Integrating Score-Based Diffusion Models with Machine Learning-Enhanced Localization for Advanced Data Assimilation in Geological Carbon Storage

Accurate characterization of subsurface heterogeneity is important for the safe and effective implementation of geological carbon storage (GCS) projects. This paper explores how machine learning methods can enhance data assimilation for GCS with a framework that integrates score-based diffusion models with machine learning-enhanced localization in channelized reservoirs during CO$_2$ injection. We employ a machine learning-enhanced localization framework that uses large ensembles ($N_s = 5000$) with permeabilities generated by the diffusion model and states computed by simple ML algorithms to improve covariance estimation for the Ensemble Smoother with Multiple Data Assimilation (ESMDA). We apply ML algorithms to a prior ensemble of channelized permeability fields, generated with the geostatistical model FLUVSIM. Our approach is applied on a CO$_2$ injection scenario simulated using the Delft Advanced Research Terra Simulator (DARTS). Our ML-based localization maintains significantly more ensemble variance than when localization is not applied, while achieving comparable data-matching quality. This framework has practical implications for GCS projects, helping improve the reliability of uncertainty quantification for risk assessment.

Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

In Data Assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is computationally expensive and infeasible to run in real-time for complex systems. Here, we present a novel particle filter methodology, the Deep Latent Space Particle filter or D-LSPF, that uses neural network-based surrogate models to overcome this computational challenge. The D-LSPF enables filtering in the low-dimensional latent space obtained using Wasserstein AEs with modified vision transformer layers for dimensionality reduction and transformers for parameterized latent space time stepping. As we demonstrate on three test cases, including leak localization in multi-phase pipe flow and seabed identification for fully nonlinear water waves, the D-LSPF runs orders of magnitude faster than a high-fidelity particle filter and 3-5 times faster than alternative methods while being up to an order of magnitude more accurate. The D-LSPF thus enables real-time data assimilation with uncertainty quantification for physical systems.