arXiv subjects

Xiantao Fan

Publications and source records attributed to Xiantao Fan.

14 recordsLinked to original sources

arXiv2026

Differentiable Hybrid Neural-CFD Modelling of Wall-Bounded Turbulence: Coupled Learning of Subgrid-Scale and Wall Closures

Wall-modelled large-eddy simulation (WMLES) treats the subgrid-scale (SGS) closure, wall closure and numerical discretization as independent components, although their effects are coupled through the same resolved field. We present a differentiable hybrid neural--CFD framework in which the SGS and wall closures are learned jointly, end-to-end, within a differentiable flow solver, using only low-order statistics as training targets. Each closure is a composed neural operator: a trainable neural network followed by a fixed differentiable layer that preserves the structure of its conventional counterpart, so that the network learns only the functions left undetermined by the conventional form. Because every operation is differentiable, gradients of the training loss are back-propagated through the coupled solver, allowing both neural closures to be optimized consistently against the flow field, rather than fitted offline or in isolation. We demonstrate the framework, denoted Hybrid-Joint, on a zero-pressure-gradient turbulent boundary layer across a posteriori tests spanning Re_\theta = 600--6500, computational domains and mesh resolutions. The model outperforms WMLES baselines, extrapolates to more than four times the highest training Reynolds number, and transfers to grids and domains absent from training. It recovers a logarithmic mean-velocity region, not imposed by the wall closure, and reproduces the resolved energy spectra accurately, although spectral information is excluded from the training objective. Ablation studies show that learning either closure alone is insufficient and that only joint optimization recovers the full set of statistics, confirming that SGS closure, wall closure and discretization are coupled and must be trained jointly. Once trained, the closures are reused without retraining across all cases, so that training cost is amortized over repeated deployment.

physics.flu-dyn↗

arXiv2026

A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters. An effective approach to address these challenges is leveraging physics priors in training neural networks, known as physics-informed deep learning (PiDL). In this work, we introduce the Multi-Resolution Finite-Volume-inspired network, MuRFiV, designed to capitalize on the conservative property of finite volume on the global scale and the expressive power of deep learning on the local scale. We demonstrate the effectiveness of MuRFiV on several spatio-temporal systems governed by partial differential equations (PDEs), including Burgers' equation, shallow water equations, and incompressible Navier-Stokes equations. By embedding PDE information into the deep learning architecture, MuRFiV achieves strong long-term prediction accuracy and remains stable over very long autoregressive rollouts, significantly outperforming data-driven neural network baselines. This result highlights the promise of combining multiresolution learning with finite-volume-inspired inductive bias for accurate and robust long-term prediction of complex dynamics.

cs.CE↗

arXiv2026

Offline Reinforcement Learning for Fluid Controls: Data-based Multi-observational Policy Extraction

Active flow control is a fundamental application in engineering. Recent advances in deep reinforcement learning have made progress in this field. However, the classical online RL approaches require extensive real-time interactions with the high fidelity environment, while each sensor configuration change necessitates whole policy retraining. All these factors result in prohibitive computational costs for real-world applications. In this work, we propose a novel offline RL framework that addresses both challenges through data-driven policy extraction. We develop a sensor position-conditioned architecture that enables a single policy network to adapt seamlessly to multiple sensor arrangements. The position-conditioned approach incorporated spatial relationship modeling through Point Attention layers to ensure the generalizability to varying sensor placements. We demonstrate the framework on two representative problems, mitigating chaoticity in the Kuramoto-Sivashinsky equation and flow control over airfoils governed by the Navier-Stokes equation. The result demonstrates that the policy extraction from the dataset provides unprecedented flexibility for sensor placement optimization. This approach represents a significant step towards adaptive, intelligent flow control systems.

cs.LG↗

arXiv2026

JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX

Sparse linear systems from PDE discretizations are central to scientific computing, yet no existing JAX-ecosystem solver simultaneously provides GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. JAX-AMG fills this gap by wrapping the NVIDIA AmgX solver suite as a native JAX primitive, exposing AMG and Krylov methods with configurable preconditioners through a unified interface compatible with JIT compilation, reverse-mode AD via adjoint methods, batched solves, and MPI-based distributed execution. Solver caching amortizes setup costs across repeated solves, making JAX-AMG practical for PDE-constrained optimization and inverse problems. The result is a robust, scalable sparse linear algebra layer that integrates seamlessly into differentiable simulation and scientific machine learning pipelines.

cs.MS↗

arXiv2025

Generative Reconstruction of Spatiotemporal Wall-Pressure in Turbulent Boundary Layers via Patchwise Latent Diffusion

Wall-pressure fluctuations in turbulent boundary layers drive flow-induced noise, structural vibration, and hydroacoustic disturbances, especially in underwater and aerospace systems. Accurate prediction of their wavenumber-frequency spectra is critical for mitigation and design, yet empirical/analytical models rely on simplifying assumptions and miss the full spatiotemporal complexity, while high-fidelity simulations are prohibitive at high Reynolds numbers. Experimental measurements, though accessible, typically provide only pointwise signals and lack the resolution to recover full spatiotemporal fields. We propose a probabilistic generative framework that couples a patchwise (domain-decomposed) conditional neural field with a latent diffusion model to synthesize spatiotemporal wall-pressure fields under varying pressure-gradient conditions. The model conditions on sparse surface-sensor measurements and a low-cost mean-pressure descriptor, supports zero-shot adaptation to new sensor layouts, and produces ensembles with calibrated uncertainty. Validation against reference data shows accurate recovery of instantaneous fields and key statistics.

