About

Hanming Zhou is an Associate Professor in the Department of Mathematics at the University of California, Santa Barbara, where he also serves as Graduate Vice Chair. He completed his PhD in Mathematics at the University of Washington in 2015 under the supervision of Professor Gunther Uhlmann. Prior to joining UCSB, he was a Postdoctoral Research Associate at the University of Cambridge from 2015 to 2017, working with Professor Gabriel Paternain. Zhou's research focuses on the mathematical analysis of inverse problems and their connections with concrete applications, often motivated by challenges arising in medical imaging, geophysics, classical and quantum mechanics, and astronomy. His work lies at the interface of several disciplines including partial differential equations, microlocal analysis, differential geometry, and mathematical physics. He is actively involved in teaching and supervising both undergraduate and graduate students, and he welcomes inquiries from those interested in his research area.

Research topics

• Computer Science
• Mathematics
• Mathematical analysis
• Geometry
• Physics
• Applied mathematics
• Mathematical physics
• Quantum mechanics

Selected publications

• Stable Determination of Coefficients in Nonlinear Dynamical Schrödinger Equations by Carleman Estimates

  ArXiv.org · 2025-08-10

  preprintOpen accessSenior author

  We consider the inverse problem of recovering stationary coefficients in a class of dynamical Schrödinger equations with locally analytic nonlinear terms. Upon treating the well-posedness for small initial data and trivial boundary data, we proceed to establish stable and unique determination provided knowledge of the coefficients near the boundary and the measured Neumann data of the solution. We discuss both the case of measurement on a subset of the boundary large enough to satisfy a certain geometrical condition and, under stronger assumptions on the regularity and size of the coefficients, the case of measurement on arbitrary subsets of the boundary. Our argument relies on high-order linearization and Carleman estimates for the linear Schrödinger equation.

  PublisherOA PDFDOI

• Recovery of Coefficients in Semilinear Transport Equations

  Archive for Rational Mechanics and Analysis · 2024-06-19 · 2 citations

  articleSenior authorCorresponding
  PublisherDOI

• Multi-objective construction machinery group configuration optimization based on improved particle swarm optimization algorithm

  2024-02-09

  articleSenior author

  The construction of earthwork and stonework in the roadbed base is an indispensable part of the highway engineering construction process, and the reasonable allocation of engineering machinery groups has a significant impact on the cost and duration of the roadbed base construction. To solve the optimization problem of highway construction scheduling, a construction machinery group configuration optimization model with the goal of minimum cost and minimum construction period is established. An improved particle swarm algorithm with optimized particle swarm bounding search strategy is proposed and solved. Firstly, a equipment construction model is established. Then, a particle swarm bounding search strategy is constructed based on the Grey Wolf algorithm to dynamically adjust the composition of the particle swarm, improve the initial population quality, and integrate the Grey Wolf algorithm strategy into the particle swarm algorithm to improve the population diversity in the later stage of the algorithm and retain high-quality individuals during the evolution process. Finally, the effectiveness of the improved algorithm is verified by comparing the configuration example of the construction machinery group with the algorithm

  PublisherDOI

• On the Identifiability of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds

  SIAM Journal on Applied Mathematics · 2024-10-08

  articleSenior author
  PublisherDOI

• Inverse problems for time-dependent nonlinear transport equations

  arXiv (Cornell University) · 2024-10-01

  preprintOpen accessSenior author

  In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically, it is shown that its initial boundary value problem is well-posed for small initial and incoming data. Moreover, the time-dependent coefficient appearing in the nonlinear term can be uniquely determined from boundary measurements as well as initial and final data. To achieve this, the central techniques we utilize include the linearization technique and the construction of special geometrical optics solutions for the linear transport equation. This allows us to reduce the inverse coefficient problem to the inversion of certain weighted light ray transforms. Based on the developed methodology, the inverse source problem for the nonlinear transport equation in the scattering-free media is also studied.

  PublisherOA PDFDOI

• A Scheduling Method Based on an Improved Niche Genetic Algorithm for Engineering Machinery and Equipment Considering Construction Processes

  2024-03-01 · 3 citations

  article

  The coordination of multiple processes in roadbed construction can achieve corresponding engineering goals, and the reasonable scheduling of process combination equipment is conducive to the reduction of overall engineering costs and the improvement of overall construction efficiency. Based on genetic algorithm, this paper uses genetic algorithm with penalty function to optimize the selection of mechanical equipment for different processes of several objectives in highway construction. By establishing an optimization model with the goal of reducing construction costs and construction power, and using the construction requirements of each equipment as constraint conditions, multi-objective optimization is carried out using genetic algorithm settings to find the optimal mechanical equipment process scheduling plan. Case analysis shows that using genetic algorithm for mechanical equipment optimization can output the optimal results of minimum cost and minimum energy consumption while considering the completion of the project. Compared with genetic algorithm, the improved niche genetic algorithm with penalty function can achieve optimal scheduling and reduce the overall number of iterations.

  PublisherDOI

• Stability and statistical inversion of travel time tomography

  Inverse Problems · 2024-05-09 · 1 citations

  articleOpen accessSenior authorCorresponding

  Abstract In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.

  PublisherOA PDFDOI

• On the Identifiablility of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds

  arXiv (Cornell University) · 2023-05-21 · 1 citations

  preprintOpen accessSenior author

  In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the interaction kernels can be identified given infinite i.i.d observational derivative data sampled from a distribution. Our methodology involves casting the learning problem as a linear statistical inverse problem using a operator theoretical framework. We prove the well-posedness of inverse problem by establishing the strict positivity of a related integral operator and our analysis allows us to refine the results on specific manifolds such as the sphere and Hyperbolic space. Our findings indicate that a numerically stable procedure exists to recover the interaction kernel from finite (noisy) data, and the estimator will be convergent to the ground truth. This also answers an open question in [MMQZ21] and demonstrate that least square estimators can be statistically optimal in certain scenarios. Finally, our theoretical analysis could be extended to the mean-field case, revealing that the corresponding nonparametric inverse problem is ill-posed in general and necessitates effective regularization techniques.

  PublisherOA PDFDOI

• Stability and Statistical Inversion of Travel time Tomography

  arXiv (Cornell University) · 2023-09-22

  preprintOpen accessSenior author

  In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.

  PublisherOA PDFDOI

• Recovery of coefficients in semilinear transport equations

  arXiv (Cornell University) · 2022 · 2 citations

  Senior authorCorresponding
  • Mathematics
  • Mathematical analysis
  • Applied mathematics

  We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a stable way, from the boundary measurements by applying a linearization scheme and Carleman estimates for the linear transport equations. We establish results in both Euclidean and general geometry settings.

  PublisherOA PDFDOI

Recent grants

• Bridging the Mathematical Analysis and Reconstruction Algorithms for Transmission and Reflection Seismic Tomography

  NSF · $280k · 2021–2025

Frequent coauthors

• Günther Uhlmann

  75 shared

• Gabriel P. Paternain

  53 shared

• Mikko Salo

  KTH Royal Institute of Technology

  50 shared

• Ru-Yu Lai

  10 shared

• Yernat M. Assylbekov

  10 shared

• Andrew Homan

  3 shared

• Teemu Saksala

  3 shared

• Matti Lassas

  3 shared

Labs

• Hanming Zhou's LabPI

  Research on the mathematical analysis of inverse problems and their connections with concrete applications in medical imaging, geophysics, classical and quantum mechanics, and astronomy.