Project: Efficient Data Generation for Simulations

Edgar Torres, M.Sc.
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Project status: running

Problem Statement

Numerical simulations are a fundamental tool in science and engineering, offering insight into complex systems. However, these simulations are often computationally expensive, with some taking weeks to complete. This creates challenges in scenarios requiring the evaluation of multiple configurations, such as design optimization, or in real-time applications where rapid assessments are necessary.

Existing alternatives, such as reduced-order modeling (ROM), offer faster computations but typically suffer from poor generalization and reduced accuracy across varying conditions. Recently, surrogate models built using machine learning have shown potential in addressing these challenges. However, a significant problem is that these methods often require pre-existing datasets, which are costly to obtain. Therefore, data-efficient methods need to be developed that are both accurate and reliable.

Solutions

This PhD project aims to tackle these challenges by developing adaptive machine learning models that are pre-trained on one task and efficiently adapted to similar tasks. The goal is to enable these models to generate data for new simulation problems, such as different partial differential equation (PDE) tasks, with minimal additional data. By leveraging prior knowledge of the system, incorporating sparse data observations, and reusing information from related domains, the project will create techniques that enhance model adaptability and efficiency in generating data for new simulations.

Key techniques such as transfer learning, meta-learning, and few-shot learning will be explored to efficiently adapt machine learning models to new simulation tasks with minimal data. These approaches promise not only to reduce the reliance on large datasets but also to improve model accuracy and generalization in new or unseen simulation scenarios.

Key Publications

  • Torres, Edgar; Niepert, Mathias: Survey: Adaptive Physics-Informed Neural Networks. In: NeurIPS 2024 Workshop FM4Science, Vancouver, Canada, 2024.