physics.flu-dyn↗

arXiv2025

Conditional neural field for spatial dimension reduction of turbulence data: a comparison study

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.

physics.flu-dyn↗

arXiv2025

Simulating Three-dimensional Turbulence with Physics-informed Neural Networks

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.

cs.LG↗

arXiv2025

Diff-FlowFSI: A GPU-Optimized Differentiable CFD Platform for High-Fidelity Turbulence and FSI Simulations

Turbulent flows and fluid-structure interactions (FSI) are ubiquitous in scientific and engineering applications, but their accurate and efficient simulation remains a major challenge due to strong nonlinearities, multiscale interactions, and high computational demands. Traditional CFD solvers, though effective, struggle with scalability and adaptability for tasks such as inverse modeling, optimization, and data assimilation. Recent advances in machine learning (ML) have inspired hybrid modeling approaches that integrate neural networks with physics-based solvers to enhance generalization and capture unresolved dynamics. However, realizing this integration requires solvers that are not only physically accurate but also differentiable and GPU-efficient. In this work, we introduce Diff-FlowFSI, a GPU-accelerated, fully differentiable CFD platform designed for high-fidelity turbulence and FSI simulations. Implemented in JAX, Diff-FlowFSI features a vectorized finite volume solver combined with the immersed boundary method to handle complex geometries and fluid-structure coupling. The platform enables GPU-enabled fast forward simulations, supports automatic differentiation for gradient-based inverse problems, and integrates seamlessly with deep learning components for hybrid neural-CFD modeling. We validate Diff-FlowFSI across a series of benchmark turbulence and FSI problems, demonstrating its capability to accelerate scientific computing at the intersection of physics and machine learning.

physics.flu-dyn↗

arXiv2025

Conditional flow matching for generative modeling of near-wall turbulence with quantified uncertainty

Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow-wall coupling challenge deterministic estimation strategies. To address this, we introduce a novel generative modeling framework based on conditional flow matching for synthesizing instantaneous velocity fluctuation fields from wall observations, with explicit quantification of predictive uncertainty. Our method integrates continuous-time flow matching with a probabilistic forward operator trained using stochastic weight averaging Gaussian (SWAG), enabling zero-shot conditional generation without model retraining. We demonstrate that the proposed approach not only recovers physically realistic, statistically consistent turbulence structures across the near-wall region but also effectively adapts to various sensor configurations, including sparse, incomplete, and low-resolution wall measurements. The model achieves robust uncertainty-aware reconstruction, preserving flow intermittency and structure even under significantly degraded observability. Compared to classical linear stochastic estimation (LSE) and deterministic convolutional neural networks (CNN) methods, our stochastic generative learning framework exhibits superior generalization and resilience under measurement sparsity with quantified uncertainty. This work establishes a robust semi-supervised generative modeling paradigm for data-consistent flow reconstruction and lays the foundation for uncertainty-aware, sensor-driven modeling of wall-bounded turbulence.

physics.flu-dyn↗

arXiv2024

CoNFiLD-inlet: Synthetic Turbulence Inflow Using Generative Latent Diffusion Models with Neural Fields

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 ($Re_\tau$ 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.

physics.flu-dyn↗

arXiv2024

Neural Differentiable Modeling with Diffusion-Based Super-resolution for Two-Dimensional Spatiotemporal Turbulence

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.

physics.flu-dyn↗

arXiv2024

CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence

This study introduces the Conditional Neural Field Latent Diffusion (CoNFiLD) model, a novel generative learning framework designed for rapid simulation of intricate spatiotemporal dynamics in chaotic and turbulent systems within three-dimensional irregular domains. Traditional eddy-resolved numerical simulations, despite offering detailed flow predictions, encounter significant limitations due to their extensive computational demands, restricting their applications in broader engineering contexts. In contrast, deep learning-based surrogate models promise efficient, data-driven solutions. However, their effectiveness is often compromised by a reliance on deterministic frameworks, which fall short in accurately capturing the chaotic and stochastic nature of turbulence. The CoNFiLD model addresses these challenges by synergistically integrating conditional neural field encoding with latent diffusion processes, enabling the memory-efficient and robust probabilistic generation of spatiotemporal turbulence under varied conditions. Leveraging Bayesian conditional sampling, the model can seamlessly adapt to a diverse range of turbulence generation scenarios without the necessity for retraining, covering applications from zero-shot full-field flow reconstruction using sparse sensor measurements to super-resolution generation and spatiotemporal flow data restoration. Comprehensive numerical experiments across a variety of inhomogeneous, anisotropic turbulent flows with irregular geometries have been conducted to evaluate the model's versatility and efficacy, showcasing its transformative potential in the domain of turbulence generation and the broader modeling of spatiotemporal dynamics.

physics.flu-dyn↗

arXiv2023

Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation

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.

physics.flu-dyn↗

arXiv2023

Differentiable hybrid neural modeling for fluid-structure interaction

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.

physics.comp-ph↗