Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation.
Romit Maulik,
Purdue University
In this presentation, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.
Romit Maulik is an assistant professor in the School of Mechanical Engineering at Purdue University. He obtained his Ph.D. in mechanical and aerospace engineering at Oklahoma State University (in 2019) and was the Margaret Butler Postdoctoral Fellow (from 2019-2021) before becoming an assistant computational scientist at Argonne National Laboratory (from 2021-2023). From 2023-2025, he was an assistant professor in informatics and intelligent systems at Penn State University. His group studies high-performance multifidelity scientific machine learning algorithm development with applications to various multiphysical nonlinear dynamical systems such as those that arise in mechanical and aerospace engineering, Earth systems modeling, nuclear fusion, and beyond. He is an Early Career Awardee of the Army Research Office and a Perry Academic Excellence Scholar at Purdue University.