Comparison of the classic FEM and the FEMnet 2.0 neural network

PrometheusCore

Translate this page:

Comparison of the FEM and the FEMnet 2.0 neural network

From 2020 to the end of 2024, the FEMnet neural network underwent more than 500 epochs of training model changes. But in 2025, it became possible to significantly increase the training speed. In March 2025 alone, the FEMnet neural network underwent more than 40,000 epochs of model changes.

The new version of the neural network is now called FEMnet 2.0, it has become 5 times larger than its predecessor. And now, in addition to layers with weight distribution, it also stores the bias. Previously, the PromCore program downloaded 3 files from the server when the program was launched, now it is 6 files with a total volume of about 61 MB.

In total, the new neural network FEMnet 2.0 was trained on more than 5,000,000 data points of classical calculations using FEM. Thanks to the new mechanics of shifting the neural network weights, it began to really think about its decisions, just like a neuron in the human brain.

The article contains a lot of materials and comparisons. The first part will be devoted to the comparison of the old and new versions of the FEMnet neural network. The second part of the article will be devoted to the comparison of the new version of FEMnet 2.0 and the classic FEM.

Comparison of FEMnet 1.0 and FEMnet 2.0

Further in the comparisons, on the left side is FEMnet 2.0, on the right side is FEMnet 1.0.
In all the examples considered, the pylons are placed by the SmartPylon neural network, which will provide a certain pattern, which will be discussed in detail towards the end of the article.

Example #1

Fig. 1 Vertical movement of the floor slab

Maximum deflection -28.82 mm | Maximum deflection -35.3 mm

Fig. 2 Мx, T*m

Мx -2.54 ... +7.54 T*m | Мx -1.45 ... +3 T*m

Fig. 3 Мy, T*m

Мy -2.24 ... +6.22 T*m | Мy -2.13 ... +7.12 T*m

Fig. 4 A_s_x lower, sm^2

A_s_x lower 0 ... 7.37, sm^2 | A_s_x lower 0 ... 3.36, sm^2

Fig. 5 A_s_y lower, sm^2

A_s_y lower 0 ... 6.60, sm^2 | A_s_y lower 0 ... 7.83, sm^2

Fig. 6 A_s_x upper, sm^2

A_s_x upper 0 ... 21.48, sm^2 | A_s_x upper 0 ... 11.88, sm^2

Fig. 7 A_s_y upper, sm^2

A_s_y upper 0 ... 17.06, sm^2 | A_s_y upper 0 ... 33.08, sm^2

Fig. 8 Cracks

Fig. 9 Material costs

Steel consumption for the floor slab is 84.2 kg/m^3 | Steel consumption for the floor slab is 93.2 kg/m^3

General result of example #1:

The upper reinforcement zones of the FEMnet 1.0 neural network are significantly worse than in the new version.
Many reinforcement zones of the FEMnet 1.0 neural network are not smooth, it is clear that the neural network is not confident in the result.
FEMnet 2.0 demonstrates much more accurate upper and lower reinforcement zones.

Example #2

Fig. 10 Vertical movement of the floor slab

Maximum deflection -25.38 mm | Maximum deflection -32.53 mm

Fig. 11 Мx, T*m

Мx -2.21 ... +5.32 T*m | Мx -2.47 ... +4.22 T*m

Fig. 12 Мy, T*m

Мy -2.3 ... +5.45 T*m | Мy -2.14 ... +3.98 T*m

Fig. 13 A_s_x lower, sm^2

A_s_x lower 0 ... 6.47, sm^2 | A_s_x lower 0 ... 9.14, sm^2

Fig. 14 A_s_y lower, sm^2

A_s_y lower 0 ... 6.75, sm^2 | A_s_y lower 0 ... 7.13, sm^2

Fig. 15 A_s_x upper, sm^2

A_s_x upper 0 ... 15.71, sm^2 | A_s_x upper 0 ... 17.77, sm^2

Fig. 16 A_s_y upper, sm^2

A_s_y upper 0 ... 15.99, sm^2 | A_s_y upper 0 ... 15.05, sm^2

Fig. 17 Cracks

Fig. 18 Material costs

Steel consumption for the floor slab is 84.5 kg/m^3 | Steel consumption for the floor slab is 78.4 kg/m^3

General result of example #2:

FEMnet 2.0 shows the ideal distribution of both bending moments in the span and support zones.
The ratio of moments in FEMnet 2.0, between the moments in the span zone of the slabs and the support part, almost fits into the theoretical 1/2 = (q*l^2/12) / (q*l^2/24).
FEMnet 1.0 does not quite accurately generate the moment distribution zones along the X and Y axes.

