Yaozhong Shi

Yaozhong Shi, Grigorios Lavrentiadis, Domniki Asimaki et al.

We present a data-driven framework for ground-motion synthesis that generates three-component acceleration time histories conditioned on moment magnitude, rupture distance , time-average shear-wave velocity at the top $30m$ ($V_{S30}$), and style of faulting. We use a Generative Adversarial Neural Operator (GANO), a resolution invariant architecture that guarantees model training independent of the data sampling frequency. We first present the conditional ground-motion synthesis algorithm (cGM-GANO) and discuss its advantages compared to previous work. We next train cGM-GANO on simulated ground motions generated by the Southern California Earthquake Center Broadband Platform (BBP) and on recorded KiK-net data and show that the model can learn the overall magnitude, distance, and $V_{S30}$ scaling of effective amplitude spectra (EAS) ordinates and pseudo-spectral accelerations (PSA). Results specifically show that cGM-GANO produces consistent median scaling with the training data for the corresponding tectonic environments over a wide range of frequencies for scenarios with sufficient data coverage. For the BBP dataset, cGM-GANO cannot learn the ground motion scaling of the stochastic frequency components; for the KiK-net dataset, the largest misfit is observed at short distances and for soft soil conditions due to the scarcity of such data. Except for these conditions, the aleatory variability of EAS and PSA are captured reasonably well. Lastly, cGM-GANO produces similar median scaling to traditional GMMs for frequencies greater than 1Hz for both PSA and EAS but underestimates the aleatory variability of EAS. Discrepancies in the comparisons between the synthetic ground motions and GMMs are attributed to inconsistencies between the training dataset and the datasets used in GMM development. Our pilot study demonstrates GANO's potential for efficient synthesis of broad-band ground motions

Yaozhong Shi, Angela F. Gao, Zachary E. Ross et al.

Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that remains mathematically tractable for functional regression. To do this, we develop Neural Operator Flows (OpFlow), an infinite-dimensional extension of normalizing flows. OpFlow is an invertible operator that maps the (potentially unknown) data function space into a Gaussian process, allowing for exact likelihood estimation of functional point evaluations. OpFlow enables robust and accurate uncertainty quantification via drawing posterior samples of the Gaussian process and subsequently mapping them into the data function space. We empirically study the performance of OpFlow on regression and generation tasks with data generated from Gaussian processes with known posterior forms and non-Gaussian processes, as well as real-world earthquake seismograms with an unknown closed-form distribution.

Yaozhong Shi, Zachary E. Ross, Domniki Asimaki et al.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.