 0.01442639997373944
epoch = 4
loss = -0.0303257319240136
loss_decrease = 2.872450662155998e-05
epoch = 5
loss = -0.030325770009963338
loss_decrease = 1.25589548285783e-06
epoch = 6
loss = -0.030325770009963338
loss_decrease = 0.0
epoch = 7
loss = -0.030325770009963338
loss_decrease = 0.0
epoch = 8
loss = -0.030325770009963338
loss_decrease = 0.0
epoch = 9
loss = -0.030325770009963338
loss_decrease = 0.0
epoch = 10
loss = -0.030325770009963338
loss_decrease = 0.0
* Final training loss: -3.0326e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 0.6868532130420811
loss_decrease = 0.31314678695791887
epoch = 2
loss = 0.33258021568764573
loss_decrease = 0.5157914247577821
epoch = 3
loss = -0.030143617946295807
loss_decrease = 1.0906356317196158
epoch = 4
loss = -0.031259937034514976
loss_decrease = 0.037033347828651995
epoch = 5
loss = -0.03125993910246115
loss_decrease = 6.61532418676022e-08
epoch = 6
loss = -0.03125993918539132
loss_decrease = 2.652921664499861e-09
epoch = 7
loss = -0.03125993926832103
loss_decrease = 2.652907007177523e-09
epoch = 8
loss = -0.031259939351250314
loss_decrease = 2.6528932377513206e-09
epoch = 9
loss = -0.03125993943417913
loss_decrease = 2.6528783584552073e-09
* Final training loss: -3.126e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.933291485191642
loss_decrease = -0.9332914851916421
epoch = 2
loss = 0.8795092035897054
loss_decrease = 0.5450715992252343
epoch = 3
loss = 0.549270765610834
loss_decrease = 0.37548036635774534
epoch = 4
loss = 0.38703992005641163
loss_decrease = 0.29535678159388
epoch = 5
loss = 0.29122350792790863
loss_decrease = 0.24756209156548406
epoch = 6
loss = -0.02978660777068426
loss_decrease = 1.1022809181258053
epoch = 7
loss = -0.030780834352890807
loss_decrease = 0.03337830846200142
epoch = 8
loss = -0.03123777581233126
loss_decrease = 0.014844999138158167
epoch = 9
loss = -0.031238869387010516
loss_decrease = 3.500808398863338e-05
epoch = 10
loss = -0.031327765653151256
loss_decrease = 0.002845694094732619
epoch = 11
loss = -0.031327826913562576
loss_decrease = 1.955466980899557e-06
epoch = 12
loss = -0.031327826913562576
loss_decrease = 0.0
epoch = 13
loss = -0.031327826913562576
loss_decrease = 0.0
epoch = 14
loss = -0.031327826913562576
loss_decrease = 0.0
epoch = 15
loss = -0.031327826913562576
loss_decrease = 0.0
epoch = 16
loss = -0.031327826913562576
loss_decrease = 0.0
* Final training loss: -3.1328e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 10.209207735244682
loss_decrease = -9.209207735244682
epoch = 2
loss = 10.208962003413127
loss_decrease = 2.4069627920943993e-05
epoch = 3
loss = 10.208931474702181
loss_decrease = 2.9903834430651055e-06
epoch = 4
loss = 10.208930709429717
loss_decrease = 7.496107364040436e-08
epoch = 5
loss = 10.208930693532352
loss_decrease = 1.5572017926753344e-09
epoch = 6
loss = 10.208930677634985
loss_decrease = 1.5572019691004957e-09
epoch = 7
loss = 10.208930661737613
loss_decrease = 1.5572024935262264e-09
epoch = 8
loss = 10.208930645840244
loss_decrease = 1.557202147950537e-09
* Final training loss: 1.0209e+01
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.013542667867031025
loss_decrease = 1.013542667867031
epoch = 2
loss = -0.013542667867031025
loss_decrease = 0.0
epoch = 3
loss = -0.013542667867031025
loss_decrease = 0.0
epoch = 4
loss = -0.013542667867031025
loss_decrease = 0.0
epoch = 5
loss = -0.013542667867031025
loss_decrease = 0.0
epoch = 6
loss = -0.013542667867031025
