Abstract: A method is provided for using a hierarchical polynomial model for physics simulation. The method includes obtaining coupled equations for a physics simulation. The coupled equations have variables and boundary conditions that constrain the variables. The method also includes generating meshes corresponding to the coupled equations. The method iteratively solves for the boundary conditions that depend on the variables within the meshes to convergence to improve numerical stability of the physics simulation, including: (i) solving for each variable in a first mesh, while holding the other meshes to a weak convergence, to obtain a first solution; (ii) applying the first solution to resolve a second mesh, to obtain a second solution; and (iii) generating a hierarchical polynomial based on the second solution. The hierarchical polynomial is a functional form of a pre-determined physics equation. The method also (iv) computes new boundary conditions for resolving the meshes, using the hierarchical polynomial.

Abstract: A method inspects weld quality in-situ. The method obtains a plurality of sequenced images of an in-progress welding process and generates a multi-dimensional data input based on the plurality of sequenced images and/or one or more weld process control parameters. The parameters may include: (i) shield gas flow rate, temperature, and pressure; (ii) voltage, amperage, wire feed rate and temperature (if applicable); (iii) part preheat/inter-pass temperature; and (iv) part and weld torch relative velocity). The method generates defect probability and analytics information by applying one or more computer vision techniques on the multi-dimensional data input. The analytics information includes predictive insights on quality features of the in-progress welding process. The method then generates a 3-D visualization of one or more as-welded regions, based on the analytics information, and the plurality of sequenced images.