arXiv:2607. 28903v1 Announce Type: cross Abstract: Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response.
arXiv:2606. 17233v1 Announce Type: new Abstract: In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.
arXiv:2507.04553v2 Announce Type: replace-cross Abstract: Reliability analysis traditionally relies on deterministic simulators, where identical inputs yield identical outputs. However, many real-wor...
arXiv:2606. 14053v1 Announce Type: cross Abstract: Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses remains a major challenge in global sensitivity analysis (GSA).
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.
arXiv:2507. 03631v4 Announce Type: replace Abstract: Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data.
arXiv:2608. 01968v1 Announce Type: new Abstract: Transformer models are most often understood through what they do: their benchmark performance, generation quality, or behavior on downstream tasks.
arXiv:2609.38998v1 Announce Type: new Abstract: A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected unit...
arXiv:2608. 08003v1 Announce Type: cross Abstract: As machine learned models increase in complexity and expressive power, features of simpler models, such as interpretability and control over the shape of the modeled function are lost.
arXiv:2607. 17990v1 Announce Type: new Abstract: Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency.
The paper introduces Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.
arXiv:2608. 16340v1 Announce Type: cross Abstract: The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs.
arXiv:2608. 09071v1 Announce Type: cross Abstract: Forward uncertainty propagation in complex physical systems can induce structured covariance across field-valued outputs.