config/config.yaml

project:
  name: DeepONet
  paper: "DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators"
  arxiv: "1910.03193v3"
  paper_url: "https://arxiv.org/abs/1910.03193"
  implementation_policy: "paper_first_independent_reimplementation"
  paper_scale: true

paths:
  checkpoint: weight/best_model.pth
  results: results
  cache: results/cache

runtime:
  seed: 0                    # ASSUMPTION: the paper does not report seeds.
  device: auto
  dtype: float32             # ASSUMPTION: precision is not reported.
  num_workers: 0

function_space:
  type: grf
  length_scale: 0.2          # PAPER: default RBF-GRF length scale.
  grf_grid_size: 1000        # OFFICIAL_REPO_REFERENCE: paper omits this discretization.
  jitter: 1.0e-13            # OFFICIAL_REPO_REFERENCE: numerical Cholesky stabilizer.
  interpolation: cubic       # OFFICIAL_REPO_REFERENCE.
  generation_chunk_size: 128
  chebyshev:
    degree: 10
    coefficient_bound: 1.0

model_defaults:
  architecture: deeponet
  activation: relu           # OFFICIAL_REPO_REFERENCE: paper does not state activation.
  initializer: xavier_normal # OFFICIAL_REPO_REFERENCE: PyTorch equivalent of Glorot normal.
  dense_bias: true
  branch_depth: 2            # ASSUMPTION: number of Dense layers after the input.
  trunk_depth: 3             # ASSUMPTION: number of Dense layers after the input.
  width: 40
  latent_dim: 40

variants:
  unstacked_bias:
    architecture: deeponet
    stacked: false
    branch_output_bias: true
    global_bias: true
  unstacked_no_bias:
    architecture: deeponet
    stacked: false
    branch_output_bias: false
    global_bias: false
  stacked_bias:
    architecture: deeponet
    stacked: true
    branch_output_bias: true
    global_bias: true
  stacked_no_bias:
    architecture: deeponet
    stacked: true
    branch_output_bias: false
    global_bias: false
  fnn:
    architecture: fnn
    depth: 3
    width: 40
    output_bias: true

training_defaults:
  optimizer: adam
  learning_rate: 1.0e-3      # PAPER.
  batch_size: null           # OFFICIAL_REPO_REFERENCE: null means full batch.
  evaluation_batch_size: 8192
  weight_decay: 0.0          # No paper evidence; disabled.
  print_every: 1000
  evaluate_every: 1000
  checkpoint_metric: test_mse
  resume: false

solver_defaults:
  method: RK45               # PAPER: Runge-Kutta (4,5); method name from official reference.
  rtol: 1.0e-7               # ASSUMPTION: solver tolerances are not reported.
  atol: 1.0e-9
  pde_newton_tolerance: 1.0e-10
  pde_newton_max_iterations: 20

experiments:
  antiderivative:
    equation: "ds/dx = u(x), s(0) = 0"
    sensor_points: 100
    trunk_dim: 1
    domain_end: 1.0
    train_size: 10000
    test_size: 100000
    iterations: 50000
    default_variant: unstacked_bias
    sweeps:
      architectures: [fnn, unstacked_no_bias, unstacked_bias, stacked_no_bias, stacked_bias]
      fnn_depths: [2, 3, 4]
      fnn_widths: [20, 40, 100]
      learning_rates: [0.0001, 0.001, 0.01]

  nonlinear_ode:
    equation: "ds/dx = -s^2 + u(x), s(0) = 0"
    sensor_points: 100
    trunk_dim: 1
    domain_end: 1.0
    train_size: 10000
    test_size: 100000
    iterations: 100000
    default_variant: unstacked_bias
    trim_fraction: 0.001
    ood_functions: [linear, sin_pi, sin_2pi]
    sweeps:
      architectures: [stacked_no_bias, stacked_bias, unstacked_no_bias, unstacked_bias]

  pendulum:
    equation: "ds1/dt = s2; ds2/dt = -k*sin(s1) + u(t); s(0) = (0,0)"
    sensor_points: 100
    trunk_dim: 1
    domain_end: 1.0
    k: 1.0
    train_size: 10000
    test_size: 100000
    iterations: 100000
    default_variant: unstacked_bias
    convergence_iterations: 500000
    convergence_test_size: 1000000
    sweeps:
      sensor_points: [10, 20, 50, 100, 200]
      domain_end: [1.0, 2.0, 3.0, 4.0]
      length_scale: [0.1, 0.2, 0.5, 1.0]
      k: [0.5, 1.0, 2.0]
      width: [20, 40, 100]
      train_size: [1000, 5000, 10000]
      chebyshev_degree: [5, 10, 20]

  diffusion_reaction:
    equation: "s_t = D*s_xx + k*s^2 + u(x)"
    sensor_points: 100
    trunk_dim: 2
    domain_end: 1.0
    train_functions: 100
    points_per_function: 1000
    test_functions: 1000
    test_points_per_function: 1000
    test_size: 1000000
    iterations: 500000
    default_variant: unstacked_bias
    diffusion: 0.01
    reaction: 0.01
    space_points: 100
    time_points: 100
    branch_depth: 2
    trunk_depth: 3
    width: 100
    latent_dim: 100
    sweeps:
      train_functions: [50, 100, 200, 400]
      points_per_function: [10, 100, 1000, 10000]

inference:
  batch_size: 8192
  ood_query_points: 100
  save_inputs: true

smoke_test:
  project:
    paper_scale: false
  function_space:
    grf_grid_size: 32
    generation_chunk_size: 16
  training_defaults:
    batch_size: 16
    evaluation_batch_size: 32
    print_every: 1
    evaluate_every: 1
  experiments:
    antiderivative:
      sensor_points: 16
      train_size: 32
      test_size: 24
      iterations: 2
    nonlinear_ode:
      sensor_points: 16
      train_size: 24
      test_size: 16
      iterations: 2
    pendulum:
      sensor_points: 16
      train_size: 24
      test_size: 16
      iterations: 2
    diffusion_reaction:
      sensor_points: 16
      train_functions: 4
      points_per_function: 8
      test_functions: 2
      test_points_per_function: 8
      test_size: 16
      space_points: 12
      time_points: 12
      iterations: 2