1import numpy as np
 2
 3META = {
 4    "name": "exact_gradient_harmonic_field",
 5    "domain": "pde",
 6    "description": "Unit-square harmonic PDE surrogate: supervised samples of the curl-free gradient field (2x,-2y) from the harmonic potential x^2-y^2; the exact-gradient backbone enforces curl-free structure by construction."
 7}
 8
 9def get_dataset(seed, n_train, n_test):
10    rng = np.random.default_rng(int(seed))
11    xtr = rng.uniform(-1.0, 1.0, size=(int(n_train), 2)).astype(np.float32)
12    xte = rng.uniform(-1.0, 1.0, size=(int(n_test), 2)).astype(np.float32)
13    def field(x):
14        return np.stack((2.0 * x[:, 0], -2.0 * x[:, 1]), axis=1).astype(np.float32)
15    return {"xtr": xtr, "ytr": field(xtr), "xte": xte, "yte": field(xte),
16            "task": "regression", "metric": "mse", "input_shape": (2,), "out_dim": 2}