import numpy as np
META = {"name":"poisson_manufactured", "domain":"pde", "description":"2D Dirichlet Poisson manufactured-solution regression track"}
def get_dataset(seed, n_train, n_test):
    rng=np.random.default_rng(seed)
    def pts(n): return rng.uniform(0.015,0.985,size=(n,2)).astype(np.float32)
    def sol(x): return (np.sin(np.pi*x[:,0])*np.sin(np.pi*x[:,1])).astype(np.float32)[:,None]
    xtr,xte=pts(n_train),pts(n_test)
    return {"xtr":xtr,"ytr":sol(xtr),"xte":xte,"yte":sol(xte),"task":"regression","metric":"mse","out_dim":1}