Fit equations in particular shape

[kmegahed]

Hello everyone,

I want to fit my equation to be as a sum of two equations, each equation is function of particular variables, for example
my function = f(x,y) + g(z,u)
My function is sum of two functions, the first function is function in x, y variables, and the second one is function in z,u variables

also other shape like 1/f(x,y) + 1/g(z,u)

[MilesCranmer]

There's an example here: https://astroautomata.com/PySR/examples/#9-custom-objectives

Also see:

• Fixing functional form #291
• Make PySR look for strictly factorised functions #465
• A priori functional form with repeated functions #528
• Specific functional solutions #557

Other potentially related:

• Symbolic integrals with SymbolicRegression.jl #401

[kmegahed]

Hi Miles, thank you for your swift reply and thorough answers, I read the later discussions, especially #557 and applied it in the following function y = f(x4,x5) * g(x3,x4) + h(x1,x2) where f = 3 * np.sin(X[:, 3] + X[:, 4]), g = np.sin(X[:, 2]*2.0)+X[:, 3] ** 2, h = 2.0*X[:, 0]*X[:, 1] ** 2 + X[:, 1] But it fail to search for the right function Any further recommendations would be very appreciated! import numpy as np from pysr import PySRRegressor # Create a synthetic dataset np.random.seed(0) X = np.random.rand(100, 5) * 5.0 # 100 samples, 6 features y = (3 * np.sin(X[:, 3] + X[:, 4])) * (np.sin(X[:, 2]*2.0)+X[:, 3] ** 2) + (2.0*X[:, 0]*X[:, 1] ** 2 + X[:, 1] )+ np.random.randn(100) * 0.01 # Target variable # y = f(x4,x5) * g(x3,x4) + h(x1,x2) # where f = 3 * np.sin(X[:, 3] + X[:, 4]), g = np.sin(X[:, 2]*2.0)+X[:, 3] ** 2, h = 2.0*X[:, 0]*X[:, 1] ** 2 + X[:, 1] # Define the custom objective function objective = """ function contains(t, features) if t.degree == 0 return !t.constant && t.feature in features elseif t.degree == 1 return contains(t.l, features) else return contains(t.l, features) || contains(t.r, features) end end function my_custom_objective(tree, dataset::Dataset{T,L}, options) where {T,L} tree.degree != 2 && return L(Inf) left = tree.l right = tree.r left.degree != 2 && return L(Inf) bot_left = left.l bot_right = left.r bot_left_pred, flag = eval_tree_array(bot_left, dataset.X, options) !flag && return L(Inf) bot_right_pred, flag = eval_tree_array(bot_right, dataset.X, options) !flag && return L(Inf) right_pred, flag = eval_tree_array(right, dataset.X, options) !flag && return L(Inf) prediction = bot_left_pred .* bot_right_pred .+ right_pred right_violating = Int(contains(right, (5,3,4))) + Int(!contains(right, (1,2))) # h(x1,x2) and apply penalty if contains x3,x4 or x5 bot_left_violating = Int(contains(bot_left, (1,2))) + Int(!contains(bot_left, (4,5))) # f(x4,x5) and apply penalty if contains others say x1 or x2 bot_right_violating = Int(contains(bot_right, (1,2,5))) + Int(!contains(bot_right, (3,4))) # g(x3,x4) and apply penalty if contains others say x1 or x2 or x5 regularization = L(100) * (right_violating .+ bot_left_violating .+ bot_right_violating) diffs = (prediction .- dataset.y) .^ 2 pp = (sum(diffs) / length(dataset.y))^ 0.5 return pp + regularization end my_custom_objective """ # Initialize and train the PySRRegressor model = PySRRegressor( procs=16, maxsize=30, maxdepth=7, populations=48, population_size=65, niterations=500, ncyclesperiteration=500, binary_operators=["+", "*", "-", "/", "^"], unary_operators=["sin"], parsimony=0.05, adaptive_parsimony_scaling=1000, precision=64, loss_function=objective ) # Train the model model.fit(X, y) # Predict on the test set y_pred = model.predict(X) print(model.equations_)

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On Mon, Jun 3, 2024 at 1:48 AM Miles Cranmer ***@***.***> wrote: See - #291 <#291> - #465 <#465> - #528 <#528> - #557 <#557> Other potentially related: - #401 <#401> — Reply to this email directly, view it on GitHub <#637 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ATB6Q46DVJLED5F3RWCLGB3ZFOONNAVCNFSM6AAAAABIVLQKOKVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4TMNBRGI3DC> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[MilesCranmer]

Can you edit your comment to use the ` backquotes? Otherwise it is hard to see what is code or not. See https://docs.github.com/en/get-started/writing-on-github/getting-started-with-writing-and-formatting-on-github/basic-writing-and-formatting-syntax#GitHub-flavored-markdown