loss_decrease = 0.0
* Final training loss: -1.3543e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.02635573541256923
loss_decrease = 1.0263557354125692
epoch = 2
loss = -0.026462930467839305
loss_decrease = 0.004067238253535968
epoch = 3
loss = -0.026462930467839305
loss_decrease = 0.0
epoch = 4
loss = -0.026462930467839305
loss_decrease = 0.0
epoch = 5
loss = -0.026462930467839305
loss_decrease = 0.0
epoch = 6
loss = -0.026462930467839305
loss_decrease = 0.0
epoch = 7
loss = -0.026462930467839305
loss_decrease = 0.0
* Final training loss: -2.6463e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.29171896271812603
loss_decrease = 0.708281037281874
epoch = 2
loss = -0.0298807432177514
loss_decrease = 1.1024298967037798
epoch = 3
loss = -0.029969800286411295
loss_decrease = 0.002980416785851136
epoch = 4
loss = -0.029969800286411295
loss_decrease = 0.0
epoch = 5
loss = -0.029969800286411295
loss_decrease = 0.0
epoch = 6
loss = -0.029969800286411295
loss_decrease = 0.0
epoch = 7
loss = -0.029969800286411295
loss_decrease = 0.0
epoch = 8
loss = -0.029969800286411295
loss_decrease = 0.0
* Final training loss: -2.997e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 0.6254651974492185
loss_decrease = 0.37453480255078153
epoch = 2
loss = 0.30261095817844763
loss_decrease = 0.5161825799220162
epoch = 3
loss = -0.030259656233735104
loss_decrease = 1.099995242789229
epoch = 4
loss = -0.031056634439859836
loss_decrease = 0.02633797951862446
epoch = 5
loss = -0.03110018601033477
loss_decrease = 0.0014023274337491452
epoch = 6
loss = -0.03110018601033477
loss_decrease = 0.0
epoch = 7
loss = -0.03110018601033477
loss_decrease = 0.0
epoch = 8
loss = -0.03110018601033477
loss_decrease = 0.0
epoch = 9
loss = -0.03110018601033477
loss_decrease = 0.0
epoch = 10
loss = -0.03110018601033477
loss_decrease = 0.0
* Final training loss: -3.1100e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.2952913177425895
loss_decrease = -0.29529131774258954
epoch = 2
loss = 0.6452367921456259
loss_decrease = 0.5018597103930774
epoch = 3
loss = 0.4318772548309303
loss_decrease = 0.3306685854121934
epoch = 4
loss = 0.3115412163222917
loss_decrease = 0.2786348138564216
epoch = 5
loss = -0.02913760435272417
loss_decrease = 1.093527285720619
epoch = 6
loss = -0.030558046446821953
loss_decrease = 0.04874944682832104
epoch = 7
loss = -0.031100736377671315
loss_decrease = 0.01775931363262267
epoch = 8
loss = -0.031364509632902424
loss_decrease = 0.008481254335202307
epoch = 9
loss = -0.031407769976179
loss_decrease = 0.0013792768891625067
epoch = 10
loss = -0.031407813659804856
loss_decrease = 1.3908541067585077e-06
epoch = 11
loss = -0.031407813659804856
loss_decrease = 0.0
epoch = 12
loss = -0.031407813659804856
loss_decrease = 0.0
epoch = 13
loss = -0.031407813659804856
loss_decrease = 0.0
epoch = 14
loss = -0.031407813659804856
loss_decrease = 0.0
epoch = 15
loss = -0.031407813659804856
loss_decrease = 0.0
* Final training loss: -3.1408e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 2.7573772079196663
loss_decrease = -1.7573772079196663
epoch = 2
loss = 1.3630908785062368
loss_decrease = 0.5056567253144753
epoch = 3
loss = 0.8773318970547981
loss_decrease = 0.35636580738018353
epoch = 4
loss = 0.6652499444542499
loss_decrease = 0.24173514414841976
epoch = 5
loss = 0.5315996815653323
loss_decrease = 0.20090232852038797
epoch = 6
loss = 0.44113937474186943
loss_decrease = 0.1701662170998602
epoch = 7
loss = 0.36807265478988255