Example #3

Fig. 19 Vertical movement of the floor slab

Maximum deflection -25.38 mm | Maximum deflection -32.53 mm

Fig. 20 Мx, T*m

Мx -2.02 ... +6.56 T*m | Мx -1.84 ... +5.15 T*m

Fig. 21 Мy, T*m

Мy -2.16 ... +6.31 T*m | Мy -1.94 ... +3.03 T*m

Fig. 22 A_s_x lower, sm^2

A_s_x lower 0 ... 5.93, sm^2 | A_s_x lower 0 ... 6.20, sm^2

Fig. 23 A_s_y lower, sm^2

A_s_y lower 0 ... 6.32, sm^2 | A_s_y lower 0 ... 6.18, sm^2

Fig. 24 A_s_x upper, sm^2

A_s_x upper 0 ... 19.25, sm^2 | A_s_x upper 0 ... 18.21, sm^2

Fig. 25 A_s_y upper, sm^2

A_s_y upper 0 ... 18.08, sm^2 | A_s_y upper 0 ... 11.31, sm^2

Fig. 26 Cracks

Fig. 27 Material costs

Steel consumption for the floor slab is 88.8 kg/m^3 | Steel consumption for the floor slab is 77.1 kg/m^3

Overall result of example #3:

FEMnet 1.0 does not show a completely correct picture of deflections compared to FEMnet 2.0.
FEMnet 1.0 makes a mistake in determining the upper reinforcement in one of the zones and generally slightly underestimates the reinforcement results.

Comparison of FEM and FEMnet 2.0

Further in the comparisons, on the left side is FEM, on the right side is FEMnet 2.0.
In all the examples considered, the pylons are placed by the SmartPylon neural network, which will provide a certain pattern, which will be discussed in detail towards the end of the article.

Example #4

Fig. 28 Vertical movement of the floor slab

Maximum deflection -33.75 mm | Maximum deflection -34.48 mm

Fig. 29 Мx, T*m

Мx -3.01 ... +13.71 T*m | Мx -2.39 ... +4.91 T*m

Since the FEM has singularities, we will sometimes add additional explanations and images to them. In this case, the FEM variant has a distortion in the lower zone of the plates (-3.01 T*m), a sharp jump in voltage, which is absent in FEMnet 2.0.
Just as in the upper zone, local finite elements have a value that is multiple times higher than the neighboring finite elements:

Fig. 30 FEM Мx, T*m

Fig. 31 FEM Мx, T*m

Fig. 32 Мy, T*m

Мy -3.86 ... +15.51 T*m | Мy -2.74 ... +6.71 T*m

Here is the same situation, the results of FEM are strongly distorted due to singularities in both positive and negative directions. Here is a visual representation of them:

Fig. 33 FEM Мy, T*m

Fig. 34 FEM Мy, T*m

In the new version of the PromCore 4.0 program, the value of theoretical reinforcement is displayed when you hover the mouse cursor over the FE. Further in the comparison for FEMnet 2.0, the value of maximum reinforcement will be indicated on the isofields of theoretical reinforcement themselves.

Fig. 35 A_s_x lower, sm^2

A_s_x lower 0 ... 6.35, sm^2 | A_s_x lower 0 ... 6.98, sm^2

Fig. 36 A_s_y lower, sm^2

A_s_y lower 0 ... 8.13, sm^2 | A_s_y lower 0 ... 8.01, sm^2

Fig. 37 A_s_x upper, sm^2

A_s_x upper 0 ... 29.23, sm^2 | A_s_x upper 0 ... 14.36, sm^2

Fig. 38 A_s_y upper, sm^2

A_s_y upper 0 ... 32.68, sm^2 | A_s_y upper 0 ... 19.65, sm^2

Fig. 39 Material costs

Steel consumption for the floor slab is 108.0 kg/m^3 | Steel consumption for the floor slab is 83.2 kg/m^3

Overall result of example #4:

FEM shows a big difference with respect to FEMnet 2.0 due to singularities. If we analyze them in detail, there is almost no difference in the forces between the different methods.
FEMnet 2.0 shows much better convergence in the stress results.
There is no difference in vertical displacements between FEM and FEMnet 2.0.

