Projects

This project applies Hidden Markov Models (HMMs) to fMRI for studying time-varying brain activity and functional connectivity. HMMs provide a probabilistic framework for identifying recurring brain states and characterizing how the brain transitions between different patterns of activity over time.

Our work uses HMM-based analysis across resting-state and task fMRI to investigate brain dynamics and their relationships with neurological and cognitive processes.

This project develops nonlinear Kernel Canonical Correlation Analysis (KCCA) for task-fMRI activation detection. By extending conventional linear KCCA to nonlinear kernel spaces, the method captures more complex relationships between fMRI signals and task-related neural responses while retaining efficient whole-brain activation analysis.

We further developed self-supervised optimization for parameter selection and robust back-reconstruction methods for mapping nonlinear representations back to voxel-level activation patterns. Together with systematic kernel selection, these developments improve activation accuracy and robustness across simulated and real task-fMRI datasets.

This project explores meta-learning for scientific applications where labeled data are extremely limited. Optimization-based meta-learning uses a nested learning process to identify neural networks that can rapidly adapt to new tasks from only a few examples.

We applied this idea to quantum scar detection, where distinct scarring states are rare and conventional deep learning is limited by the lack of training data. By combining meta-learning and few-shot classification, we developed a fully automated detector that can identify quantum scars from thousands of wave functions using only a few labeled examples, demonstrating the potential of meta-learning for data-limited detection problems across science and engineering.

This project develops deep-learning-based inverse-design methods for electronic devices, replacing computationally expensive physics solvers with neural networks and directly optimizing device configurations for desired physical responses.

We first applied this approach to graphene quantum dots to design gate-potential configurations for extreme quantum scattering, including cloaking and superscattering. We further developed deep-learning-designed graphene electronic metasurfaces for controlling Dirac electron waves, enabling applications such as electron holography, wavefront engineering, and multifunctional electronic devices.

This project develops physics-enhanced neural networks that incorporate governing physical laws directly into model learning. We introduced two physics-driven neural-network frameworks for learning classical and quantum dynamical systems from limited data.

The first, an adaptable Hamiltonian neural network, incorporates Hamilton's equations and system parameters to predict nonlinear dynamics across unseen parameter regimes, including transitions to chaos. The second, a Heisenberg neural network, incorporates the Heisenberg equation of motion to reconstruct time-dependent quantum Hamiltonians and their interaction structures from sparse local measurements.

This project investigates electronic and optical phenomena in two-dimensional pseudospin-1 Dirac systems, whose energy bands consist of two Dirac cones intersected by a flat band. We studied how this unique band structure modifies Coulomb-impurity physics, electronic transport, and optical response.

A central contribution was, to our knowledge, the first analytical treatment of atomic collapse in pseudospin-1 systems and the derivation of a complete analytical expression for the optical conductivity of flat-band Dirac materials. These results reveal distinctive flat-band effects, including singular conductivity, unusual interband transitions, and resonant optical scattering.