I’m currently working through your codebase/paper and trying to understand how the reported learned parameters map back to the governing equations for the Rössler system (typically written as dx/dt=−y−z, dy/dt=x+ay, dz/dt=b+z(x−c)).
When I run the script (e.g., rossler_model.py), the program reports learned dynamics that look like a polynomial decomposition, and I’m unsure how to interpret these coefficients relative to the true Rössler form. Concretely, I obtain:
Learned:
dx/dt = 0.0100·y + 0.0110·z - 0.0101·z²
dy/dt = -0.0100·x + 0.0020·y
dz/dt = -0.0440·x - 0.0290·z + 0.0050·x²
True Rössler system:
dx/dt = -y - z
dy/dt = x + 0.2y
dz/dt = 0.2 + z(x - 5.7)
My confusion is mainly about interpretation:
-
How should the learned parameters relate to the governing equation—are they expected to match the standard coefficients directly, or do they correspond to a rescaled/normalized coordinate system?
-
In the implementation, what exactly do the keys 'linear' and 'quadratic' represent—are they coefficients of a polynomial feature library (e.g., x,y,z,x^2,xy,xz,y^2,yz,z^2) that is then combined into the ODE right-hand side?
-
If so, is there a recommended procedure to convert the learned 'linear' / 'quadratic' coefficients into the canonical Rössler form dx/dt=−y−z, dy/dt=x+ay, dz/dt=b+zx−cz (including recovering the constant term b and the bilinear term zx)?
I tried reconstructing the governing equations directly from the printed coefficients, but the result doesn’t match the true equations—especially the absence of a constant term in dz/dt and the appearance of z² and x² terms instead of the expected zx and −cz.
If possible, could you clarify (1) whether the reported coefficients are in scaled units, (2) how the feature terms are ordered/defined for 'linear' and 'quadratic', and (3) how to map the learned model back to the standard Rössler parameterization? Thank you!
I’m currently working through your codebase/paper and trying to understand how the reported learned parameters map back to the governing equations for the Rössler system (typically written as dx/dt=−y−z, dy/dt=x+ay, dz/dt=b+z(x−c)).
When I run the script (e.g., rossler_model.py), the program reports learned dynamics that look like a polynomial decomposition, and I’m unsure how to interpret these coefficients relative to the true Rössler form. Concretely, I obtain:
Learned:
dx/dt = 0.0100·y + 0.0110·z - 0.0101·z²
dy/dt = -0.0100·x + 0.0020·y
dz/dt = -0.0440·x - 0.0290·z + 0.0050·x²
True Rössler system:
dx/dt = -y - z
dy/dt = x + 0.2y
dz/dt = 0.2 + z(x - 5.7)
My confusion is mainly about interpretation:
How should the learned parameters relate to the governing equation—are they expected to match the standard coefficients directly, or do they correspond to a rescaled/normalized coordinate system?
In the implementation, what exactly do the keys 'linear' and 'quadratic' represent—are they coefficients of a polynomial feature library (e.g., x,y,z,x^2,xy,xz,y^2,yz,z^2) that is then combined into the ODE right-hand side?
If so, is there a recommended procedure to convert the learned 'linear' / 'quadratic' coefficients into the canonical Rössler form dx/dt=−y−z, dy/dt=x+ay, dz/dt=b+zx−cz (including recovering the constant term b and the bilinear term zx)?
I tried reconstructing the governing equations directly from the printed coefficients, but the result doesn’t match the true equations—especially the absence of a constant term in dz/dt and the appearance of z² and x² terms instead of the expected zx and −cz.
If possible, could you clarify (1) whether the reported coefficients are in scaled units, (2) how the feature terms are ordered/defined for 'linear' and 'quadratic', and (3) how to map the learned model back to the standard Rössler parameterization? Thank you!