Vanquishing the computational cost of passive gamma emission tomography simulations: a physics-aware reduced order modeling approach

TL;DR

A physics-aware reduced order modeling approach that brings the essence of the physics to obtain a real-time high-fidelity solution at all angular views but at a fraction of the computational cost is addressed.

Abstract

Passive Gamma Emission Tomography (PGET) has been developed by the International Atomic Energy Agency as a way to directly image the spatial distribution of individual fuel pins in a spent nuclear fuel assembly and so determine potential diversion. Constructing the analysis and interpretation of PGET measurements rely on the availability of comprehensive datasets. Experimental data are expensive, limited, and so are augmented by Monte Carlo simulations. The main issue concerning Monte Carlo simulations is the high computational cost to simulate the 360 angular views of the tomography. Similar challenges pervade numerical science. To address this challenge, we have developed a physics-aware reduced order modeling approach. It provides a framework to combine a small subset of the 360 angular views with a computationally inexpensive proxy solution, that brings the essence of the physics, to obtain a real-time high-fidelity solution at all angular views, but at a fraction of the computational cost.

Figures (10)

• Figure 1: The figure reports the major steps in our PA-POD method. On top left we represent the actual sinogram for the PWR assembly from the IAEA competition (our ground truth), as high fidelity data, named $\mathbf{S}$ in our formulation. With the orange color we highlight the subset of limited views that construct the database matrix. We present the POD solution space and plot the first three modes $\mathbf{u}_0, \mathbf{u}_1, \mathbf{u}_2$ for the case of $N_s = k = 60$ randomly chosen views. On bottom left, the sinogram $\mathbf{R}$, on the same pin configuration, as obtained by the Real-Time Approximate Forward Model. At the bottom right the PA-POD formulation and resulting sinogram $\tilde{\mathbf{S}}$.
• Figure 2: Here we represent the ground truth (a) together with the error that characterizes the real time model (b) and our PA-POD approximation (c). In the PA-POD case we randomly sample sixty views of the spent fuel, we repeat the sample one hundred times, and for each pixel, we collect the median of the sampled data. (d) The improvement from the Real Time Model to PA-POD is quantified by the area between the blue and orange lines. (d) More precisely, considering a 10% error, PA-POD describes 57% of the total area, while the Real Time Model describes 29% of the area.
• Figure 3: (a) With $k = N_s$, we vary $N_s$ from 30 to 120, with a spacing of 10 units. For each value of $N_s$ we select 100 random uniform sets of views, evaluate the pixel fraction at 10% and report the mean and the standard deviation for each distribution. The method delivers its best performance between 60 and 80 samples. In figure (b) a closer view of the pixel fraction distribution with respect the sample choice. With $N_s = k = 60$ we pick 1000 random uniform sets of views, evaluate the 10% pixel fraction for each set and plot the distribution. We observe that the mean is 0.545 and the standard deviation is 0.017, both the measures are expressed in terms of pixel fraction.
• Figure 4: (a) Logarithmic plot of the singular values spectrum for the IAEA PWR fuel assembly sinogram, and (b) the related information variance. We highlight that it takes respectively 8, 27, and 45 modes to capture 80%, 90% and 95% of the total information variance.
• Figure 5: This picture shows a side by side comparison between the PODI and PA-POD. In PODI we interpolate accurate but scarce data, while with PA-POD we evaluate dense real time approximated data.