loss_decrease = 0.16563182553074415
epoch = 8
loss = 0.31994356535998325
loss_decrease = 0.1307597530095633
epoch = 9
loss = 0.2367833919038301
loss_decrease = 0.2599213813304412
epoch = 10
loss = -0.02872321262511112
loss_decrease = 1.1213058584648414
epoch = 11
loss = -0.030086523022104544
loss_decrease = 0.047463715663948976
epoch = 12
loss = -0.030529937734107355
loss_decrease = 0.014737984567942067
epoch = 13
loss = -0.030888410247896004
loss_decrease = 0.011741671958543554
epoch = 14
loss = -0.031120355555601553
loss_decrease = 0.007509137111429958
epoch = 15
loss = -0.03127995261446018
loss_decrease = 0.005128381601343782
epoch = 16
loss = -0.031421507497365574
loss_decrease = 0.004525418713069224
epoch = 17
loss = -0.03146641081897259
loss_decrease = 0.0014290632494568401
epoch = 18
loss = -0.03148609590489223
loss_decrease = 0.0006255904441369856
epoch = 19
loss = -0.03148704889209841
loss_decrease = 3.0266921915692053e-05
epoch = 20
loss = -0.03148727707357457
loss_decrease = 7.246835895621246e-06
epoch = 21
loss = -0.031487327706681514
loss_decrease = 1.6080497156041193e-06
epoch = 22
loss = -0.03148733944274161
loss_decrease = 3.7272328110199755e-07
epoch = 23
loss = -0.03148734056466741
loss_decrease = 3.563101303942106e-08
epoch = 24
loss = -0.03148734056466741
loss_decrease = 0.0
epoch = 25
loss = -0.03148734056466741
loss_decrease = 0.0
epoch = 26
loss = -0.03148734056466741
loss_decrease = 0.0
epoch = 27
loss = -0.03148734056466741
loss_decrease = 0.0
* Final training loss: -3.1487e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.023207696731171436
loss_decrease = 1.0232076967311714
epoch = 2
loss = -0.023292071253471883
loss_decrease = 0.0036356267180585778
epoch = 3
loss = -0.023292151563880828
loss_decrease = 3.4479719759842975e-06
epoch = 4
loss = -0.023292152957851885
loss_decrease = 5.984724308602813e-08
epoch = 5
loss = -0.0232921530131866
loss_decrease = 2.3756806026516155e-09
epoch = 6
loss = -0.023292153016101512
loss_decrease = 1.251456387988184e-10
epoch = 7
loss = -0.02329215301901643
loss_decrease = 1.251459366900915e-10
epoch = 8
loss = -0.023292153019019126
loss_decrease = 1.1573684405503675e-13
* Final training loss: -2.3292e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.026397244158221582
loss_decrease = 1.0263972441582216
epoch = 2
loss = -0.026635327205662192
loss_decrease = 0.009019238751347386
epoch = 3
loss = -0.02663538877443094
loss_decrease = 2.311545425032607e-06
epoch = 4
loss = -0.026635405537522968
loss_decrease = 6.293541337435259e-07
epoch = 5
loss = -0.026635411305629474
loss_decrease = 2.1655786311175084e-07
epoch = 6
loss = -0.026635411872909878
loss_decrease = 2.1297977969937705e-08
epoch = 7
loss = -0.0266354118729139
loss_decrease = 1.509677806560962e-13
epoch = 8
loss = -0.026635411877558506
loss_decrease = 1.7437716515664938e-10
epoch = 9
loss = -0.02663541188000495
loss_decrease = 9.184924060869709e-11
epoch = 10
loss = -0.026635411880008966
loss_decrease = 1.5083752368696387e-13
* Final training loss: -2.6635e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.3055076886980332
loss_decrease = 0.6944923113019668
epoch = 2
loss = -0.030090811977810376
loss_decrease = 1.0984944506832115
epoch = 3
loss = -0.03026462369813123
loss_decrease = 0.005776238954569489
epoch = 4
loss = -0.030264640473316635
loss_decrease = 5.542836273560684e-07
epoch = 5
loss = -0.030264641563091547
loss_decrease = 3.6008189610985185e-08
epoch = 6
loss = -0.03026464156342549
