Hojin Kim

Hojin Kim, Dibyajyoti Chakraborty, Takahiko Toki et al.

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

Dibyajyoti Chakraborty, Hojin Kim, Romit Maulik

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are deterministic, for example when neural operators are involved. However, deterministic models often fail to capture the intrinsic distributional uncertainty of chaotic systems. This work presents a surrogate modeling formulation that leverages generative machine learning, where a deep learning diffusion model is used to probabilistically forecast turbulent flows over long horizons. We introduce a multi-step autoregressive diffusion objective that significantly enhances long-rollout stability compared to standard single-step training. To handle complex, unstructured geometries, we utilize a multi-scale graph transformer architecture incorporating diffusion preconditioning and voxel-grid pooling. More importantly, our modeling framework provides a unified platform that also predicts spatiotemporally important locations for sensor placement, either via uncertainty estimates or through an error-estimation module. Finally, the observations of the ground truth state at these dynamically varying sensor locations are assimilated using diffusion posterior sampling requiring no retraining of the surrogate model. We present our methodology on two-dimensional homogeneous and isotropic turbulence and for a flow over a backwards-facing step, demonstrating its utility in forecasting, adaptive sensor placement, and data assimilation for high dimensional chaotic systems.