KAHIBARO
39.3. Independent Simulations
Table of Contents
Different seeds
When you repeat a Monte Carlo simulation in GATE, you usually want each run to produce a different random history, but with the same physics, geometry, and source definitions. This is what makes independent simulations useful for estimating uncertainties, performing parameter scans, or running jobs in parallel on a cluster.
GATE uses Geant4 random number engines, which are driven by integer seeds. If two simulations are started with the same random seed and the same configuration, they will produce identical event histories and thus identical statistical results. If you change only the seed and keep everything else fixed, you obtain a different realization of the same experiment.
In GATE, same configuration + same random seed = bitwise identical simulation outcome.
Different seeds create statistically different but physically equivalent realizations of the same setup.
For independent simulations you must ensure two things. First, each run that contributes to the same statistical ensemble must use a unique seed or set of seeds. Second, these seeds must not overlap in a way that causes correlations between runs. In simple terms for an absolute beginner, do not just rerun a script that reuses the default seed, and do not manually reset the seed inside the same run.
A common practical approach is to define a base seed and then derive per run seeds from it using simple arithmetic on job indices or run numbers, for example a seed equal to a base value plus the job ID. For batch jobs on HPC systems, job arrays or environment variables are usually available and can be used to build unique integer seeds for each submitted task. The same concept applies if you launch several runs from a Python loop, where you can pass the loop index into the simulation as a seed.
What matters for reproducibility is that you record the seeds you used. If a particular run shows an interesting or suspicious result, you can repeat that specific simulation exactly by rerunning with the same configuration and the same seed values. Good habits include writing seeds into log files, output metadata, or the directory names of each run, so that you can trace any dataset back to its originating configuration and random initialization.
Statistical independence
Independent simulations are useful only if they are statistically independent. In this context, statistical independence means that random numbers drawn in one simulation are not correlated with those in another, so the results of one run do not influence or predict the results of another. When you later combine results from several runs, you can then safely apply standard statistical formulas that assume independence.
In practice, independence is approximated through the use of high quality pseudo random number generators and carefully chosen seeds. If you choose distinct seeds that are sufficiently separated in the state space of the random engine, the corresponding sequences should behave as independent to a very good approximation. From a user perspective, you aim for seeds that do not overlap in random number streams and do not repeat any part of another simulation’s sequence.
When you split a large simulation into many smaller independent runs, for example on multiple cores, your combined results should follow the expected Monte Carlo convergence. The mean of a quantity such as dose or count rate should approach the true value, and its statistical uncertainty should approximately scale as $1/\sqrt{N}$, where $N$ is the total number of events over all runs. If you observe deviations from this expected behavior that are not explained by physics or geometry, it can be a sign that your runs are not statistically independent, often due to seed misuse.
For multiple GATE runs that you later combine, always ensure:
- Each run uses a unique seed sequence.
- No two runs reuse the same seed values.
- You never reset seeds during a run in a way that repeats earlier random states.
Only then can you safely treat runs as statistically independent and combine their results using standard error formulas.
From a workflow standpoint, you can think of each run as one experimental repetition. Independent runs allow you to estimate not only the average value of quantities of interest, but also their variability due to finite sampling. For example, you can compute the mean and standard deviation of a detector count rate across several runs, or you can combine dose images voxel by voxel, and then evaluate the uncertainty in each voxel.
To support this, it is vital to keep track of which outputs belong to which seeds and which configuration. Simple strategies like consistent directory naming, run index labels in output files, and a small text file that stores seed values and configuration settings can make your independent simulations truly useful for robust, reproducible medical physics studies.
Views: 7