loss_decrease = 1.1034038097668685e-11
epoch = 7
loss = -0.03026464156342549
loss_decrease = 0.0
epoch = 8
loss = -0.03026464156342549
loss_decrease = 0.0
epoch = 9
loss = -0.03026464156342549
loss_decrease = 0.0
* Final training loss: -3.0265e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 12.461084635114837
loss_decrease = -11.461084635114837
epoch = 2
loss = 0.6603159484370842
loss_decrease = 0.9470097533423102
epoch = 3
loss = 0.3242398765142742
loss_decrease = 0.5089625242556621
epoch = 4
loss = -0.030010003501493795
loss_decrease = 1.092554943655034
epoch = 5
loss = -0.03108229666309542
loss_decrease = 0.035731190819363
epoch = 6
loss = -0.031082307408197413
loss_decrease = 3.456984568632848e-07
epoch = 7
loss = -0.031082307408378352
loss_decrease = 5.821273017541983e-12
epoch = 8
loss = -0.031082307408559277
loss_decrease = 5.8208265323863355e-12
epoch = 9
loss = -0.03108230740874022
loss_decrease = 5.82138463875465e-12
epoch = 10
loss = -0.031082307408921164
loss_decrease = 5.821496260001201e-12
epoch = 11
loss = -0.03108230740910209
loss_decrease = 5.820826532284683e-12
* Final training loss: -3.1082e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.6397814437475833
loss_decrease = -0.6397814437475833
epoch = 2
loss = 0.763293226547608
loss_decrease = 0.5345152675937318
epoch = 3
loss = 0.49592376026859253
loss_decrease = 0.3502840808483699
epoch = 4
loss = 0.3474249825647802
loss_decrease = 0.29943872345092987
epoch = 5
loss = 0.028415802566407185
loss_decrease = 0.918210249715969
epoch = 6
loss = -0.030156605152211753
loss_decrease = 2.0612617779046127
epoch = 7
loss = -0.03089870142286731
loss_decrease = 0.024608083930864184
epoch = 8
loss = -0.031216924978406342
loss_decrease = 0.010298929757077817
epoch = 9
loss = -0.031216925019515694
loss_decrease = 1.316893065606066e-09
epoch = 10
loss = -0.03121692506062479
loss_decrease = 1.3168848395168241e-09
epoch = 11
loss = -0.031216925101733628
loss_decrease = 1.3168766134276149e-09
epoch = 12
loss = -0.031216925142842154
loss_decrease = 1.3168666090995163e-09
epoch = 13
loss = -0.031216925183950438
loss_decrease = 1.3168588275701066e-09
* Final training loss: -3.1217e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 18.211272680906774
loss_decrease = -17.211272680906774
epoch = 2
loss = 4.819815114828993
loss_decrease = 0.7353389189607694
epoch = 3
loss = 2.2602514413321804
loss_decrease = 0.5310501777592823
epoch = 4
loss = 1.4178653725606714
loss_decrease = 0.3726957334777812
epoch = 5
loss = 0.9627597534151244
loss_decrease = 0.3209794300312336
epoch = 6
loss = 0.7366928208465717
loss_decrease = 0.23481136572924105
epoch = 7
loss = 0.5976304147631619
loss_decrease = 0.18876579511607838
epoch = 8
loss = 0.4982904081984846
loss_decrease = 0.1662231441216815
epoch = 9
loss = 0.4216335043213912
loss_decrease = 0.15383981432481952
epoch = 10
loss = 0.358810569727875
loss_decrease = 0.14899891481496033
epoch = 11
loss = 0.3152161247201598
loss_decrease = 0.12149710372461324
epoch = 12
loss = 0.22602547980508741
loss_decrease = 0.2829507690771003
epoch = 13
loss = -0.02551325196443344
loss_decrease = 1.1128777692958987
epoch = 14
loss = -0.02957056081487299
loss_decrease = 0.15902750680687874
epoch = 15
loss = -0.03012342171786734
loss_decrease = 0.018696327961297166
epoch = 16
loss = -0.030123440611529877
loss_decrease = 6.272083800513457e-07
epoch = 17
loss = -0.030123442712940013
loss_decrease = 6.975996411827697e-08
epoch = 18
