US 6,473,746 B1 · Method of verifying pretrained neural net mapping for use in safety-critical software

Abstract

A method of verifying pretrained, static, feedforward neural network mapping software using Lipschitz constants for determining bounds on output values and estimation errors is disclosed. By way of example, two cases of interest from the point of view of safety-critical software, like aircraft fuel gauging systems, are discussed. The first case is the simpler case of when neural net mapping software is trained to replace look-up table mapping software. A detailed verification procedure is provided to establish functional equivalence of the neural net and look-up table mapping functions on the entire range of inputs accepted by the look-up table mapping function. The second case is when a neural net is trained to estimate the quantity of interest form the process (such as fuel mass, for example) from redundant and noisy sensor signals. Given upper and lower bounds on sensor noises and on modeling inaccuracies, it is demonstrated how to verify the performance of such a neural network estimator (a “black box”) when compared to a true value of the estimated quantity.

Claims31

Dependent claims

A method of verifying the behavior of pretrained, static, feedforward neural network mapping software having a neural net mapping function ƒ(x) that is intended to replace look up table mapping software having a look up table mapping function φ(x), said method comprising executing the following steps on the neural network mapping software and look up table mapping software in a digital computer:

establishing a multi-axis rectangular domain including upper and lower limits of each axis to bound all input vectors x of both said look up table mapping function φ(X) and said neural net mapping function ƒ(x);
determining a set of test points within the rectangular domain based on said upper and lower limits of each axis;
determining Lipschitz constant Kƒ for said neural net mapping function ƒ(x);
determining upper and lower value bounds of said neural net mapping function ƒ(x) for said domain based on a function of said set of test points and said Lipschitz constant Kƒ;
and
verifying the behavior of the neural network mapping software based on the determination of said upper and lower value bounds.

3 more elements

A method of verifying the behavior of pretrained, static, feedforward neural network mapping software having a neural network mapping function ƒ(ψ(x)+ζ), where ψ(x) is a predetermined mapping of n dimensional state vectors x of a process into m dimensional measurement vectors z=ψ(x), ζ is representative of a noise component of the process, and ƒ(ψ(x)+ζ) is an estimate of the desired output parameter y(est) of the process, said method comprising the steps of:

providing model mapping software including a predetermined mapping function φ(x) for mapping said n dimensional state vectors x directly into a true value y(true) of said desired output parameter;
executing the following steps on the neural network mapping software and model mapping software in a digital computer:
establishing a multi-axis rectangular domain including upper and lower limits of each axis to bound all state vectors x of both said predetermined mapping functions φ(x) and ψ(x);
determining a set of test points within the rectangular domain based on said upper and lower limits of each axis;
determining Lipschitz constant Kƒ for neural net mapping function ƒ(ψ(x));
determining an upper bound ζup and a lower bound ζlo of the noise component ζ;
determining upper and lower value bounds of said neural net mapping function ƒ(ψ(x)+ζ) for said domain based on a function of said set of test points, said Lipschitz constant Kƒ and said upper bound ζup and lower bound ζlo and
verifying the behavior of the neural network mapping software based on the determination of said upper and lower value bounds.

5 more elements

Dependencies are inferred from the claim text.

Method of verifying pretrained neural net mapping for use in safety-critical software

Life of this patent

Method of verifying pretrained neural net mapping for use in safety-critical software

Life of this patent

Abstract

Claims31