4. Evaluation Procedure

Numerically Solving the ODE System with Learned Parameters - Evaluation Procedure

What is the Evaluation Procedure

  We seek a system of ODEs that accurately models the simulated system. What we have done so far for equation learning is

1. Trained BINNs on the data
2. Estimated the learned parameters (trained neural networks) with equations

  The learned parameter networks are only an approximation of the parameter function that would provide a solution to the ODE system for the approximated solutions. And the inferred equations are even further approximations of these learned parameter networks.

  Numerically solving the system of ODEs and comparing these approximate solutions with the observed data is the only way to see for certain if the learned equations provide solutions that accurately model our system. Keep in mind that the data we are dealing with is stochastic in nature. Therefore, just because the observed data does not perfectly align with the solutions does not necessarily mean that they are "wrong" are "poor".

• Numerical Integration

• Parameter Networks vs. Parameter Learned Equations

Plot Example

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