Dongzhe (Denzel) Zheng

Ph.D. Researcher, MAE, Princeton University
Gordon Y.S. Wu Fellow in Engineering, Princeton University
Master of Mathematics, University of Cambridge

◊ Scientific Machine Learning

Accepted · ICML 2026

Topology-Preserving Neural Operator Learning via Hodge Decomposition

Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette

International Conference on Machine Learning (ICML) 2026 · Regular Paper [Avg. Score: 5/6 (est. Top 1% via PaperCopilot)]

Introducing a hybrid Eulerian–Lagrangian architecture, Hodge Spectral Duality (HSD), that exploits Hodge orthogonality to decouple unlearnable topological features from learnable geometric dynamics. Combining discrete differential forms with an auxiliary ambient space, the method markedly improves accuracy, efficiency, and fidelity to physical invariants when solving field equations on geometric meshes.

⚛ Physics

Accepted · March 16, 2026

Toroidal Loop-Current Order in Kagome \(AV_3Sb_5\): Zero-Field Diode and Anomalous Hall

Journal of Physics: Condensed Matter (JPCM)

Resolving the phenomenological coexistence of charge density wave-driven anomalous Hall effect (AHE) and zero-field superconducting diode effect (SDE) in kagome metals. This work establishes a unified theoretical framework connecting microscopic orbital current patterns to macroscopic transport signatures.

Provisionally Accepted · April 23, 2026

Operator-norm Control of Projected Density Algebras in Chern Bands: Toeplitz Correspondence and Adiabatic Equivalence to the Lowest Landau Level

Journal of Physics A: Mathematical and Theoretical

Turning the founding question of the fractional Chern insulator (FCI) field—in what precise sense is a Chern band "close to" the lowest Landau level?—from a decade of heuristic band-geometry correlations into rigorous, quantitative control: operator-norm bounds on the projected density algebra that cleanly separate geometric effects (Berry curvature, Fubini–Study metric) from interband-mixing dispersion, with quasi-adiabatic continuation then tying single-particle algebraic deviation to many-body gap stability. A new finite-volume indicator \(\mathcal{E}_{\Lambda,L}\) correlates with the many-body gap in Harper–Hofstadter and kagome models far more sharply than the conventional Berry-curvature proxy \(\sigma_B\), giving a quantitative single-particle criterion for zero-field topological many-body phases.

Moderate Revision · JPCM

Linear Visibility of the Higgs Mode and Odd-Frequency Mixing Mechanism in Time-Reversal Symmetry Breaking Kagome Superconductors

Journal of Physics: Condensed Matter (JPCM)

Proving that in time-reversal-symmetry-breaking superconductors, the unique symmetry-allowed channel through which a pseudoscalar background field activates the Higgs mode is odd-frequency mixing—static coupling is strictly forbidden. This identifies a previously unrecognized selection rule for TRSB collective-mode coupling.

⎈ Control

Accepted · April 6, 2026

A Posteriori Second-Order Guarantees for Bolza Problems via Collocation

Dongzhe Zheng, Wenjie Mei

IEEE Control Systems Letters (L-CSS)

Providing a posteriori second-order sufficient conditions for Bolza-type optimal control problems solved via collocation methods, enabling rigorous local optimality verification of numerically computed trajectories.