Benchmarking
Uncertainty Quantification of Thermal Expansion Modeling
When designing products that operate at varying or extreme temperatures, it is vital for engineers to have accurate knowledge of a specific structural object’s thermal expansion, as a function of the object material’s thermal expansion coefficient and deployment temperature. This example application calculates the thermal expansion of a rod from its initial length and temperature after controlled exposure to heat. Following convention, the input length and temperature parameters are modeled as Student’s-t random variables. Traditionally, calculating the thermal expansion, affected by uncertainty in a material’s measured properties, would typically involve implementing Monte Carlo simulations.
When running on the Signaloid Cloud Compute Engine (SCCE), the kernels implementing the calculation of thermal expansion can replace the usual approach of sampling from the distributions of input parameter values followed by application of the kernel to these sample inputs, replacing it with a direct computation on representations of the probability distributions of the inputs. Thus, in a single computation, the code kernel running on SCCE can compute the same type of output distribution that would take a Monte Carlo simulation millions of iterations.
The thermal expansion model uncertainty quantification kernel running on the Signaloid Cloud Compute Engine with a single-threaded Signaloid C0Pro-XL core achieves runtimes 29x faster than an optimized C-language Monte-Carlo-based implementation of the same kernel running on an Amazon EC2 R7iz instance. With 95% confidence, a 17M-iteration Monte Carlo implementation will have the same accuracy as the Signaloid UxHw®-based version, yet the Signaloid UxHw-based version gives the speedup quoted above; if requiring higher confidence in the accuracy of the Monte Carlo compared to UxHw, the speedups of UxHw are even greater.
The underlying distribution representations are not literal histograms: The distribution plots use an adaptive algorithm to render a mutually-consistent and human-interpretable depiction for both the Signaloid distribution representations and the Monte Carlo samples, to permit qualitative comparison.
Plot of output distribution when running on Signaloid C0Pro-XL core that provides the 29.7x speedup.
Plot of the output of an 17.8M-iteration Monte Carlo for this use case. This Monte Carlo iteration count provides the same or better Wasserstein distance to ground truth (20M-iteration) Monte Carlo as execution on a Signaloid C0Pro-XL core (which is 29.7x faster).
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.