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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
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