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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
This project aims to develop solutions that are both computationally and data-efficient for generating PDE data. By leveraging advanced machine learning techniques—such as transfer learning, meta-learning, and few-shot learning—the goal is to create models that can generalize across varying conditions and reduce the need for extensive training datasets. These methods will enable faster and more reliable data generation, facilitating the use of simulations in high-demand applications like real-time decision-making, design optimization, and uncertainty quantification.
Keywords: Physics-informed Neural Networks (PINNs), Meta-learning, Transfer-learning, Neural Operators, Partial Differential Equations, Few-shot Learning, Implicit Neural Fields