Xiantao Fan

Han Gao, Xu Han, Xiantao Fan et al.

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. We introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, and scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: 1) the synthesis of LES simulated instantaneous flow sequences from URANS inputs; 2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; 3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation.

Sifan Wang, Shyam Sankaran, Xiantao Fan et al.

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically different approach that trains neural networks directly from physical equations rather than data, offering the potential for continuous, mesh-free solutions. Here we show that appropriately designed PINNs can successfully simulate fully turbulent flows in both two and three dimensions, directly learning solutions to the fundamental fluid equations without traditional computational grids or training data. Our approach combines several algorithmic innovations including adaptive network architectures, causal training, and advanced optimization methods to overcome the inherent challenges of learning chaotic dynamics. Through rigorous validation on challenging turbulence problems, we demonstrate that PINNs accurately reproduce key flow statistics including energy spectra, kinetic energy, enstrophy, and Reynolds stresses. Our results demonstrate that neural equation solvers can handle complex chaotic systems, opening new possibilities for continuous turbulence modeling that transcends traditional computational limitations.

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.

Junyi Guo, Pan Du, Xiantao Fan et al.

We investigate conditional neural fields (CNFs), mesh-agnostic, coordinate-based decoders conditioned on a low-dimensional latent, for spatial dimensionality reduction of turbulent flows. CNFs are benchmarked against Proper Orthogonal Decomposition and a convolutional autoencoder within a unified encoding-decoding framework and a common evaluation protocol that explicitly separates in-range (interpolative) from out-of-range (strict extrapolative) testing beyond the training horizon, with identical preprocessing, metrics, and fixed splits across all baselines. We examine three conditioning mechanisms: (i) activation-only modulation (often termed FiLM), (ii) low-rank weight and bias modulation (termed FP), and (iii) last-layer inner-product coupling, and introduce a novel domain-decomposed CNF that localizes complexities. Across representative turbulence datasets (WMLES channel inflow, DNS channel inflow, and wall pressure fluctuations over turbulent boundary layers), CNF-FP achieves the lowest training and in-range testing errors, while CNF-FiLM generalizes best for out-of-range scenarios once moderate latent capacity is available. Domain decomposition significantly improves out-of-range accuracy, especially for the more demanding datasets. The study provides a rigorous, physics-aware basis for selecting conditioning, capacity, and domain decomposition when using CNFs for turbulence compression and reconstruction.