def test_make(self): ## Models build md_cantilever_beam = models.make_cantilever_beam() md_ishigami = models.make_ishigami() md_linear_normal = models.make_linear_normal() md_plane_laminate = models.make_composite_plate_tension([0]) md_plate_buckling = models.make_plate_buckle() md_poly = models.make_poly() md_test = models.make_test() md_trajectory_linear = models.make_trajectory_linear() ## Models evaluate df_cantilever = md_cantilever_beam >> gr.ev_nominal(df_det="nom") df_ishigami = md_ishigami >> gr.ev_nominal(df_det="nom") df_ln = md_linear_normal >> gr.ev_nominal(df_det="nom") df_plane = md_plane_laminate >> gr.ev_nominal(df_det="nom") df_plate = md_plate_buckling >> gr.ev_nominal(df_det="nom") df_poly = md_poly >> gr.ev_nominal(df_det="nom") df_test = md_test >> gr.ev_nominal(df_det="nom") df_traj = md_trajectory_linear >> gr.ev_nominal(df_det="nom")
def test_nls(self): ## Ground-truth model c_true = 2 a_true = 1 md_true = (gr.Model() >> gr.cp_function( fun=lambda x: a_true * np.exp(x[0] * c_true) + x[1], var=["x", "epsilon"], out=["y"], ) >> gr.cp_marginals(epsilon={ "dist": "norm", "loc": 0, "scale": 0.5 }) >> gr.cp_copula_independence()) df_data = md_true >> gr.ev_monte_carlo( n=5, seed=101, df_det=gr.df_make(x=[0, 1, 2, 3, 4])) ## Model to fit md_param = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] * np.exp(x[0] * x[1]), var=["x", "c", "a"], out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0])) ## Fit the model md_fit = df_data >> gr.ft_nls( md=md_param, verbose=False, uq_method="linpool", ) ## Unidentifiable model throws warning # ------------------------- md_unidet = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] / x[3] * np.exp(x[0] * x[1]), var=["x", "c", "a", "z"], out=["y"], ) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0], z=[0, 1])) with self.assertWarns(RuntimeWarning): gr.fit_nls( df_data, md=md_unidet, uq_method="linpool", ) ## True parameters in wide confidence region # ------------------------- alpha = 1e-3 self.assertTrue( (md_fit.density.marginals["c"].q(alpha / 2) <= c_true) and (c_true <= md_fit.density.marginals["c"].q(1 - alpha / 2))) self.assertTrue( (md_fit.density.marginals["a"].q(alpha / 2) <= a_true) and (a_true <= md_fit.density.marginals["a"].q(1 - alpha / 2))) ## Model with fixed parameter # ------------------------- md_fixed = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] * np.exp(x[0] * x[1]), var=["x", "c", "a"], out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[1, 1])) md_fit_fixed = df_data >> gr.ft_nls( md=md_fixed, verbose=False, uq_method="linpool") # Test that fixed model can evaluate successfully gr.eval_monte_carlo(md_fit_fixed, n=1, df_det="nom") ## Trajectory model # ------------------------- md_base = models.make_trajectory_linear() md_fit = data.df_trajectory_windowed >> gr.ft_nls( md=md_base, method="SLSQP", tol=1e-3) df_tmp = md_fit >> gr.ev_nominal(df_det="nom")
def test_nls(self): ## Ground-truth model c_true = 2 a_true = 1 md_true = (gr.Model() >> gr.cp_function( fun=lambda x: a_true * np.exp(x[0] * c_true) + x[1], var=["x", "epsilon"], out=["y"], ) >> gr.cp_marginals(epsilon={ "dist": "norm", "loc": 0, "scale": 0.5 }) >> gr.cp_copula_independence()) df_data = md_true >> gr.ev_sample( n=5, seed=101, df_det=gr.df_make(x=[0, 1, 2, 3, 4])) ## Model to fit md_param = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] * np.exp(x[0] * x[1]), var=["x", "c", "a"], out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0])) ## Fit the model md_fit = df_data >> gr.ft_nls( md=md_param, verbose=False, uq_method="linpool", ) ## Unidentifiable model throws warning # ------------------------- md_unidet = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] / x[3] * np.exp(x[0] * x[1]), var=["x", "c", "a", "z"], out=["y"], ) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0], z=[0, 1])) with self.assertWarns(RuntimeWarning): gr.fit_nls( df_data, md=md_unidet, uq_method="linpool", ) ## True parameters in wide confidence region # ------------------------- alpha = 1e-3 self.assertTrue( (md_fit.density.marginals["c"].q(alpha / 2) <= c_true) and (c_true <= md_fit.density.marginals["c"].q(1 - alpha / 2))) self.assertTrue( (md_fit.density.marginals["a"].q(alpha / 2) <= a_true) and (a_true <= md_fit.density.marginals["a"].q(1 - alpha / 2))) ## Model with fixed parameter # ------------------------- md_fixed = (gr.Model() >> gr.cp_function( fun=lambda x: x[2] * np.exp(x[0] * x[1]), var=["x", "c", "a"], out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[1, 1])) md_fit_fixed = df_data >> gr.ft_nls( md=md_fixed, verbose=False, uq_method="linpool") # Test that fixed model can evaluate successfully gr.eval_sample(md_fit_fixed, n=1, df_det="nom") ## Trajectory model # ------------------------- md_base = models.make_trajectory_linear() md_fit = data.df_trajectory_windowed >> gr.ft_nls( md=md_base, method="SLSQP", tol=1e-3) df_tmp = md_fit >> gr.ev_nominal(df_det="nom") ## Select output for fitting # ------------------------- # Split model has inconsistent "true" parameter value md_split = (gr.Model("Split") >> gr.cp_vec_function( fun=lambda df: gr.df_make( f=1 * df.c * df.x, g=2 * df.c * df.x, ), var=["c", "x"], out=["f", "g"], ) >> gr.cp_bounds( x=(-1, +1), c=(-1, +1), )) df_split = (gr.df_make(x=gr.linspace(-1, +1, 100)) >> gr.tf_mutate( f=X.x, g=X.x)) # Fitting both outputs: cannot achieve mse ~= 0 df_both = (df_split >> gr.ft_nls(md_split, out=["f", "g"]) >> gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >> gr.tf_summarize( mse_f=gr.mse(X.f, X.f_t), mse_g=gr.mse(X.g, X.g_t), )) self.assertTrue(df_both.mse_f[0] > 0) self.assertTrue(df_both.mse_g[0] > 0) # Fitting "f" only df_f = (df_split >> gr.ft_nls(md_split, out=["f"]) >> gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >> gr.tf_summarize( mse_f=gr.mse(X.f, X.f_t), mse_g=gr.mse(X.g, X.g_t), )) self.assertTrue(df_f.mse_f[0] < 1e-16) self.assertTrue(df_f.mse_g[0] > 0) # Fitting "g" only df_g = (df_split >> gr.ft_nls(md_split, out=["g"]) >> gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >> gr.tf_summarize( mse_f=gr.mse(X.f, X.f_t), mse_g=gr.mse(X.g, X.g_t), )) self.assertTrue(df_g.mse_f[0] > 0) self.assertTrue(df_g.mse_g[0] < 1e-16)