2024

Aug 19 - 23

Main goals

  • Breakdown of error discrepancy
    • Data variance, parameterization style (gauss-leg, uniform, arc), model invariance
    • TODO:
      • a) Old training, old geometry, old data gen, G-L - RMSE = 1% error
      • b) Old training, old geometry, old data gen, both riesz, G-L - RMSE = 2%
      • c) Old training, old geometry, new data gen, G-L - RMSE = 7%
      • d) Old training, old geometry, new data gen, Arc - RMSE = 7%
      • e) Old training, old geometry, new data gen, Uni - RMSE = 4%
      • f) Old training, new geometry, new data gen, G-L - RMSE =
      • g) Old training, new geometry, new data gen, Uni - RMSE =
      • h) New training, new geometry, new data gen, G-L - RMSE =
      • i) New training, new geometry, new data gen, Arc - RMSE = a vs c shows high variance data, c vs d vs e shows parameterization, c vs f shows new geometry,
  • Second draft
    • Figures are done
    • Theory
      • Computational complexity
      • Stability of iterations
  • New direction
    • Inversa problem?
      • Prata med Shervin Bagheri
      • Multiskaligt?
        • Seismic imaging (elastiska vågekv / elektromagnetism)
        • Vågutbrednin gaussian beams
        • Travel time tomography
      • Vågfrontsmängden
        • Signal och operator som verkar
        • Hur propagerar singulariteter under operatorn
    • Learned Homogenization:
      • Multiscale methods for Fredholm integral equations - Book
      • Homogenization as an operator learning problem \(A_\epsilon \mapsto \tilde A\)
      • Homogenization of Fredholm integral operators on rough surfaces: \(K_\epsilon (I - K_\epsilon)\sigma_\epsilon \approx \tilde K(I - \tilde K)\tilde\sigma.\) Reading about wavelets and representations using isometries. Possibly homogenize using sparse wavelet strategy? How to do that without needing to compare on all levels. Reinforcement learning
      • Possible colab with phillip scholl
    • Game theory perspective on optimization
      • Reinforcement learning
      • Placement of computational boxes in HMM -> Heterogeneous problems
      • Mart
    • Natural gradient boosting (marius, also open to other collab)
      • Finish up the code, is it useful? How to regularize
    • Reading
      • Multiscale methods for Fredholm integral equations - Book