loss = -0.03012344271324667
loss_decrease = 1.0180027565625704e-11
epoch = 19
loss = -0.030123442713553314
loss_decrease = 1.0179566868252509e-11
epoch = 20
loss = -0.030123442713859964
loss_decrease = 1.0179797216783663e-11
epoch = 21
loss = -0.030123442714166643
loss_decrease = 1.0180718611219141e-11
* Final training loss: -3.0123e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.013568297011566404
loss_decrease = 1.0135682970115665
epoch = 2
loss = -0.013568297011566404
loss_decrease = 0.0
epoch = 3
loss = -0.013568297011566404
loss_decrease = 0.0
epoch = 4
loss = -0.013568297011566404
loss_decrease = 0.0
epoch = 5
loss = -0.013568297011566404
loss_decrease = 0.0
epoch = 6
loss = -0.013568297011566404
loss_decrease = 0.0
* Final training loss: -1.3568e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.02638053554840373
loss_decrease = 1.0263805355484037
epoch = 2
loss = -0.026486618557287914
loss_decrease = 0.004021260625643513
epoch = 3
loss = -0.026486618557287914
loss_decrease = 0.0
epoch = 4
loss = -0.026486618557287914
loss_decrease = 0.0
epoch = 5
loss = -0.026486618557287914
loss_decrease = 0.0
epoch = 6
loss = -0.026486618557287914
loss_decrease = 0.0
epoch = 7
loss = -0.026486618557287914
loss_decrease = 0.0
* Final training loss: -2.6487e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.29105294413699784
loss_decrease = 0.7089470558630022
epoch = 2
loss = -0.029930544914158044
loss_decrease = 1.1028353965045954
epoch = 3
loss = -0.02998274060732807
loss_decrease = 0.0017438938489000289
epoch = 4
loss = -0.02998274060732807
loss_decrease = 0.0
epoch = 5
loss = -0.02998274060732807
loss_decrease = 0.0
epoch = 6
loss = -0.02998274060732807
loss_decrease = 0.0
epoch = 7
loss = -0.02998274060732807
loss_decrease = 0.0
epoch = 8
loss = -0.02998274060732807
loss_decrease = 0.0
* Final training loss: -2.9983e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 0.6264896111198306
loss_decrease = 0.3735103888801694
epoch = 2
loss = 0.3088025677267145
loss_decrease = 0.5070906807620648
epoch = 3
loss = -0.030126534280363704
loss_decrease = 1.0975592091158557
epoch = 4
loss = -0.031043465185332145
loss_decrease = 0.030435990294645023
epoch = 5
loss = -0.03110686700207658
loss_decrease = 0.0020423563015893797
epoch = 6
loss = -0.03110686700207658
loss_decrease = 0.0
epoch = 7
loss = -0.03110686700207658
loss_decrease = 0.0
epoch = 8
loss = -0.03110686700207658
loss_decrease = 0.0
epoch = 9
loss = -0.03110686700207658
loss_decrease = 0.0
epoch = 10
loss = -0.03110686700207658
loss_decrease = 0.0
* Final training loss: -3.1107e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.296766994622226
loss_decrease = -0.296766994622226
epoch = 2
loss = 0.6389788552998099
loss_decrease = 0.5072523761402817
epoch = 3
loss = 0.4252552593217217
loss_decrease = 0.3344767893419709
epoch = 4
loss = 0.31235085921043454
loss_decrease = 0.2654979512572488
epoch = 5
loss = -0.02854930641617909
loss_decrease = 1.0914014018989622
epoch = 6
loss = -0.03051179260764148
loss_decrease = 0.06874024058077417
epoch = 7
loss = -0.03109530516191368
loss_decrease = 0.01912416493438219
epoch = 8
loss = -0.03136107325139721
loss_decrease = 0.008546887965873728
epoch = 9
loss = -0.031410926853987615
loss_decrease = 0.001589665066331318
epoch = 10
loss = -0.03141113348572412
loss_decrease = 6.578339361538073e-06
epoch = 11
loss = -0.03141113348572412
loss_decrease = 0.0
epoch = 12
loss = -0.03141113348572412
loss_decrease = 0.0
