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This paper introduces an adaptive surrogate modeling framework tailored for problems with extremely high‑dimensional spatio‑temporal outputs. The approach first reduces dimensionality by mapping outputs to a low‑dimensional latent space, then builds a surrogate model there, and finally employs a novel adaptive sampling strategy that balances exploration and exploitation to refine the surrogate with minimal expensive physics‑model runs. The method is validated on a thermo‑mechanical analysis of a gas turbine engine blade.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
arXiv:2608.27590v1 Announce Type: cross Abstract: Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral dat...
arXiv:2608. 11019v1 Announce Type: new Abstract: Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions.
arXiv:2606. 16737v1 Announce Type: cross Abstract: Engineers often measure many quantities-speed, pressure, temperature, length-expressed in different physical units.
The paper tackles the challenge of predicting multiple high‑dimensional physical fields that must satisfy linear equality constraints, a common scenario in physics‑informed machine learning. It critiques the conventional approach of deducing one field from others, showing its sensitivity to arbitrary choices and its impact on accuracy and uncertainty. To address this, the authors introduce a symmetric framework that first applies a row‑wise PCA to preserve constraints in a latent space, then trains a linearly‑constrained multi‑output Gaussian process using a specially parametrized kernel, and validate the method on population dynamics and CFD problems involving Reynolds stress tensors.