Bayesian neural networks for optimization and control
First Claim
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1. A method for determining the optimum operation of a system, comprising the steps of:
- receiving the outputs of the system and the measurable inputs to the system; and
optimizing select ones of the outputs as a function of the inputs by minimizing an objective function J to provide optimal values for select ones of the inputs;
wherein the step of optimizing includes the step of predicting the select ones of the outputs with a plurality of models of the system, each model operable to map the inputs through a representation of the system to provide predicted outputs corresponding to the select ones of the outputs which predicted outputs of each of the plurality of models are combined in accordance with a predetermined combination algorithm to provide a single output corresponding to each of the select ones of the outputs.
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Abstract
An optimization system is provided utilizing a Bayesian neural network calculation of a derivative wherein an output is optimized with respect to an input utilizing a stochastical method that averages over many regression models. This is done such that constraints from first principal models are incorporated in terms of prior art distributions.
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Citations
20 Claims
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1. A method for determining the optimum operation of a system, comprising the steps of:
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receiving the outputs of the system and the measurable inputs to the system; and
optimizing select ones of the outputs as a function of the inputs by minimizing an objective function J to provide optimal values for select ones of the inputs;
wherein the step of optimizing includes the step of predicting the select ones of the outputs with a plurality of models of the system, each model operable to map the inputs through a representation of the system to provide predicted outputs corresponding to the select ones of the outputs which predicted outputs of each of the plurality of models are combined in accordance with a predetermined combination algorithm to provide a single output corresponding to each of the select ones of the outputs. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method for optimizing the parameters of a system having a vector input x(t) and a vector output y(t), comprising the steps of:
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storing a representation of the system in a plurality of models, each model operable to map the inputs through a representation of the system to provide a predicted output, each of the models operable to predict the output of the system for a given input value of x(t), each model operable to map the inputs through a representation of the system to provide a predicted output;
providing predetermined optimization objectives; and
determining a single optimized input vector value {circumflex over (x)}(t) by applying a predetermined optimization algorithm to the plurality of models to achieve a minimum error to the predetermined optimization objective. - View Dependent Claims (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
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Specification