2026
Drifting Fields are not Conservative
Drift fields in generative models are generally non-conservative; sharp normalization makes them gradients of a scalar potential, bridging to Wasserstein gradient flows and denoising score matching.
Publications
2026
Scaling up Probabilistic PDE Simulators with Structured Volumetric Information
Introduces GP-FVM, a probabilistic counterpart to the finite volume method, enabling large-scale probabilistic PDE simulations.
2026
Hierarchical Bayesian Quadrature
Bayesian quadrature for nonstationary integrands, through an adaptive tree of local stationary models.
2026
Scalable Bayesian Inference for Nonlinear Conservation Laws
Numerically conservative Bayesian simulation of nonlinear conservation laws, scaled up with sparse approximations.
2025
Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields
Fast probabilistic counterparts to numerical PDE solvers, powered by SPDEs & sparse linear algebra.