Regenerate data from 114fccdc

README.md

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+---
+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 `114fccdc6e9c6950f192a9f63075cf210bbcbcff` of the
+  repository above. `metadata.json` in this repo records all parameters.
+
+## 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.

metadata.json

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+{
+  "seed": 0,
+  "n_train": 2000,
+  "n_test": 500,
+  "n_sensors": 100,
+  "n_query": 100,
+  "length_scale": 0.2,
+  "k_range": [
+    0.1,
+    2.0
+  ],
+  "sensor_grid": [
+    0.0,
+    0.010101010101010102,
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+    0.04040404040404041,
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+    0.5757575757575758,
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+    0.6464646464646465,
+    0.6565656565656566,
+    0.6666666666666667,
+    0.6767676767676768,
+    0.686868686868687,
+    0.696969696969697,
+    0.7070707070707072,
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+    0.7575757575757577,
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+    0.9797979797979799,
+    0.98989898989899,
+    1.0
+  ],
+  "fine_grid_size": 991,
+  "generator": "scripts/generate_data.py",
+  "github": "https://github.com/tha2002-tech/deeponet-ode-demo",
+  "git_commit": "114fccdc6e9c6950f192a9f63075cf210bbcbcff"
+}

test.parquet

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+size 574140

train.parquet

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