Introduction
In modern engineering, high-fidelity simulations like Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) are essential for validating and improving product performance. However, these simulations can be computationally expensive, often taking hours or even days to run. This time constraint creates a significant bottleneck, limiting the number of design variations an engineer can explore.
3DEXPERIENCE Platform addresses this challenge with powerful automation tools. The Optimization Process Composer app, allows engineers to build automated simulation workflows. Within this ecosystem, the Approximations Trainer feature offers a game-changing solution: it creates fast-running mathematical models that accurately predict simulation outcomes in a fraction of the time.
These "approximations" or "metamodels" are built using data from a set of initial high-fidelity simulations. Once trained, they can provide near-instantaneous results, enabling rapid design exploration and optimization. But which Machine Learning model should you choose?
Let's explore three common techniques.
Choosing Your ML Model: A Comparison of Approximation Techniques
The effectiveness of your approximation model depends heavily on the chosen mathematical method. Here are three primary types available.
Response Surface Model (RSM)
This is the default method, which works by fitting a polynomial equation—essentially a complex curve or surface—to your data points. The complexity of the equation automatically adjusts according to the amount of data you provide.
- Best For: Problems that have a simple, smooth, and continuous relationship between inputs and outputs, especially when exploring a small, localized design region.
- Pros ✅: Uses simple equations that are easy to fit to the data.
- Cons ❌: Can be inaccurate for highly non-linear or complex problems. The time it takes to build the model can become very slow if you have a large number of data points.
Radial Basis Function (RBF)
RBF is a type of neural network model. It's a powerful alternative to RSM, especially when the underlying physics are more complex or when inputs are not all equally important.
- Best For:
- Non-linear data.
- When you know all inputs are independent and equally important.
- When data falls into distinct categories (e.g., using material names like "Steel" or "Aluminum" as an input).
- Pros ✅: Generally faster to build than RSM when dealing with a large dataset.
- Cons ❌: Its strengths suggest it might not be the best choice if inputs are highly correlated.
Universal Kriging
Kriging is a sophisticated statistical interpolation method. Think of it as an intelligent "connect-the-dots" that understands the spatial relationship between your data points to make highly accurate predictions, even with sparse data.
- Best For:
- Problems where the data is spatially correlated (i.e., points close to each other are expected to have similar results).
- Creating a very accurate model from a small number of data points.
- Pros ✅: Very flexible. It can be set up to pass exactly through your data points (exact interpolation) or to smooth out noise in the data (inexact interpolation).
- Cons ❌: The model-building process can be very slow and computationally expensive, especially as the number of data points or inputs increases.