Example #5

Fig. 40 Vertical movement of the floor slab

Maximum deflection -22.46 mm | Maximum deflection -19.65 mm

Fig. 41 Мx, T*m

Мx -9.72 ... +12.54 T*m | Мx -2.14 ... +5.97 T*m

Fig. 42 Мy, T*m

Мy -7.88 ... +10.19 T*m | Мy -1.88 ... +7.47 T*m

Fig. 43 A_s_x lower, sm^2

A_s_x lower 0 ... 20.49, sm^2 | A_s_x lower 0 ... 6.26, sm^2

Fig. 44 A_s_y lower, sm^2

A_s_y lower 0 ... 16.61, sm^2 | A_s_y lower 0 ... 5.50, sm^2

Fig. 45 A_s_x upper, sm^2

A_s_x upper 0 ... 27.95, sm^2 | A_s_x upper 0 ... 17.48, sm^2

Fig. 46 A_s_y upper, sm^2

A_s_y upper 0 ... 26.41, sm^2 | A_s_y upper 0 ... 21.85, sm^2

Fig. 47 Loads on vertical structures

Loads on vertical structures are found not by FEMnet, but by Mikhail Dubko's engineering author's method. Based on finding loading areas using the Cone Subtraction Method.

Fig. 48 Material costs

Steel consumption for the floor slab is 101.2 kg/m^3 | Steel consumption for the floor slab is 85.7 kg/m^3

Overall result of example #4:

FEM shows a big difference with respect to FEMnet 2.0 due to singularities. If we analyze them in detail, there is almost no difference in the forces between the different methods.
FEMnet 2.0 shows much better convergence in the stress results.
The difference in vertical displacement is up to 11%

Overall results for all comparisons

1. FEMnet 2.0 shows a much smoother picture of stress isofields compared to the previous version of the neural network.

2. FEMnet 2.0 has become more accurate in determining the values of stresses Mx and My.

FEMnet 2.0 copes better with determining stresses in places of stress concentration for the classic FEM.

3. If we take as an example a building that is slightly rotated along its vertical axis on each floor, then the convergence of the reinforcement results will visually demonstrate a distinct smooth pattern without chaotic stress values and vertical displacements:

Fig. 50 Building plan and facade

Fig. 51 Vertical movement of the floor slab

Fig. 52 Мx, T*m

Fig. 53 Мy, T*m

Fig. 54 A_s_x lower, sm^2

In this case, it is clearly visible how the crack resistance of reinforced concrete slabs on the 16th floor comes into play:

The reinforcement increases from 4.23 , sm^2 to 5.97 , sm^2. And the larger the floor slab console becomes, the higher the reinforcement in this area.

Fig. 55 A_s_y lower, sm^2

Fig. 56 A_s_x upper, sm^2

Fig. 57 A_s_y upper, sm^2

4. If we look at the picture of isofields of the upper reinforcement along the Y axis, we can see the ideal convergence of all the results of each floor without any local distortions. It seems that this is a picture of isofields of one level:

Fig. 58 A_s_x upper, sm^2

5. During all comparisons on various complex configurations of floor plans, one common difference was revealed between the neural network FEMnet 2.0 and FEMnet 1.0. FEMnet 2.0 forms a common field without breaks into 2 local ones inside one common one:

A break occurs when the neural network begins to doubt a certain local subset of values.

6. All examples in this work were generated by the SmartPylon neural network. This neural network tried to arrange the pylons while maintaining the average distance between the pylons at 4500 mm +/- 10%. And while maintaining the minimum ratio of maximum and minimum bending moments. Therefore, all reinforcement options from the FEMnet 2.0 neural network make up the range of values from 83.2 to 88.8 kg/m3. That is, the SmartPylon and FEMnet 2.0 neural networks find one common reinforcement pattern in completely different floor plans.

7. Reinforcement of floor slabs based on the results of classical FEM differs from neural network variants only due to the fact that FEM has many singularities, along which very large diameters of reinforcement are laid out, above diameter 18. If you look at all the specifications in detail and remove the reinforcement at the singularity locations, then the reinforcement according to FEM will coincide with the variant obtained according to FEMnet 2.0.

8. At the moment, the FEMnet neural network can solve problems of finding the stress-strain state of flat slabs under:

static loads on slabs
uniformly distributed loads over the entire area of the slab
without taking into account holes/beams, etc.