Burgers Robustness Eval

burgers-robustness-eval

Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators — Roy et al. (2026) (arXiv:2604.13316, 2026)

What this evaluates

Evaluates the adversarial robustness and baseline accuracy of neural operators trained to solve the viscous Burgers’ equation. It probes whether targeted active learning and architectural denoising can mitigate sensitivity to input perturbations compared to uniform or random sampling strategies.

Datasets

• Viscous Burgers’ Equation (Spectral Solver) — total 600; splits: full (600)

Metrics

• Baseline (%) — range: percent
  • Percentage error of the model's prediction on clean, smooth initial conditions relative to the spectral solver ground truth.
• Robust (%) — range: percent
  • Percentage error under adversarial input perturbations (random Gaussian bumps or differential evolution attacks) relative to ground truth.
• Combined (%) (primary) — range: percent
  • Sum of Baseline (%) and Robust (%) errors. Lower values indicate a better accuracy-robustness trade-off.

Input / output format

Input: Initial condition functions discretized at 64 spatial points, representing either smooth profiles or adversarially perturbed profiles.

Output: Predicted solution field to the viscous Burgers’ equation at terminal time T=1.0, evaluated as a percentage error against the spectral solver ground truth.

Scoring recipe

# Compute L2 error relative to ground truth
error = np.linalg.norm(pred - gold) / np.linalg.norm(gold) * 100
baseline_error = error(clean_inputs)
robust_error = error(perturbed_inputs)
combined_error = baseline_error + robust_error
return combined_error

Common pitfalls

• Assuming high validation accuracy on clean data guarantees robustness; the paper explicitly shows a ~3.7x degradation under attack despite low baseline error.
• Using uniform or random perturbation sampling for training data generation, which the authors show is suboptimal compared to active learning targeting vulnerable subspaces.
• Treating the 600-simulation budget as a fixed test set rather than a training budget dynamically allocated across active learning rounds.

Evidence (verbatim from paper)

Table 1: Performance comparison across defense strategies. All methods operate under the same 600-simulation budget. Combined = Baseline + Robustness error. Lower is better for all metrics.

Citation

@misc{roy2026beyond,
  title={Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators},
  author={Roy et al. (2026)},
  year={2026},
  note={arXiv:2604.13316}
}

• arXiv: 2604.13316