Introduces structured DRO for learned inverse problem reconstructions with ambiguity sets aligned to the forward operator, yielding explicit dual representations and a worst-case bound that induces Tikhonov regularization on the operator Lipschitz constant.
Stochastic inverse problem: stability, regularization and wasserstein gradient flow.arXiv preprint arXiv:2410.00229
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Distributional inverse homogenization learns microstructural statistics from bulk mechanical measurements by inverting the homogenization process statistically.
A quadratic self-test loss derived from the weak-form evolution equation allows robust learning of particle interaction potentials directly from unlabeled data without trajectory recovery.
SCSI iteratively refines a self-consistent transport map to invert black-box corruptions and enable generative modeling of clean data.
A perturbation-based conformal prediction wrapper on Fourier Neural Operators yields narrower uncertainty bands than prior methods for 2D incompressible Navier-Stokes while preserving coverage in data-scarce regimes.
Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.
A methodology for populational inverse problems that simultaneously deconvolves unknown observational noise and recovers parameter distributions via structured gradient descent and adaptive empirical measure-based active learning for surrogates.
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Distributional Inverse Homogenization
Distributional inverse homogenization learns microstructural statistics from bulk mechanical measurements by inverting the homogenization process statistically.