Meet Hemant Parikh

Meet Hemant Parikh, Yaqin Chen, Jian-Xun Wang

Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and governing physics. While training-free conditional generation is well developed for diffusion models, corresponding conditioning and posterior sampling strategies for Flow Matching (FM) priors remain comparatively under-explored, especially on scientific benchmarks where fidelity must be assessed beyond measurement misfit. In this work, we study training-free conditional generation for scientific inverse problems under FM priors and organize existing inference-time strategies by where measurement information is injected: (i) guided transport dynamics that perturb sampling trajectories using likelihood information, and (ii) source-distribution inference that performs posterior inference over the source variable while keeping the learned transport fixed. Building on the latter, we propose D-Flow SGLD, a source-space posterior sampling method that augments differentiable source inference with preconditioned stochastic gradient Langevin dynamics, enabling scalable exploration of the source posterior induced by new measurement operators without retraining the prior or modifying the learned FM dynamics. We benchmark representative methods from both families on a hierarchy of problems: 2D toy posteriors, chaotic Kuramoto-Sivashinsky trajectories, and wall-bounded turbulence reconstruction. Across these settings, we quantify trade-offs among measurement assimilation, posterior diversity, and physics/statistics fidelity, and establish D-Flow SGLD as a practical FM-compatible posterior sampler for scientific inverse problems.

Xin-Yang Liu, Meet Hemant Parikh, Xiantao Fan et al.

Eddy-resolving turbulence simulations require stochastic inflow conditions that accurately replicate the complex, multi-scale structures of turbulence. Traditional recycling-based methods rely on computationally expensive precursor simulations, while existing synthetic inflow generators often fail to reproduce realistic coherent structures of turbulence. Recent advances in deep learning (DL) have opened new possibilities for inflow turbulence generation, yet many DL-based methods rely on deterministic, autoregressive frameworks prone to error accumulation, resulting in poor robustness for long-term predictions. In this work, we present CoNFiLD-inlet, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field (CNF)-encoded latent space to produce realistic, stochastic inflow turbulence. By parameterizing inflow conditions using Reynolds numbers, CoNFiLD-inlet generalizes effectively across a wide range of Reynolds numbers ($Re_τ$ between $10^3$ and $10^4$) without requiring retraining or parameter tuning. Comprehensive validation through a priori and a posteriori tests in Direct Numerical Simulation (DNS) and Wall-Modeled Large Eddy Simulation (WMLES) demonstrates its high fidelity, robustness, and scalability, positioning it as an efficient and versatile solution for inflow turbulence synthesis.

Zhao Feng, Xin-Yang Liu, Meet Hemant Parikh et al.

Geological Carbon Sequestration (GCS) has emerged as a promising strategy for mitigating global warming, yet its effectiveness heavily depends on accurately characterizing subsurface flow dynamics. The inherent geological uncertainty, stemming from limited observations and reservoir heterogeneity, poses significant challenges to predictive modeling. Existing methods for inverse modeling and uncertainty quantification are computationally intensive and lack generalizability, restricting their practical utility. Here, we introduce a Conditional Neural Field Latent Diffusion (CoNFiLD-geo) model, a generative framework for efficient and uncertainty-aware forward and inverse modeling of GCS processes. CoNFiLD-geo synergistically combines conditional neural field encoding with Bayesian conditional latent-space diffusion models, enabling zero-shot conditional generation of geomodels and reservoir responses across complex geometries and grid structures. The model is pretrained unconditionally in a self-supervised manner, followed by a Bayesian posterior sampling process, allowing for data assimilation for unseen/unobserved states without task-specific retraining. Comprehensive validation across synthetic and real-world GCS scenarios demonstrates CoNFiLD-geo's superior efficiency, generalization, scalability, and robustness. By enabling effective data assimilation, uncertainty quantification, and reliable forward modeling, CoNFiLD-geo significantly advances intelligent decision-making in geo-energy systems, supporting the transition toward a sustainable, net-zero carbon future.