Evaluating MPI Efficiency

Overview

This example demonstrates the efficiency of Message Passing Interface (MPI) parallelization in MonolixSuite for a large-scale quantitative systems pharmacology (QSP) job.
The benchmark used here is a Neuro-Dynamic QSP model with 4056 subjects and 20 iterations of SAEM.

The results illustrate how distributing the workload across multiple compute nodes significantly reduces execution time compared to single-node symmetric multiprocessing (SMP) execution.

Benchmark Configuration

Parameter	Description
Model	Neuro-Dynamic QSP
SAEM Iterations	20
Nodes	1 – 20
Cores per node	96
Parallel modes tested	SMP (1 node) and MPI (1 – 20 nodes)

Results Summary

Parallel Mode	# of Nodes	# of Cores	Wallclock Time (mins)	Speed-up (fold)
SMP	1	96	55	1.0
MPI	1	96	43	1.3
MPI	2	192	25	2.2
MPI	3	288	18	3.0
MPI	4	384	13.8	4.0
MPI	5	480	12	4.6
MPI	10	960	8	6.9
MPI	20	1920	5.8	9.5

Performance Analysis

Speed-Up Behavior

The performance improves nearly linearly up to around 5 nodes, achieving a 4.6× speed-up over the single-node SMP run.
Beyond 5 nodes, speed-up continues to increase, reaching 9.5× with 20 nodes (1920 cores).
The curve indicates diminishing returns at higher node counts, typical for communication-bound workloads.

The following plot shows the scaling behavior:

2866934b-cb99-495d-8627-e63d0de1f15d-20251106-155011.png

The trend reflects a strong scaling regime where computational work is distributed effectively but inter-node communication gradually becomes the dominant factor.

Efficiency Calculation

Parallel efficiency is defined as:

# of Nodes	Speed-up	Efficiency (%)
1	1.3	130 %*
2	2.2	110 %*
3	3.0	100 %
4	4.0	100 %
5	4.6	92 %
10	6.9	69 %
20	9.5	48 %

* Values > 100 % at small scale reflect measurement noise and cache effects rather than true superlinear scaling.

Interpretation

Up to 4 nodes, MPI scales almost perfectly (≈ 100 % efficiency).
Between 5 – 10 nodes, efficiency drops moderately due to increased communication overhead.
At 20 nodes, performance remains strong but efficiency decreases to ~50 %, which is typical for distributed workloads with high synchronization needs.

Best Practices for MPI Execution

Use sufficient problem size:
The computational load per core should be high enough to offset communication costs.
Monitor scaling efficiency:
Efficiency <70% typically signals that further node scaling is not cost-effective.

Conclusion

MPI parallelization in MonolixSuite offers near-linear speed-up up to 4–5 nodes and substantial performance gains up to 20 nodes.
For large QSP simulations, this enables reducing multi-hour runs to just a few minutes, making high-throughput parameter estimation and simulation studies practical on modern HPC clusters.