5 papers · 1 filter
Compatible Likelihoods for Flow Matching on Manifolds
Lucas Ng, Georgios Batzolis, Mark Girolami
On the simplest non-Euclidean manifold, the 1D flat torus, we exhibit a distribution where a recently proposed extension of Riemannian flow matching is globally optimized by a velo…
Beyond Unimodal Bases: Pullback Geometry for Multimodal Data
Honglei Brinkmann, Lucas Ng, Georgios Batzolis +3
Data-driven Riemannian geometry provides nonlinear interpolation and geometric representations of high-dimensional data. For these operations to be statistically meaningful, paths…
Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEs
Pengyu Zhang, Mark Girolami, Arnaud Vadeboncoeur
Inferring quantities of interest (QoI) from data is a central task in Science and Engineering. In such contexts, we often have access to both quantitative data and qualitative data…
Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach
Rares Grozavescu, Pengyu Zhang, Mark Girolami +1
We investigate the Continuous-Time Koopman Autoencoder (CT-KAE) as a lightweight surrogate model for long-horizon ocean state forecasting in a two-layer quasi-geostrophic (QG) syst…
Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs
Pengyu Zhang, Arnaud Vadeboncoeur, Alex Glyn-Davies +1
Inverse problems are the task of calibrating models to match data. They play a pivotal role in diverse engineering applications by allowing practitioners to align models with reali…