epoch = 13
loss = -0.03141113348572412
loss_decrease = 0.0
epoch = 14
loss = -0.03141113348572412
loss_decrease = 0.0
epoch = 15
loss = -0.03141113348572412
loss_decrease = 0.0
* Final training loss: -3.1411e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 2.7604525557468165
loss_decrease = -1.7604525557468165
epoch = 2
loss = 1.352019185782925
loss_decrease = 0.5102182854154695
epoch = 3
loss = 0.8844260701945239
loss_decrease = 0.3458479883313401
epoch = 4
loss = 0.6662344222574493
loss_decrease = 0.2467042246833415
epoch = 5
loss = 0.5358717157236526
loss_decrease = 0.1956709262966023
epoch = 6
loss = 0.44441930892813003
loss_decrease = 0.17066100731221323
epoch = 7
loss = 0.3685404530694294
loss_decrease = 0.1707370817026573
epoch = 8
loss = 0.31934220773091304
loss_decrease = 0.13349483056408978
epoch = 9
loss = 0.20423183967789413
loss_decrease = 0.36046086382046383
epoch = 10
loss = -0.02830483115187442
loss_decrease = 1.1385916671784164
epoch = 11
loss = -0.030096656894006944
loss_decrease = 0.06330459039017679
epoch = 12
loss = -0.03049570075148389
loss_decrease = 0.013258743616684075
epoch = 13
loss = -0.03085382899522531
loss_decrease = 0.011743564991665126
epoch = 14
loss = -0.031143820042128297
loss_decrease = 0.009398867380378024
epoch = 15
loss = -0.0312801874387609
loss_decrease = 0.004378634234597288
epoch = 16
loss = -0.03141093010249309
loss_decrease = 0.004179727630729616
epoch = 17
loss = -0.031465294498397293
loss_decrease = 0.0017307477278392192
epoch = 18
loss = -0.03148629400269494
loss_decrease = 0.0006673862308428623
epoch = 19
loss = -0.03148849151221906
loss_decrease = 6.979257463363733e-05
epoch = 20
loss = -0.0314889276517559
loss_decrease = 1.3850759940998274e-05
epoch = 21
loss = -0.031488976943364076
loss_decrease = 1.565363188045005e-06
epoch = 22
loss = -0.031488976943364076
loss_decrease = 0.0
epoch = 23
loss = -0.031488976943364076
loss_decrease = 0.0
epoch = 24
loss = -0.031488976943364076
loss_decrease = 0.0
epoch = 25
loss = -0.031488976943364076
loss_decrease = 0.0
epoch = 26
loss = -0.031488976943364076
loss_decrease = 0.0
* Final training loss: -3.1489e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 10
epoch = 1
loss = -0.022788103024302203
loss_decrease = 1.0227881030243022
epoch = 2
loss = -0.022788169446435094
loss_decrease = 2.9147723625903417e-06
epoch = 3
loss = -0.022788175876572503
loss_decrease = 2.821699840242167e-07
epoch = 4
loss = -0.022788175952014232
loss_decrease = 3.310564639362596e-09
epoch = 5
loss = -0.022788175952444256
loss_decrease = 1.887049111839217e-11
epoch = 6
loss = -0.022788175952444256
loss_decrease = 0.0
epoch = 7
loss = -0.022788175952444256
loss_decrease = 0.0
epoch = 8
loss = -0.022788175952444256
loss_decrease = 0.0
* Final training loss: -2.2788e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 21
epoch = 1
loss = -0.026472253484031667
loss_decrease = 1.0264722534840316
epoch = 2
loss = -0.026570734051182182
loss_decrease = 0.0037201429492929273
epoch = 3
loss = -0.02657073713881506
loss_decrease = 1.1620427469532804e-07
epoch = 4
loss = -0.026570738701584648
loss_decrease = 5.881543967652577e-08
epoch = 5
loss = -0.026570738701584648
loss_decrease = 0.0
epoch = 6
loss = -0.026570738701584648
loss_decrease = 0.0
epoch = 7
loss = -0.026570738701584648
loss_decrease = 0.0
epoch = 8
loss = -0.026570738701584648
loss_decrease = 0.0
* Final training loss: -2.6571e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 41
