What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Artificial intelligence
Mathematical analysis, Algorithm, Numerical analysis, Level set method and Discretization are his primary areas of study.
His Fast marching method research extends to Mathematical analysis, which is thematically connected.
His study in the field of Time complexity is also linked to topics like Interface.
His Numerical analysis research is multidisciplinary, incorporating elements of Iterative method and Hamilton–Jacobi equation.
Hongkai Zhao interconnects Signed distance function, Energy functional, Data set and Level set in the investigation of issues within Level set method.
His studies in Discretization integrate themes in fields like Fluid dynamics and Eikonal equation.
His most cited work include:
- Regular Article: A PDE-Based Fast Local Level Set Method (1013 citations)
- A Variational Level Set Approach to Multiphase Motion (911 citations)
- A fast sweeping method for Eikonal equations (743 citations)
What are the main themes of his work throughout his whole career to date?
Hongkai Zhao mainly focuses on Mathematical analysis, Algorithm, Applied mathematics, Inverse problem and Discretization.
Hongkai Zhao works mostly in the field of Mathematical analysis, limiting it down to topics relating to Solver and, in certain cases, Discontinuous Galerkin method.
The concepts of his Algorithm study are interwoven with issues in Level set method, Hybrid Monte Carlo, Markov chain Monte Carlo, Surface and Mathematical optimization.
His Level set method study integrates concerns from other disciplines, such as Data set and Level set.
His studies deal with areas such as Numerical analysis, Polygon mesh and Eikonal equation as well as Applied mathematics.
His research investigates the connection between Discretization and topics such as Finite difference method that intersect with issues in Grid.
He most often published in these fields:
- Mathematical analysis (38.31%)
- Algorithm (24.03%)
- Applied mathematics (13.64%)
What were the highlights of his more recent work (between 2017-2021)?
- Applied mathematics (13.64%)
- Mathematical analysis (38.31%)
- Algorithm (24.03%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Applied mathematics, Mathematical analysis, Algorithm, Phase retrieval and Inverse problem.
His studies in Applied mathematics integrate themes in fields like Basis, Reduction, Dimensionality reduction, Discretization and Intrinsic dimension.
The study incorporates disciplines such as Stokes flow and Knudsen number in addition to Mathematical analysis.
His Algorithm research includes themes of Boundary, Domain, Outlier and Convex hull.
His Phase retrieval research is multidisciplinary, incorporating elements of Discrete mathematics, Quadratic equation, Gaussian and Semidefinite programming.
The Inverse problem study combines topics in areas such as Open problem, Work, Instability and Radiative transport.
Between 2017 and 2021, his most popular works were:
- Approximate Separability of the Green's Function of the Helmholtz Equation in the High Frequency Limit (19 citations)
- Neural-Response-Based Extreme Learning Machine for Image Classification (10 citations)
- Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit (8 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Geometry
Hongkai Zhao spends much of his time researching Mathematical analysis, Inverse problem, Work, Instability and Green's function.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Phase function and Radiative transfer.
Hongkai Zhao has included themes like Phase space method, Reflection, Tomography and Bounded function in his Inverse problem study.
The concepts of his Work study are interwoven with issues in Heavy traffic approximation and Scattering, Radiative transport.
He interconnects Knudsen number, Perturbation, Logarithm, Open problem and Exponential function in the investigation of issues within Instability.
His Green's function study combines topics in areas such as Helmholtz equation and Limit.
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