Registered Data

[CT029]

  • Session Time & Room
    • CT029 (1/1) : 4E @G501 [Chair: Daniel Zhengyu Huang]
  • Classification
    • CT029 (1/1) : Representations of solutions to partial differential equations (35C)

[01390] Neural Operator for Multidisciplinary Engineering Design

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
  • Type : Contributed Talk
  • Abstract : Deep learning surrogate models have shown promise in solving PDEs, which enable many-query computations in science and engineering. In this talk, I will first introduce a geometry-aware Fourier neural operator (Geo-FNO) to solve PDEs on arbitrary geometries, inspired by adaptive mesh motion and spectral methods. Furthermore, we study the cost-accuracy trade-off of different deep learning-based surrogate models, following traditional numerical error analysis. Finally, we demonstrate our approach on challenging engineering design problems.
  • Classification : 35C99, 65M99, 65Z05, 68T07
  • Format : Talk at Waseda University
  • Author(s) :
    • Daniel Zhengyu Huang (Caltech)
    • Andrew M. Stuart (Caltech)
    • Elizabeth Qian ( Georgia Tech)
    • Maarten de Hoop (Rice University)

[02689] Double Dirac Cone in Subwavelength Bandstructure

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
  • Type : Contributed Talk
  • Abstract : In this talk we wish to rigorously justify the existence of the double Dirac point for the super-honeycomb lattice in the subwavelength regime. First, we will give a rigorous characterization of the symmetry conditions. Then, representing the solution by periodic layer potentials when the frequency is nonzero, we can asymptotically solve the band structure by the periodic capacitance matrix. We also study how the perturbation to the inclusions affect the band structure numerically.
  • Classification : 35C20
  • Format : Talk at Waseda University
  • Author(s) :
    • Borui Miao (Tsinghua University)
    • Yi Zhu (Yau Mathematical Sciences Center)

[01224] Collision-induced amplitude dynamics of nD solitons in a perturbed saturable nonlinear medium

  • Session Time & Room : 4E (Aug.24, 17:40-19:20) @G501
  • Type : Contributed Talk
  • Abstract : We study the amplitude dynamics of two-dimensional (2D) fast solitons in an interaction under a framework of coupled (2+1)D nonlinear Schrodinger equations with a saturable nonlinearity and weak perturbation. We derive a theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is mainly based on the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. The theoretical results are validated by numerical simulations with the coupled perturbed nonlinear Schrodinger equations with saturable nonlinearity.
  • Classification : 35C08, 35Q51, 35Q60, 78A10, 78M10
  • Format : Online Talk on Zoom
  • Author(s) :
    • Quan Minh Nguyen (International University, Vietnam National University Ho Chi Minh City)
    • Toan Thanh Huynh (Department of Mathematics, University of Medicine and Pharmacy at Ho Chi Minh City, Vietnam)