What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Algebra
The scientist’s investigation covers issues in Mathematical analysis, Algorithm, Computation, Fast multipole method and Discretization.
His work carried out in the field of Mathematical analysis brings together such families of science as Kohn–Sham equations, Basis set and Atomic orbital.
The various areas that Lexing Ying examines in his Algorithm study include Binary logarithm and Diagonal.
His Binary logarithm research incorporates themes from Computational complexity theory and Interpolation.
His Interpolation research incorporates elements of Scale parameter, Theoretical computer science, Phase correlation and Cartesian coordinate system.
His Fast Fourier transform research is multidisciplinary, relying on both Fourier transform and Curvelet.
His most cited work include:
- Fast Discrete Curvelet Transforms (2058 citations)
- A kernel-independent adaptive fast multipole algorithm in two and three dimensions (383 citations)
- Wave atoms and sparsity of oscillatory patterns (237 citations)
What are the main themes of his work throughout his whole career to date?
His main research concerns Applied mathematics, Algorithm, Mathematical analysis, Preconditioner and Discretization.
The study incorporates disciplines such as Artificial neural network, Stochastic gradient descent, Linear system, Factorization and Function in addition to Applied mathematics.
His Algorithm research includes elements of Binary logarithm, Simple and Representation.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Scattering and Boundary.
Lexing Ying has included themes like Helmholtz equation, Solver and Linear algebra in his Preconditioner study.
His biological study deals with issues like Integral equation, which deal with fields such as Fast multipole method.
He most often published in these fields:
- Applied mathematics (29.29%)
- Algorithm (26.78%)
- Mathematical analysis (24.69%)
What were the highlights of his more recent work (between 2018-2021)?
- Applied mathematics (29.29%)
- Algorithm (26.78%)
- Artificial neural network (10.04%)
In recent papers he was focusing on the following fields of study:
Lexing Ying mostly deals with Applied mathematics, Algorithm, Artificial neural network, Stochastic gradient descent and Discretization.
His biological study spans a wide range of topics, including Factorization, Type, Preconditioner, Function and Relaxation.
The Algorithm study combines topics in areas such as Energy and Wavelet, Wavelet transform.
His Artificial neural network research also works with subjects such as
- Nonlinear system together with Artificial intelligence,
- Partial differential equation that connect with fields like High dimensional, Fast multipole method and Nonlinear Schrödinger equation,
- Boundary, Fourier transform and Radiative transfer most often made with reference to Convolution,
- Field together with Helmholtz equation, Inverse scattering problem, Wave equation and Near and far field.
His Boundary research integrates issues from Basis and Interpolation.
His Discretization study integrates concerns from other disciplines, such as Solver and Integral equation.
Between 2018 and 2021, his most popular works were:
- Solving for high-dimensional committor functions using artificial neural networks (52 citations)
- SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems (29 citations)
- BCR-Net: A neural network based on the nonstandard wavelet form (21 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Algebra
His primary areas of investigation include Artificial neural network, Applied mathematics, Nonlinear system, Algorithm and Artificial intelligence.
His study in Artificial neural network is interdisciplinary in nature, drawing from both Field, Time evolution, Mathematical optimization and Inverse problem.
Lexing Ying has researched Field in several fields, including Mathematical analysis and Near and far field.
His research in Applied mathematics intersects with topics in Type, Partial differential equation, Regular polygon, Discretization and Function.
Lexing Ying combines subjects such as Multiple time dimensions, Fractional Laplacian, Solver and Laplace operator with his study of Discretization.
By researching both Algorithm and Operator, Lexing Ying produces research that crosses academic boundaries.
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