epoch = 1
loss = 0.31695462574144573
loss_decrease = 0.6830453742585543
epoch = 2
loss = -0.030038206742051262
loss_decrease = 1.0947713152057128
epoch = 3
loss = -0.030274581240629466
loss_decrease = 0.007869128160946348
epoch = 4
loss = -0.030275053953108096
loss_decrease = 1.561417067579926e-05
epoch = 5
loss = -0.030275105464998953
loss_decrease = 1.701463222387257e-06
epoch = 6
loss = -0.030275105464998953
loss_decrease = 0.0
epoch = 7
loss = -0.030275105464998953
loss_decrease = 0.0
epoch = 8
loss = -0.030275105464998953
loss_decrease = 0.0
epoch = 9
loss = -0.030275105464998953
loss_decrease = 0.0
epoch = 10
loss = -0.030275105464998953
loss_decrease = 0.0
* Final training loss: -3.0275e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 80
epoch = 1
loss = 12.692851873214762
loss_decrease = -11.692851873214762
epoch = 2
loss = 0.6735531310715173
loss_decrease = 0.9469344527298164
epoch = 3
loss = 0.31894975318401875
loss_decrease = 0.5264668242628169
epoch = 4
loss = -0.029963942455490257
loss_decrease = 1.0939456518036637
epoch = 5
loss = -0.03065983583056695
loss_decrease = 0.02322435961524094
epoch = 6
loss = -0.0311285566103271
loss_decrease = 0.01528777852400796
epoch = 7
loss = -0.031128564005626188
loss_decrease = 2.3757282359609576e-07
epoch = 8
loss = -0.031128564628445966
loss_decrease = 2.0007982966293258e-08
epoch = 9
loss = -0.031128564632172593
loss_decrease = 1.1971726581814847e-10
epoch = 10
loss = -0.031128564632172593
loss_decrease = 0.0
epoch = 11
loss = -0.031128564632172593
loss_decrease = 0.0
epoch = 12
loss = -0.031128564632172593
loss_decrease = 0.0
* Final training loss: -3.1129e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 160
epoch = 1
loss = 1.5749792974477554
loss_decrease = -0.5749792974477554
epoch = 2
loss = 0.7197839659749309
loss_decrease = 0.5429883001374453
epoch = 3
loss = 0.47436439959771465
loss_decrease = 0.34096281381428256
epoch = 4
loss = 0.3366524769471212
loss_decrease = 0.2903083004698081
epoch = 5
loss = -0.025704552183442586
loss_decrease = 1.0763533731180004
epoch = 6
loss = -0.030227142798530397
loss_decrease = 0.1759451237590907
epoch = 7
loss = -0.030928242850412
loss_decrease = 0.02319438712929524
epoch = 8
loss = -0.03129076652456104
loss_decrease = 0.011721444244421711
epoch = 9
loss = -0.031414069926406184
loss_decrease = 0.003940568274297825
epoch = 10
loss = -0.031414781727759286
loss_decrease = 2.2658679845366464e-05
epoch = 11
loss = -0.03141478172776871
loss_decrease = 2.9995490667947194e-13
epoch = 12
loss = -0.03141478172777812
loss_decrease = 2.995131468757304e-13
epoch = 13
loss = -0.03141478172778751
loss_decrease = 2.9885050717016363e-13
epoch = 14
loss = -0.03141478172779691
loss_decrease = 2.992922669737256e-13
epoch = 15
loss = -0.03141478172780632
loss_decrease = 2.9951314687546156e-13
* Final training loss: -3.1415e-02
_ _ ____ ___ __ __
| \ | | ___ _ _| _ \ / _ \| \/ |
| \| |/ _ \ | | | |_) | | | | |\/| |
| |\ | __/ |_| | _ <| |_| | | | |
|_| \_|\___|\__,_|_| \_\ ___/|_| |_|
2024.09.16
************ MESH READING COMPLETE ************
* Dimension of the problem: 1D
* Elements type: 2-node bar
* Number of Dofs: 324
epoch = 1
loss = 4.941238997228815
loss_decrease = -3.9412389972288153
epoch = 2
loss = 2.5996320846828196
loss_decrease = 0.47389064035543194
epoch = 3
loss = 1.5387339519881718
loss_decrease = 0.40809549126029027
epoch = 4
loss = 1.0641694202446053
loss_decrease = 0.308412335433549
epoch = 5
