AI, Artificial Intelligence, is disrupting one industry after another. In this article, we will show you how our new artificial neural network can help you significantly improve the simulation time of GHEtool.
The overarching problem
Central to the simulation of borefields is the calculation of g-functions. These non-dimensional functions describe how a borefield behaves in the long-term, with the different boreholes interacting with each other and with the surrounding ground. (If you have not read our article on g-functions, you can find it hier.)
Historically, the simulation of g-functions, especially for rather large borefields, was extremely slow. Nowadays, due to some clever mathematical tricks and intelligent algorithms, humankind can calculate these g-values in about 0.5 seconds, which is more than acceptable when it comes to the straightforward simulation of borehole temperatures.
However, a problem arises when more complicated and advanced methods require multiple g-values to be simulated, for example in the method calculate required borehole depth. For every iteration, this aim requires the calculation of several g-values, leading to simulation times of ten to thirty seconds or sometimes even higher. With the trend towards more advanced methods, this increase in simulation time is not a bright prospect.
Therefore, the quest was to find a new way to speed up the simulation of these g-functions without a compromise in accuracy. This is where artificial intelligence, or more precisely an artificial neural network, came into the picture.
Artificial Neural Network
AI is a very broad term, encompassing everything from large language models (like ChatGPT) to humanoid robots and self driving systems. Within this AI field, there is something called an artificial neural network (or ANN for short). In the next sections, we will introduce these ANNs, explain how we trained them and what their accuracy is.
What is it?
The concept of an ANN is to mimic the behaviour of the human brain, or at least the way we think it works. When we receive some sensory input, whether it is smell, touch or sound, it is sent to the neurons in our brain, where the signal moves from neuron to neuron until we end up with a certain thought, action, sense and so on. This behaviour, where we start from a set of inputs and move through a series of neurons to reach a certain conclusion, is exactly what we try to model with an ANN. In the figure below, a schematic representation of an ANN is given.
Although these neural networks can come in all shapes and forms, the structure is more or less the same. Starting from a set of input parameters, which in our case is the borefield data (configuration, depth, ground thermal diffusivity and so on), the data passes to a series of nodes in the first layer. Here, in each node (or neuron), the data is weighted by the value in the neuron and sent to the neurons in the next layer. The same process occurs there, until we reach the output layer, which in our case consists of the corresponding g-values.
Depending on the model architecture of your ANN, the number of hidden layers can differ, as well as the number of neurons in each layer. The main challenge is to find a model that is just complex enough to learn or represent the physics you need, and not too over-complicated, since the more neurons you have in your model, the more extensive your training set has to be.
Training
Just like a baby that comes into this world and still has to learn almost everything, our neural network cannot do anything correctly straight out of the box. As said before, the concept of a neural network is that data passes through several weighting nodes to be transformed, in the end, into the actual output we need. However, these weighting factors are not general but very case specific and model specific. That is why we have to train it and teach the ANN how it should behave, or more specifically for our situation, what the g-values are for a certain set of inputs.
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The training and development of the ANN for this domain is based on the work of Tobias Blanke, who also developed the ANN model that is currently implemented in GHEtool.
For our training dataset, we started from regular configurations (line, L-shaped and U-shaped, rectangles and dense borefields) and simulated them with parameters in the following ranges:
- Borefield size: 30×30 boreholes, so up to 900 boreholes for our rectangle and dens shaped borefields.
- Borehole depth: 50-400m
- Borehole spacing: 2-10m
- Borehole diameters: 100-300mm
- Ground thermal diffusivity: 2.5e-7 – 2.67e-6
Given the permutations of all the above data ranges, we trained our model with over six million data points.
Accuracy
Although there are quite a lot of different formal measures for assessing the accuracy of ANNs, we like to keep it simple and understandable. Therefore, in the graph below, you can see the required borehole depth for nine different cases, calculated with both the regular model (where the g-values are calculated explicitly) and the ANN model. The cases were selected to cover a wide range of situations, such as being limited by the maximum or minimum average fluid temperature, having different geothermal heat fluxes, or having variable fluid properties and so on.
It is clear from the graph above that there is excellent agreement between the regular model and the new artificial one. For most cases, the ANN gave a slight overestimation of the required borehole depth, whereas in case 7 a slightly lower depth was simulated. Overall, the accuracy of the ANN was within 4% of the regular model, which is arguably in the order of the other uncertainties used in geothermal design.
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For accuracy reasons, after the sizing is completed, the temperature profile you see in GHEtool is calculated with the exact, regular model. This means that the AI acceleration is only used to speed up the iteration to find the required depth, but not to simulate the temperatures at this depth. In this way, you have the benefit of a faster model combined with the highest accuracy for the temperature simulation.
In the graph below, the simulation time for the different cases is shown.
n the graph above, it is clear that the ANN outperforms the regular approach significantly, with time savings ranging from 25% up to 75%. Taking into account that the difference in accuracy is only 4%, it is fair to say that this is a good trade-off.
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Besides the calculation time required for the g-functions, other parts of the code also require some time. With the ANN model, the calculation time of the g-values has been reduced significantly, which makes other aspects, such as the calculation of the effective borehole thermal resistance, more dominant in the overall simulation time.
What is next?
So what is next? Will all GHEtool calculations be based on AI models from now on? Absolutely not.
Although we have seen and demonstrated the value of relying on AI to accelerate certain methods, we still prefer the accuracy of the regular, physics-based approach. That is why, from today onwards, the ANN is available in GHEtool when using the ‘calculate required depth’ aim, under the ‘aim specific settings’. For other methods, it is, in our opinion, not yet an added value.
That being said, the implementation of our first ANN opens the door to a whole new range of possibilities, new methods and more advanced optimisations.
Blijf op de hoogte
Next week, we will introduce our first brand-new aim, made possible by this exact ANN. Stay tuned for that!
Conclusie
This article has laid the foundation for a whole new range of possibilities within GHEtool. With the implementation of an artificial neural network to speed up the simulation time of g-functions, the calculate required borehole depth function can be made 25–75% faster while maintaining similar accuracy.
Referenties
- Bekijk onze video over dit artikel op onze YouTube pagina hier.
- Blanke, T., Pfeiffer, F., Göttsche, J., & Döring, B. (2024, September). Artificial neural networks use for the design of geothermal probe fields. In BauSim Conference 2024 (Vol. 10, pp. 89-95). IBPSA-Germany and Austria.
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