Advances in Time Series Analysis and Operator Learning

The field of time series analysis and operator learning is witnessing significant developments, with a focus on improving interpretability, uncertainty quantification, and scalability. Researchers are exploring new approaches to model complex time series data, such as introducing continuous relaxation of discrete states and using generative hyper-networks to estimate predictive uncertainty. Additionally, there is a growing interest in operator learning, which has the potential to drastically reduce expensive numerical integration of PDEs. Noteworthy papers in this area include the introduction of the Gumbel Dynamical Model, which enables fast and scalable training with standard gradient descent methods, and the development of GenUQ, a measure-theoretic approach to uncertainty quantification that avoids constructing a likelihood. Furthermore, the application of Bayesian Transformer models to Pan-Arctic sea ice concentration mapping and uncertainty estimation is showing promising results. Overall, these advancements are expected to have a significant impact on various fields, including climate modeling, finance, and engineering.

Sources

Interpretable time series analysis with Gumbel dynamics

GenUQ: Predictive Uncertainty Estimates via Generative Hyper-Networks

Generation Properties of Stochastic Interpolation under Finite Training Set

Bayesian Transfer Operators in Reproducing Kernel Hilbert Spaces

Best weighted approximation of some kernels on the real axis

Spectral equivalence of unsymmetric kernel matrices and applications

Bayesian Transformer for Pan-Arctic Sea Ice Concentration Mapping and Uncertainty Estimation using Sentinel-1, RCM, and AMSR2 Data

Deep set based operator learning with uncertainty quantification

A Physics-Guided Probabilistic Surrogate Modeling Framework for Digital Twins of Underwater Radiated Noise

Reframing Generative Models for Physical Systems using Stochastic Interpolants

Modeling Market States with Clustering and State Machines

Dynamical system reconstruction from partial observations using stochastic dynamics

A Copula-Based Variational Autoencoder for Uncertainty Quantification in Inverse Problems: Application to Damage Identification in an Offshore Wind Turbine

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