Application of polynomial chaos expansion in one-dimensional inverse transport problems

Recently, the DREAM method was shown to be a robust approach for solving and quantifying uncertainty in inverse transport problems. DREAM, however, requires thousands of forward transport computations, making it impractical for all but simple ray-tracing transport models. This work shows that the PCE method can be used to form computationally inexpensive surrogate models of a measured quantity. For an inverse problem with one unknown parameter, the PCE expansion reduced the number of forward calculations required by the DREAM method from 12,436 to 32. The reduction in transport calculations obtained by this application of PCE in DREAM to a simple problem with unscattered gamma-ray measurements provides little realworld benefit because ray-tracing calculations require only a fraction of a second. It does, however, provide proof-ofprinciple for the method's capabilities. We intend to next apply the PCE/DREAM technique to models that require more sophistical transport solvers, such as discrete ordinates or Monte Carlo methods. For these problems, the PCE method can provide a significant run-time reduction.