| ---
|
| license: mit
|
| pretty_name: DeepONet linear ODE data
|
| task_categories:
|
| - tabular-regression
|
| tags:
|
| - deeponet
|
| - operator-learning
|
| - ode
|
| - physics
|
| - synthetic
|
| size_categories:
|
| - n<10K
|
| configs:
|
| - config_name: default
|
| data_files:
|
| - split: train
|
| path: train.parquet
|
| - split: test
|
| path: test.parquet
|
| ---
|
|
|
| # DeepONet linear ODE data
|
|
|
| Synthetic training data for learning the solution operator of the linear
|
| first-order ODE
|
|
|
| ```
|
| u'(t) = -k · u(t) + f(t), u(0) = 0, t ∈ [0, 1]
|
| ```
|
|
|
| with a DeepONet. The input is a pair (f, k): `f` is a random smooth forcing
|
| function and `k ∈ [0.1, 2]` is a damping constant. The target is the exact
|
| solution `u(t) = ∫₀ᵗ e^{-k (t-s)} f(s) ds`.
|
|
|
| Code that generates this dataset and trains a DeepONet on it:
|
| **https://github.com/tha2002-tech/deeponet-ode-demo**
|
|
|
| ## Splits
|
|
|
| | split | rows |
|
| |-------|------|
|
| | train | 2000 |
|
| | test | 500 |
|
|
|
| ## Schema
|
|
|
| | column | type | length | meaning |
|
| |-------------|-----------------|--------|----------------------------------------------|
|
| | `f_sensors` | list<float32> | 100 | f evaluated at 100 equally spaced sensors on [0, 1] |
|
| | `k` | float32 | 1 | damping constant, uniform in [0.1, 2.0] |
|
| | `t` | list<float32> | 100 | query times (same 100-point grid as the sensors) |
|
| | `u` | list<float32> | 100 | exact solution at `t` |
|
|
|
| ## Generation
|
|
|
| - `f` is sampled from a zero-mean Gaussian random field on [0, 1] with an RBF
|
| kernel of length scale 0.2 and unit variance, on a 991-point grid.
|
| - `u` is computed by the variation-of-constants integral with the cumulative
|
| trapezoid rule on that grid (error about 1e-6), then subsampled to the
|
| 100-point sensor grid.
|
| - Seed 0 for train, seed 0+1 for test.
|
| - Produced by `scripts/generate_data.py` at commit `bf1ebab27e006e973715aa343437793bc2e78cf8` of the
|
| repository above. `metadata.json` in this repo records all parameters.
|
| - Reproducibility: the same seed regenerates these files byte-for-byte on the
|
| same numpy/LAPACK build (eigenvector signs are canonicalized, so other builds
|
| should agree to floating-point rounding); if not, the regenerated data is
|
| equal in distribution. `metadata.json` records the numpy version and platform
|
| used.
|
|
|
| ## Usage
|
|
|
| ```python
|
| from datasets import load_dataset
|
| import numpy as np
|
|
|
| ds = load_dataset("tha2002-tech/deeponet-ode-data")
|
| f = np.array(ds["train"]["f_sensors"], dtype=np.float32) # (N, 100)
|
| k = np.array(ds["train"]["k"], dtype=np.float32) # (N,)
|
| u = np.array(ds["train"]["u"], dtype=np.float32) # (N, 100)
|
| ```
|
|
|
| ## Reference
|
|
|
| Lu, L., Jin, P., Pang, G., Zhang, Z., Karniadakis, G. E. (2021). Learning
|
| nonlinear operators via DeepONet based on the universal approximation theorem
|
| of operators. *Nature Machine Intelligence* 3, 218–229.
|
|
|
