Benchmarking
Uncertainty Propagation Through Arithmetic and Trigonometric Functions and OpenTURNS
Performing uncertainty propagation through arithmetic expressions involving trigonometric functions is a challenging but necessary task during safety analyses in nuclear energy facility design. Monte Carlo methods, traditionally the go-to method for these analyses, struggle to maintain the required speed for iterative design. This example application demonstrates uncertainty propagation through mathematical models derived from OpenTURNS [1] but implemented using Signaloid’s UxHw technology. (Signaloid has also created a port of the OpenTURNS Python package, accelerated by our UxHw technology.)
Figure 1. Monte Carlo UQ implementation
When running on the Signaloid Cloud Compute Engine (SCCE), the implementation replaces the usual approach of sampling followed by sample evaluation with a direct computation on a representation of the probability distribution. Thus, in a single computation, the implementation running on SCCE computes the same output distribution that traditional Monte Carlo simulations require hundreds of thousands of iterations to achieve.
Figure 2. Signaloid UQ implementation
An uncertainty propagation through a three-variable trigonometric kernel, taken from OpenTURNS, and running on a single-threaded Signaloid C0Pro-Jupiter-XS core, achieves runtimes 58× faster than an optimized C-language Monte-Carlo-based implementation (i.e., the industry standard and status quo) of the same kernel running on an Amazon EC2 R7iz instance. With 95% confidence, an 810k-iteration Monte Carlo implementation matches the accuracy of the Signaloid UxHw-based version; if higher confidence is required for the Monte Carlo results, the speedup of the UxHw approach becomes even more pronounced.
Key Performance Indicator
Signaloid Platform Solution
Competing Solution
Signaloid Benefit
Speed for the same uncertainty quantification accuracy.
Run existing non-Monte-Carlo code and use either the Signaloid Compute Engine's automated ingestion of distribution information, or use the Signaloid UxHw API to set program variables as probability distributions.
Run existing Monte Carlo code, or, starting from non-Monte-Carlo code, modify code to implement Monte Carlo sampling, iteration, and aggregation of the results from the Monte Carlo iterations of the computation.
58x faster execution time than 810k-iteration Monte Carlo, while achieving same fidelity of full distribution result.
Plot of output distribution when running on a Signaloid C0Pro-Jupiter-XS core that provides the 58× speedup.
Plot of the output of an 810k-iteration Monte Carlo for this use case. Signaloid C0Pro-Jupiter-XS core is 58× faster than this Monte Carlo, while achieving the same or better Wasserstein distance to the ground-truth (20M-iteration) Monte Carlo.
Plot of ground truth (20M-iteration) Monte Carlo.
Benchmarking Methodology
Monte Carlo simulations work by statistical sampling and therefore each multi-iteration Monte Carlo run will result in a slightly different output distribution. By contrast, Signaloid's platform is deterministic and each run produces the same distribution for a given Signaloid C0 core type.
The performance improvements are calculated by comparing Signaloid's platform with a Monte Carlo simulation of a similar quality of distribution. First, we run a large Monte Carlo simulation (about 50M iterations) on an AWS r7iz high-performance AWS instance: We use this distribution result as a baseline or ground truth reference of distribution quality. Then we calculate the performance of Signaloid's technology, and compare it with the performance of a Monte Carlo iteration count where the output distribution's Wasserstein distance (to the output distribution of the ground truth reference) is as accurate as the Signaloid-core-executed algorithm's output distribution, with 95% confidence level.
Performance data based on Fall 2025 release of Signaloid's technology.