Presented are rapid and robust techniques for estimating the uncertainty in product attributes (performance, cost, etc.) during the multi-disciplinary design and analysis phase of the product life-cycle. The techniques leverage the capabilities of a preexisting constraint management system that may be used to calculate performance and cost metrics of an engineering system as a function of the design structure and operational scenarios. The techniques are particularly useful when the constraint management system is used to automate the reverse computation required when the analyst specifies cost, schedule, or performance targets using approaches such as cost as independent variable. Disclosed techniques may also be applied to constraint management systems that include compound-valued variables.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of estimating uncertainty for a data dependent constraint network, the method comprising: accessing an electronically stored bipartite graph representing the data dependent constraint network, the bipartite graph comprising variable nodes representing a plurality of variables, compound-valued variable nodes representing a plurality of compound-valued variables, relation nodes representing a plurality of relations, and arcs interconnecting at least some of the variable nodes, the compound-valued variable nodes, and the relation nodes, the plurality of variables comprising a set S of variables that have uncorrelated errors, a set I of variables for which a user may specify values, and a set V of variables for which a user may specify uncertainties, wherein at least one of the following occurs: the set S is not equal to the set V, the set V is not equal to the set I, or the set S is not equal to the set I; obtaining a user selection electronically, the user selection comprising at least one of: values for variables in the set I or uncertainties for variables in the set V; propagating electronically at least one gradient related to the user selection through the data dependent constraint network configured with a flow state in which nodes for variables in S have only outgoing arcs; recording electronically variables that are touched by the propagating electronically at least one gradient related to the user selection; propagating electronically, through the data dependent constraint network configured in a flow state in which nodes for variables in the set S have only outgoing arcs, at least one uncertainty for the variables that are touched by the propagating electronically at least one gradient related to the user selection; and outputting electronically at least one outputted uncertainty for at least one variable not in the set V, whereby setting an uncertainty for the at least one variable not in the set V to the at least one outputted uncertainty for the at least one variable not in the set V causes the user selection to be consistent for the data dependent constraint network. 2. The method of claim 1, wherein the user selection comprises values for variables in the set I, the method further comprising: propagating electronically the user selection comprising the values for variables in the set I through the data dependent constraint network configured with a flow state in which nodes for variables in the set I have only outgoing arcs; and recording electronically variables that are touched by the propagating electronically the user selection; wherein the propagating electronically at least one gradient related to the user selection comprises propagating electronically at least one gradient for the variables that are touched by the propagating electronically the user selection. 3. The method of claim 1, wherein the compound-valued variable nodes representing a plurality of compound-valued variables comprise compound-valued variable nodes representing a plurality of compound structures of scalar data types. 4. The method of claim 1, wherein the compound-valued variable nodes representing a plurality of compound-valued variables comprise compound-valued variable nodes representing a plurality of compound structures of compound structures. 5. The method of claim 1, wherein the propagating electronically at least one gradient related to the user selection through the data dependent constraint network comprises determining a derivative of at least one operator comprising a relation represented by a relation node. 6. The method of claim 1, wherein the bipartite graph comprises arcs between relation nodes and their included variable nodes, and dependent variable nodes of the bipartite graph have at most one incoming arc per world. 7. The method of claim 1, further comprising conducting a trade study based at least in part on the user selection and on the uncertainty for the at least one variable not in the set V. 8. The method of claim 1, wherein the user selection comprises an uncertainty value for at least one of cost, performance, or a risk attribute, and wherein the at least one of cost, performance, or a risk attribute is represented by a variable in the set V. 9. The method of claim 1, further comprising outputting electronically at least one outputted uncertainty range for at least one variable in the set V, whereby any uncertainty value for the at least one variable in the set V selected from within the outputted uncertainty range for the at least one variable in the set V is propagatable consistently for the data dependent constraint network. 10. The method of claim 1, wherein the user selection comprises both values for variables in the set I and uncertainties for variables in the set V. 11. A computer-implemented system for estimating uncertainty for a data dependent constraint network, the system comprising: an electronically stored bipartite graph representing the data dependent constraint network, the bipartite graph comprising variable nodes representing a plurality of variables, compound-valued variable nodes representing a plurality of compound-valued variables, relation nodes representing a plurality of relations, and arcs interconnecting at least some of the variable nodes, the compound-valued variable nodes, and the relation nodes, the plurality of variables comprising a set S of variables that have uncorrelated errors, a set I of variables for which a user may specify values, and a set V of variables for which a user may specify uncertainties, wherein at least one of the following occurs: the set S is not equal to the set V, the set V is not equal to the set I, or the set S is not equal to the set I; an electronic user interface configured to obtain a user selection, the user selection comprising at least one of: values for variables in the set I or uncertainties for variables in the set V; a gradient propagator configured to propagate electronically at least one gradient related to the user selection through the data dependent constraint network configured with a flow state in which nodes for the variables in the set S have only outgoing arcs; an electronic memory configured to store variables that are touched by the propagating electronically at least one gradient related to the user selection; a variance propagator configured to propagate electronically, through the data dependent constraint network configured in a flow state in which nodes for the variables in the set S have only outgoing arcs, at least one uncertainty for the variables that are touched by the propagating electronically at least one gradient related to the user selection; and an electronic display configured to output at least one outputted uncertainty for at least one variable not in the set V, whereby setting an uncertainty for the at least one variable not in the set V to the at least one outputted uncertainty for the at least one variable not in the set V causes the user selection to be consistent for the data dependent constraint network. 12. The system of claim 11, wherein the user selection comprises values for variables in I, the system further comprising: a value propagator configured to propagate electronically the user selection comprising the values for variables in the set I through the data dependent constraint network configured with a flow state in which nodes for the variables in the set I have only outgoing arcs; and an electronic memory configured to store electronically variables that are touched by the propagating electronically the user selection; wherein the gradient propagator is further configured to propagate electronically at least one gradient for the variables that are touched by the propagating electronically the user selection. 13. The system of claim 11, wherein the compound-valued variable nodes representing a plurality of compound-valued variables comprise compound-valued variable nodes representing a plurality of compound structures of scalar data types. 14. The system of claim 11, wherein the compound-valued variable nodes representing a plurality of compound-valued variables comprise compound-valued variable nodes representing a plurality of compound structures of compound structures. 15. The system of claim 11, wherein the gradient propagator is further configured to determine a derivative of at least one operator comprising a relation represented by a relation node. 16. The system of claim 11, wherein the bipartite graph comprises arcs between relation nodes and their included variable nodes, and dependent variable nodes of the bipartite graph have at most one incoming arc per world. 17. The system of claim 11, configured to generate a trade study based at least in part on the user selection and on the uncertainty for the at least one variable not in the set V. 18. The system of claim 11, wherein the user selection comprises an uncertainty value for at least one of cost, performance, or a risk attribute, and wherein the at least one of cost, performance, or a risk attribute is represented by a variable in the set V. 19. The system of claim 11, further configured to output electronically at least one outputted uncertainty range for at least one variable in the set V, whereby any uncertainty value for the at least one variable in the set V selected from within the outputted uncertainty range for the at least one variable in the set V is propagatable consistently for the data dependent constraint network. 20. The system of claim 11, wherein the user selection comprises both values for variables in I and uncertainties for variables in the set V.