Universal Approximation Theorem
Deep neural networks are often justified by the universal approximation theorem, yet this result alone does not explain why certain architectures perform better in practice. My research develops a refined approximation theory that characterizes how architectural choices--such as depth, recurrence, and structure--affect approximation efficiency.
In particular, I study neural networks as numerical models acting on structured function spaces. Recent work extends classical Barron-type analysis to broader settings, showing that deep architectures can approximate richer function classes with improved efficiency . The goal is to establish a predictive theory linking target function properties to optimal network design.
Physics-Informed Neural Network
Deep neural networks are often justified by the universal approximation theorem, yet this result alone does not explain why certain architectures perform better in practice. My research develops a refined approximationBeyond expressivity, practical success depends on whether a model can be trained reliably. In scientific problems, such as PDE-based modeling, training instability is a major bottleneck. My research investigates how neural network structure influences optimization dynamics and convergence.
I have studied the convergence behavior of physics-informed neural networks (PINNs), showing that architectural modifications--such as variable-splitting strategies--can significantly improve stability under weaker conditions . This direction aims to build a theoretical framework answering: when does a neural network actually learn the correct solution? theory that characterizes how architectural choices--such as depth, recurrence, and structure--affect approximation efficiency.
Scientific Machine Learning (Weather-AI)
Many real-world systems are governed by physical laws, yet data-driven models must also handle noise, sparsity, and high dimensionality. My research integrates deep learning with scientific modeling, focusing on applications such as radar-based extreme weather prediction.
Recent work develops neural architectures tailored to spatiotemporal structure and extreme-event prediction, combining physical insights with modern deep learning techniques . This line of research bridges theory and application, aiming to build models that are not only accurate but also physically consistent and interpretable.