Idaes
How this might link to other stuff
Dynamics, Surrogate modelling
How to make something more reliable
How to make digital twins that can update based on learned data/live data
How to update the centers/sigmas of a RBON to improve accuracy over just using kmeans
Purpose
To make it possible to do surrogate modelling for dynamics
To help me visualise and understand how RBONs work
Research Questions
How are RBON's implemented in surrogate modelling/pyomo?
Can RBON's be used to model dynamics?
Do they support solving backwards?
Are optimisation tools such as IPOPT a valid way to calculate parameters for a RBON?
Method
Based on the RBON paper (citation needed) a Pyomo model is created.
Sets used to specify dimensions of the input of the higher and lower networks, and the weights.
Weights can be loaded from an input file or by fixing variables.
Fitting can be done in the julia model on training data, and then the model can be run in PYOMO/IDAES.
Findings
Complexity
Complexity is dependent on:
- The number of sensor locations of the function U
- The number of query points in V (these are specified in the vector y)
- The dimesion of the query points in y
- the dimesnion of the input of the function U
As well as
- the number of rbfs in the upper network
- the number of rbfs in the lower network.
The number of centers and sigmas is equal to the total number of rbfs (upper + lower)
The number of RBF weights used in linear regression (main weight layer) is = num_lower_rbf * num_upper_rbf
The number of linear transformation weights for the affine transformation is = num__query_locations
total number of constraints from inputs to rbfs is O( num_sensor_locations num_sensor_dimensions num_upper_rbfs + num_query_dimensions ) total number of constraints from weights to rbfs is roughly O( num_lower_rbf num_upper_rbf num_query_locations) total number of cronstraints from weights to linear layer is rought