1. Generalization in Polytopic Autoencoders for Fluid Flows

In this work, we aim to develop regularization strategies to improve the extrapolation capability of polytopic autoencoders (PAEs). In previous studies, we demonstrated that PAEs perform well for feedback control and reduced-order models. Nevertheless, it was observed that, despite well-constructed polytopes, a gap remained between the empirical and optimal errors. This suggests that not only do the PAEs have sufficient capacity to represent unseen flows, but they also have the potential to further reduce reconstruction errors. Building on these observations, this study investigates physics-guided data augmentation methods. 

• Keywords: autoencoders; clustering; data augmentation

2. Surrogate Model for a Controlled Orthotropic Plate

Control systems are often computationally expensive, challenging to use in real-time control applications, or difficult to interpret in terms of the relationships between system inputs and outputs. To address these issues, one possible approach is to use surrogate models. In this work, we focus on developing surrogate models for a controlled orthotropic plate system.

• Keywords: data-driven models; control systems; time series signal data

3. Neural Networks for Solving PDEs

In recent years, physics-informed neural networks (PINNs) have been widely used to solve partial differential equations alongside numerical methods because PINNs can be trained without observations and deal with continuous-time problems directly. In contrast, optimizing the parameters of such models is difficult, and individual training sessions must be performed to predict the evolutions of each different initial condition. The research goal is to develop neural network architectures which can alleviate these problems. 

• Keywords: data-driven models; physics-informed neural networks; partial differential equations