Soft Sensors for Energy Consumption in Topographic Uncertainty Propagation

Eren Edgü
Alan Correa

Chair of Methods for Model-based Development in Computational Engineering

June 1, 2026

Table of Contents

Introduction

Figure 1: Original vs. Noisy DEM

The Impact of DEM Uncertainty

“Overlooking DEM uncertainty may lead to a bias in risk management decisions” [1]

  • Topography governs downhill flow physics.
  • Surface variations alter mathematical predictions [1].

The Solution

  • Use an “ensemble of equiprobable realizations” [1].

Figure 2: DEM for each Iteration

The Impact of DEM Uncertainty

Quantity of Interest: Water depth at the houses coordinates

\(\sigma_{input}\) (m) Mean (m) Std. Dev (m) CV (%)
0.05 0.739 \(\pm 0.050\) 6.78%
0.1 0.756 \(\pm 0.110\) 14.50%
0.2 0.774 \(\pm 0.206\) 26.61%
0.5 0.880 \(\pm 0.446\) 50.71%
1.0 1.101 \(\pm 0.817\) 74.21%

Figure 3: Water depth uncertainty propagation.

Motivation

The Computational Burden

  • Generating an ensemble of 500 realizations requires massive computational throughput.
  • Running these simulations demands significant energy.
  • Time is being used as a proxy for energy consumption.

The Attribution Challenge

  • Modern hardware often runs multiple tasks at the same time.
  • Hardware sensors report the total power of the card, not the energy used by a specific process.

Research Questions

  • How can the energy consumption of heterogeneous scientific computing workloads be accurately measured and modeled under input and execution uncertainty?
    • What methodologies enable accurate process-level energy attribution in shared heterogeneous computing infrastructures?
    • To what extent can execution time serve as a proxy for energy consumption in heterogeneous CPU–GPU computing systems?
    • How does uncertainty in simulation inputs propagate to variability in computational energy consumption?

Methodology

  • Hardware: Gaia HPC Cluster
  • Solver: Synxflow
  • Soft Sensor: Alumet
    • Isolates energy consumption by process-level GPU/CPU utilization percentages.
ITERATE

Original DEM

→

Noise Injection

→

Alumet + Synxflow

→

Ensemble Analysis

Figure 4: Computational Pipeline Flowchart

Results

  • The Failure of the Time Proxy
  • Uncertainty Propagation of Energy Consumption

Is Execution Time a Reliable Proxy?

  • Energy (\(E\)) is the product of power (\(P\)) and time (\(t\)).

\(E = A + P \cdot t\)

Is Execution Time a Reliable Proxy?

Figure 5: Comparison of Original and Downsampled DEM Resolutions

Is Execution Time a Reliable Proxy?

Figure 6: Total energy consumption vs. execution duration for all iterations

Is Execution Time a Reliable Proxy?

Figure 7: Total energy consumption vs. execution duration for all clean iterations

Is Execution Time a Reliable Proxy?

Figure 8: Average Cumulative Energy-Time Plot

Results

  • The Failure of the Time Proxy
  • Uncertainty Propagation of Energy Consumption

Uncertainty Quantification in consumed Energy

Figure 9: Raw distribution of total energy consumption for each topographic noise level

Uncertainty Quantification in consumed Energy

Figure 10: Statistical distribution of total energy consumption for each topographic noise level

Conclusion

  • Isolation is Essential: Process-level attribution is mandatory for reliable Uncertainty Quantification in shared HPC environments.
  • Time is not a Proxy: Execution duration fails to capture energy consumption due to dynamic hardware power signatures.
  • The 0.2m Tipping Point: Topographic noise beyond 20cm triggers non-linear explosions in both solver energy cost and water depth variance.

Outlook

  • Investigate why the 0.05m noise profile paradoxically exhibits higher energy variance (19.7 J) than the 0.1m profile (16.2 J).
  • Determine the exact root cause of the extreme 60-second hardware outliers present in the raw duration data.

References

[1]
H. Zhao and J. Kowalski, “Topographic uncertainty quantification for flow-like landslide models via stochastic simulations,” Natural Hazards and Earth System Sciences, vol., vol. 20, no. 5, pp. 1441–1461, May 2020, doi: 10.5194/nhess-20-1441-2020.