arXiv subjects

Ghifari Adam Faza

Publications and source records attributed to Ghifari Adam Faza.

3 recordsLinked to original sources

arXiv2026

Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences

Solving PDE-governed physical problems is computationally expensive, limiting the availability of high-fidelity (HF) data for training neural operators, which typically require large datasets. Multi-fidelity learning addresses this by combining abundant low-fidelity (LF) data with limited HF samples. To evaluate several multi-fidelity neural operator strategies, including two-step, residual, intermediate, and transfer learning, we conduct a systematic assessment across four PDE test cases: two standard grid-based problems, a modified Darcy flow with LF-HF governing equation discrepancies, and an unsteady smoke inflow with temporal dynamics. Most prior studies focus on grid-based LF-HF differences, but real-world discrepancies, such as those between RANS and LES models in CFD, can be more complex. To capture these more challenging scenarios, we introduce two new test cases specifically designed to emulate nontrivial LF-HF mismatch beyond simple grid-resolution differences, enabling a more realistic assessment of multi-fidelity strategies under substantial model discrepancies. We find that methods directly feeding LF predictions into HF models are prone to error amplification under large LF-HF discrepancies, particularly in autoregressive settings. In contrast, transfer learning, which uses LF-trained weights to initialise the HF model, consistently improves accuracy by providing a robust prior refined with HF data. These results highlight the importance of establishing transfer learning as a reliable approach for efficient multi-fidelity PDE surrogate modelling.

cs.CE↗

arXiv2026

Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design optimisation and reliability analysis. However, standard interval propagation relies on solving optimisation problems that become computationally expensive for complex systems. Surrogate models alleviate this cost but typically replace only the evaluator within the optimisation loop, still requiring many inference calls. To overcome this limitation, we reformulate interval propagation as an interval-valued regression problem that directly predicts output bounds. We present a comprehensive study of neural network-based surrogate models, including multilayer perceptrons (MLPs) and deep operator networks (DeepONet), for this task. Three approaches are investigated: (i) naive interval propagation through standard architectures, (ii) bound propagation methods such as Interval Bound Propagation (IBP) and CROWN, and (iii) interval neural networks (INNs) with interval weights. Results show that these methods significantly improve computational efficiency over traditional optimisation-based approaches while maintaining accurate interval estimates. We further discuss practical limitations and open challenges in applying interval-based propagation methods.

cs.LG↗

arXiv2026

Learning Credal Ensembles via Distributionally Robust Optimization

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.

cs.LG↗