Preprints

• Monotone inclusion methods for a class of second-order non-potential mean-field games
  L. Nurbekyan, S. Liu, Y.T. Chow
  Under review.

• State-Augmented Linear Games with Antagonistic Error for High-Dimensional, Nonlinear Hamilton-Jacobi Reachability
  W. Sharpless, Y.T. Chow, S. Herbert
  Under review.

• Conservative linear envelopes for high-dimensional, Hamilton-Jacobi reachability for nonlinear systems via the Hopf formula
  W. Sharpless, Y.T. Chow, S. Herbert
  Under review.

• Moving anchor extragradient methods for smooth structured minimax problems
  J. K. Alcala, Y.T. Chow, M. Sunkula
  Under review.

• Koopman-Hopf for Hamilton-Jacobi reachability and control in high-dimensional, nonlinear systems
  W. Sharpless, N. U. Shinde, M. Kim, Y.T. Chow, S. Herbert
  Under review.

Publications

• Quantum integrable systems and concentration of plasmon resonance
  H. Ammari, Y.T. Chow, H. Liu, M. Sunkula
  Journal of the European Mathematical Society, 1-39, 2024.

• Surface concentration of transmission eigenfunctions
  Y.T. Chow, Y. Deng, H. Liu, M. Sunkula
  Archive for Rational Mechanics and Analysis 247, 54, 2023.

• Quantum ergodicity and localization of plasmon resonances
  H. Ammari, Y.T. Chow, H. Liu
  Journal of Functional Analysis 285(4), 109976, 2023.

• A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem
  Y.T. Chow, S.W. Fung, S. Liu, L. Nurbekyan, S. Osher
  Inverse Problems 39, 014001, 2022.

• A direct sampling method for simultaneously recovering electromagnetic inhomogeneous inclusions of different nature
  Y.T. Chow, F. Han, J. Zou
  Journal of Computational Physics 470, 111584, 2022.

• Continuous data assimilation for two-phase flow: analysis and simulations
  Y.T. Chow, W.T. Leung, A. Pakzad
  Journal of Computational Physics 466, 111395, 2022.

• Localized sensitivity analysis at high-curvature boundary points of reconstructing inclusions in transmission problems
  H. Ammari, Y.T. Chow, H. Liu
  SIAM Journal of Mathematical Analysis, 54(2), 10.1137/20M1323576, 2021.

• A proof of the zeroth law of turbulence for the stochastically forced Navier-Stokes equations
  Y.T. Chow, A. Pakzad
  Discrete and Continuous Dynamical Systems Series B 27(9), 5181-5203, 2021.

• Recovery of a time-dependent bottom topography function from the shallow water equations via an adjoint approach
  J. Britton, Y.T. Chow, W. Chen, Y. Xing
  SIAM Journal of Scientific Computing 43(4), A2981–A3008, 2021.

• A direct sampling method for the inversion of the Radon transform
  Y.T. Chow, F. Han, K. Ito, J. Zou
  SIAM Journal of Imaging Sciences 14(3), 1004–1038, 2021.

• Surface-localized transmission eigenstates, super-resolution imaging and pseudo surface plasmon modes
  Y. He, H. Liu, X. Wang, Y.T. Chow
  SIAM Journal of Imaging Sciences 14(3), 946–975, 2021.

• A direct sampling method for simultaneously recovering inhomogeneous inclusions of different nature
  Y.T. Chow, F. Han, K. Ito, J. Zou
  SIAM Journal of Scientific Computing 43(3), A2161-A2189, 2021.

• Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances
  J. Liu, W. Li, W. Yin, Y.T. Chow
  SIAM Journal of Scientific Computing 43(1), A193–A220, 2021.

• Optimal Mesh Size for Inverse Medium Scattering Problems
  H. Ammari, Y.T. Chow, K. Liu
  SIAM Journal on Numerical Analysis 58(1), p. 733-756, 2020.

• A partial Laplacian as an infinitesimal generator on the Wasserstein space
  Y.T. Chow, W. Gangbo
  Journal of Differential Equations 267 (10), pp. 6065-6117, 2019.

• Optimal Human Navigation in Steep Terrain
  C. Parkinson, D.J. Arnold, A.L. Bertozzi, Y.T. Chow, S.J. Osher
  Communications in Mathematical Sciences 17 (1), pp. 227-242, 2019.

• Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
  Y.T. Chow, W. Li, S. Osher, W. Yin
  Journal of Scientific Computing, 80(2), 1195-1239, 2019.

• Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equations
  Y.T. Chow, J. Darbon, S. Osher, W. Yin
  Journal of Computational Physics 387, pp. 376-409, 2019.

• A splitting method to compute solutions to possibly nonconvex state-and-time-dependent Hamilton-Jacobi equations arising from optimal control and differential games
  A.T. Lin, Y.T. Chow, S. Osher
  Communications in Mathematical Sciences 16 (7), pp. 1933–1973, 2018.

• Parallel redistancing using the Hopf-Lax formula
  M. Royston, A. Pradhana, B. Lee, Y.T. Chow, W. Yin, J. Teran, S. Osher
  Journal of Computational Physics 365, pp.7-17, 2018.

• A Time-dependent Direct Sampling Method for Recovering Moving Potentials in Heat Equation
  Y.T. Chow, K. Ito, J. Zou
  SIAM Journal of Scientific Computing, 40(4), A2720–A2748, 2018.

• Super-resolution in imaging high contrast targets from the perspective of scattering coefficients
  H. Ammari, Y.T. Chow, J. Zou
  Journal de Mathematiques Pures et Appliquees 111, pp. 192-226, 2018.

• Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games
  Y.T. Chow, J. Darbon, S. Osher, W. Yin
  Annals of Mathematical Sciences and Applications 3, pp.369-403, 2018.

• Time-Optimal Collaborative Guidance using the Generalized Hopf Formula
  M.R. Kirchner, R. Mar, G. Hewer, J. Darbon, S. Osher, and Y.T. Chow
  IEEE Control Systems Letters 2(2), pp. 201-206, 2017.

• Algorithm for Overcoming the Curse of Dimensionality for Time-dependent Non-convex Hamilton-Jacobi Equations Arising from Optimal Control and Differential Games Problems
  Y.T. Chow, J. Darbon, S. Osher, W. Yin
  Journal of Scientific Computing, DOI 10.1007/s10915-017-0436-5, 2017.

• Cyclic Coordinate Update Algorithms for Fixed-Point Problems: Analysis and Applications
  Y.T. Chow, T. Wu, W. Yin
  SIAM Journal of Scientific Computing 39(4), A1280-A1300, 2017.

• Phased and phaseless domain reconstruction in inverse scattering problem via scattering coefficients
  H. Ammari, Y.T. Chow, J. Zou
  SIAM Journal on Applied Mathematics 76(3), pp. 1000-1030, 2016.

• Analysis on a Nonnegative Matrix Factorization and Its Applications
  Y.T. Chow, K. Ito, J. Zou
  SIAM Journal of Scientific Computing 38(5), B645–B684, 2016.

• Expander Graph and Communication-Efficient Decentralized Optimization
  Y.T. Chow, W. Shi, T. Wu, W. Yin
  50th Asilomar Conference on Signals, Systems and Computers, DIO 10.1109/ACSSC.2016.7869675, 2016.

• Optimal shape design by partial spectral data
  H. Ammari, Y.T. Chow, K. Liu, J. Zou
  SIAM Journal of Scientific Computing 37(6), B855–B883, 2015.

• Direct sampling method for diffusive optical tomography
  Y.T. Chow, K. Ito, K. Liu, J. Zou
  SIAM Journal of Scientific Computing 37(4), A1658–A1684, 2015.

• The concept of heterogeneous scattering coefficients and its application in inverse medium scattering
  H. Ammari, Y.T. Chow, J. Zou
  SIAM Journal of Mathematical Analysis 46(4), pp. 2905-2935, 2014.

• A direct sampling method for electrical impedance tomography
  Y.T. Chow, K. Ito, J. Zou
  Inverse Problems 30, 095003, DOI:10.10880266-5611309095003, 2014.

• A numerical method for reconstructing the coefficient in a wave equation
  Y.T. Chow, J. Zou
  Numerical Methods for Partial Differential Equations, DOI: 10.1002/num.21904, 2014.

Animation

A new project: Mean-field control of planes in real time 1) black dots (Planes are initially allocated in the space randomly) 2) green dots (Target locations/distribution) 3) red dots (Obstacles) Goal of the planes: move to the green dots from the black dots, avoiding self-colliding and colliding with the red dots.