loss = 0.7895379848791466
loss_decrease = 0.2580711587280276
epoch = 6
loss = 0.6244529576153954
loss_decrease = 0.20909067128546133
epoch = 7
loss = 0.5262480178452726
loss_decrease = 0.15726555310929896
epoch = 8
loss = 0.447887587843483
loss_decrease = 0.14890399078867253
epoch = 9
loss = 0.3817892950167255
loss_decrease = 0.14757786243867946
epoch = 10
loss = 0.3325103704172688
loss_decrease = 0.1290736153230747
epoch = 11
loss = 0.29582683008119937
loss_decrease = 0.1103229962122236
epoch = 12
loss = 0.0010077934097840113
loss_decrease = 0.9965932995005646
epoch = 13
loss = -0.02814904078423699
loss_decrease = 28.93136024799949
epoch = 14
loss = -0.029965531761661692
loss_decrease = 0.06453118567514053
epoch = 15
loss = -0.030334685516906632
loss_decrease = 0.012319279303337455
epoch = 16
loss = -0.030776050791950255
loss_decrease = 0.014549854976991055
epoch = 17
loss = -0.03098030714189244
loss_decrease = 0.006636860308133208
epoch = 18
loss = -0.03113534333614767
loss_decrease = 0.005004346585240481
epoch = 19
loss = -0.03125344671525692
loss_decrease = 0.0037932255261862663
epoch = 20
loss = -0.03135688316913563
loss_decrease = 0.003309601491992129
epoch = 21
loss = -0.031409856105864026
loss_decrease = 0.0016893559363876922
epoch = 22
loss = -0.03144620777073851
loss_decrease = 0.0011573330597875338
epoch = 23
loss = -0.03144620902021818
loss_decrease = 3.9733874261578256e-08
epoch = 24
loss = -0.03144620939581516
loss_decrease = 1.1944110141502402e-08
epoch = 25
loss = -0.03144620941170953
loss_decrease = 5.054462671193428e-10
epoch = 26
loss = -0.03144620942760351
loss_decrease = 5.054339099513521e-10
epoch = 27
loss = -0.0314462094434972
loss_decrease = 5.054246420115074e-10
* Final training loss: -3.1446e-02
import matplotlib.pyplot as plt
import matplotlib
plt.rcParams['text.usetex'] = False
# Plot normalized displacement error
fig = matplotlib.pyplot.gcf()
ax = plt.gca()
plt.plot(mesh_resolution, loss_u[0,:,0],'-', color = "blue", label = '10 p./e.')
plt.plot(mesh_resolution, loss_u[0,:,1],'-', color = "gold", label = '20 p./e.')
plt.plot(mesh_resolution, loss_u[0,:,2],'-', color = "green", label = '30 p./e.')
plt.plot(mesh_resolution, loss_u[1,:,0],':', color = "blue", label = '10 p./e., r-adaptivity')
plt.plot(mesh_resolution, loss_u[1,:,1],':', color = "gold", label = '20 p./e., r-adaptivity')
plt.plot(mesh_resolution, loss_u[1,:,2],':', color = "green", label = '30 p./e., r-adaptivity')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_ylim([0.00008, 29])
plt.xlabel("Number of mesh nodes")
plt.ylabel("Normalized displacement error")
plt.legend(loc="lower left", frameon=False )
plt.show()
# Plot normalized strain error
fig = matplotlib.pyplot.gcf()
ax = plt.gca()
plt.plot(mesh_resolution, loss_grad[0,:,0],'-', color = "blue", label = '10 p./e.')
plt.plot(mesh_resolution, loss_grad[0,:,1],'-', color = "gold", label = '20 p./e.')
plt.plot(mesh_resolution, loss_grad[0,:,2],'-', color = "green", label = '30 p./e.')
plt.plot(mesh_resolution, loss_grad[1,:,0],':', color = "blue", label = '10 p./e., r-adaptivity')
plt.plot(mesh_resolution, loss_grad[1,:,1],':', color = "gold", label = '20 p./e., r-adaptivity')
plt.plot(mesh_resolution, loss_grad[1,:,2],':', color = "green", label = '30 p./e., r-adaptivity')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_ylim([0.01, 23])
plt.xlabel("Number of mesh nodes")
plt.ylabel("Normalized strain error")
plt.legend(loc="lower left", frameon=False )
plt.show()
