Dongzhe (Denzel) Zheng
Ph.D. Researcher, MAE, Princeton University (2025–present)
Gordon Y.S. Wu Fellow in Engineering, Princeton University
Master, Part III of the Mathematical Tripos, University of Cambridge (2020–2021)
Bachelor of Science in Mathematics, University of New Hampshire (2017–2020)
Mathematics
Research indexI work on local-to-global questions in algebra, geometry, and analysis.
More questions 12
◊ Scientific Machine Learning
Accepted · September 24, 2026
Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivariance
Conference on Neural Information Processing Systems (NeurIPS) 2026 Spotlight (Top 1.3% of submissions; Top 5% of accepted papers)
Riemannian Hodge Message Passing (RHMP) learns positive-definite metrics on discrete field spaces, making geometry adaptable while keeping topological identities exact, Hodge energies nonnegative, and propagation equivariant under orthogonal changes of hidden feature basis.
Accepted · ICML 2026
Topology-Preserving Neural Operator Learning via Hodge Decomposition
International Conference on Machine Learning (ICML) 2026
Hodge Spectral Duality (HSD) is a hybrid Eulerian–Lagrangian architecture that uses Hodge orthogonality to separate unlearnable topological features from learnable geometric dynamics. By combining discrete differential forms with an auxiliary ambient space, it improves accuracy, efficiency, and fidelity to physical invariants when solving field equations on geometric meshes.
Other papers
Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation
Conference on Neural Information Processing Systems (NeurIPS) 2026
Symmetry Descent Neural Operators: From Local Equivariance to Global Consistency
Conference on Neural Information Processing Systems (NeurIPS) 2026 · Workshop on Symmetry and Geometry in Neural Representations · Extended Abstract Track
Library · Maintainer
NEFI — Neural-Field Inversion
NEFI is a library for recovering unknown material properties and physical fields. It covers 17 classes of inverse problems with 36 differentiable forward operators, from CT, EIT, and Darcy flow to wave propagation, optics, and photoacoustic tomography.
⚛ Physics
Accepted
Toroidal Loop-Current Order in Kagome \(AV_3Sb_5\): Zero-Field Diode and Anomalous Hall
Journal of Physics: Condensed Matter (JPCM)
This work explains how the charge density wave-driven anomalous Hall effect (AHE) and the zero-field superconducting diode effect (SDE) can coexist in kagome metals. Its theoretical framework connects microscopic orbital current patterns to macroscopic transport signatures.
Accepted
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
This work quantifies how closely a Chern band’s projected density algebra approximates that of the lowest Landau level, addressing a foundational question in fractional Chern insulator (FCI) theory. Operator-norm bounds separate the effects of band geometry (Berry curvature and the Fubini–Study metric) from interband-mixing dispersion, while quasi-adiabatic continuation connects single-particle algebraic deviation to many-body gap stability. In Harper–Hofstadter and kagome models, a new finite-volume indicator \(\mathcal{E}_{\Lambda,L}\) correlates more sharply with the many-body gap than the conventional Berry-curvature proxy \(\sigma_B\), providing a quantitative single-particle criterion for zero-field topological many-body phases.
Accepted
Linear Visibility of the Higgs Mode and Odd-Frequency Mixing Mechanism in Time-Reversal Symmetry Breaking Kagome Superconductors
Journal of Physics: Condensed Matter (JPCM)
In time-reversal-symmetry-breaking superconductors, a pseudoscalar background field can activate the Higgs mode only through odd-frequency mixing; symmetry forbids static coupling. This result identifies a previously unrecognized selection rule for collective-mode coupling in these superconductors.
⎈ Control
Accepted · L-CSS & CDC 2026
A Posteriori Second-Order Guarantees for Bolza Problems via Collocation
IEEE Control Systems Letters (L-CSS) · IEEE Conference on Decision and Control (CDC) 2026
This work establishes a posteriori second-order sufficient conditions for Bolza-type optimal control problems solved by collocation, allowing rigorous verification of the local optimality of numerically computed trajectories.