Surrogate Modelling for Problems with Large-dimensional Parameter Spaces

The proliferation of design and manufacturing complexity has necessitated the adoption of modeling techniques for problems with large-dimensional parameter spaces. It is a daunting challenge to avoid the high-fidelity finite element model and to achieve rapid modeling and efficient simulation for problems with large-dimensional parameter spaces. This project develops active learning methods for effective non-intrusive surrogate modelling and active subspace methods for efficient parameter sampling in large-dimensional parameter spaces with more than 100 independent design parameters.

Non-intrusive surrogate modeling methods have gained much attention in recent years, especially those leveraging strong approximation capability of neural networks, which can effectively avoid traditional finite element analysis and provide real-time solution prediction. However, such methods heavily rely on large amount of training data. For models with large-dimensional parameter spaces, acquiring enough training data to build highprecision non-intrusive surrogate models can be unacceptably time-consuming, or even computationally infeasible. This research project aims to propose a novel active learning method [1] and a iterative active subspace method to solve the challenges in surrogate modelling of problems with large-dimensional parameter spaces.

Figure 1. AL-AS guided CAE-FFNN surrogate modelling.

Figure 1. AL-AS guided CAE-FFNN surrogate modelling.

Our AL-AS method (Figure 1) is adopted to iteratively expand the size of the training set for convolutional autoencoder-feedforward neural network (CAE-FFNN) surrogate modeling, allowing us to complete the construction of a high-precision surrogate model under acceptable time cost.

We validate our method on a few examples, one of them is a MEMS actuator with 25 structural parameters (Figure 2). We compared our method with Latin hypercubic sampling (LHS). The result is shown in Figure 3.

Figure 3. Relative error changing with the number of training samples.

Figure 3. Relative error changing with the number of training samples.

Figure 2. MEMS magnetic actuator with 25 structral parameters.

Figure 2. MEMS magnetic actuator with 25 structral parameters.

References

[1] C. Wang, L. Feng, W. Lu, W. Bian, Z. You, P. Benner. Active learning enhanced deep-learning surrogate model for fast MEMS design with high-dimensional design parameter spaces. In Proceedings of 2024 IEEE 19th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS).