arXiv subjects

Huiyu Yang

Publications and source records attributed to Huiyu Yang.

16 recordsLinked to original sources

arXiv2026

ArtisanCAD: An Industrial-Level CAD Agent with Expert-Grounded Knowledge Distillation

Computer-aided design (CAD) for industrial components requires long-horizon procedural modeling, robust feature dependencies, editable parametric geometry, and production-grade B-Rep execution. Existing text-to-CAD methods have made promising progress in generating CAD programs from natural-language descriptions, but they still struggle when user prompts are ambiguous, underspecified, or only describe high-level design intent. They also rarely exploit expert procedural knowledge naturally available in industrial workflows, such as CATIA operation recordings, macro logs, drawing notes, and engineering descriptions. We present ArtisanCAD, a skill-guided industrial CAD agent with expert-grounded knowledge distillation. The core of ArtisanCAD is CAD intermediate representation (CAD-IR), an executable procedural representation that encodes parameters, ordered operations, MCP tool bindings, dependencies, generated entities, and verification rules. CAD-IR plays two key roles: it first serves as the carrier for distilling expert CAD procedures into reusable parameterized skills; then it provides a procedural scaffold that turns vague or intermediate-level prompts into complete executable CAD operations. ArtisanCAD retrieves expert-derived skills, instantiates and revises CAD-IR, executes the resulting procedure through a dedicated CATIA-MCP backend, and uses multi-view visual feedback for iterative refinement, and finally generates production-ready B-Rep models. On the Text2CAD benchmark, CAD-IR improves generation from intermediate prompts by reducing mean Chamfer Distance from $14.83$ to $9.88$, showing its ability to bridge ambiguous textual intent and executable CAD construction. On four complex automotive components, CAD-IR enables expert CATIA recordings to be distilled into reusable skills, allowing ArtisanCAD to generate editable CATIA-native B-Rep models for new variant requests.

cs.AI↗

arXiv2026

A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction

High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration. Machine-learning-based surface-field prediction offers a faster alternative if the model can efficiently capture both global flow context and local geometric detail. This work proposes a machine-learning-based method, named the geometry-aware triplane field network (GTF-Net), for vehicle aerodynamic pressure and wall shear stress prediction. GTF-Net constructs triplane features directly from sampled surface points through a shared multilayer perceptron (MLP) and smooth bilinear rasterization. The planes are then processed by a dual-stream backbone that combines adaptive Fourier neural operator (AFNO) spectral mixing with convolutional neural network (CNN) refinement, so long-range aerodynamic coupling and local geometry-induced variations are modeled in the same representation. At query stage, sampled triplane features are combined with vehicle-aligned directional coordinates, normal-projection features, and a voxel-based curvature proxy. GTF-Net is compared with Transolver, geometry-informed neural operator (GINO), and TripNet, a triplane-based surrogate model. GTF-Net improves the relative L2 error from the strongest baseline value of 0.157 to 0.145 for pressure prediction and from 0.237 to 0.226 for wall shear stress prediction. Ablation results show that AFNO mixing, local CNN refinement, and query-side geometric encoding each contribute to accuracy, supporting the proposed mechanism of combining structured triplane representation with explicit aerodynamic geometry cues.

cs.LG↗

arXiv2026

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics

Rapid aerodynamic evaluation is crucial for modern vehicle design, yet existing neural operators struggle to capture intricate spatial correlations. We propose the rotary-enhanced transformer operator (RETO), a novel neural solver featuring a dual-stage spatial awareness mechanism: sinusoidal-cosine encodings for global referencing and rotary positional encodings (RoPE) for relative displacements. RoPE encodes spatial relations via unitary rotations, enforcing translation invariance and enhancing local gradient resolution. RETO is validated on ShapeNet and the high-fidelity DrivAerML benchmark. On ShapeNet, RETO achieves a relative $L_2$ error of 0.063, outperforming RegDGCNN at 0.125 and representing a 16\% improvement over the Transolver baseline, which yields an error of 0.075. These performance gains are further amplified on the DrivAerML dataset, where RETO achieves relative $L_2$ errors of 0.089 for surface pressure and 0.097 for velocity. In comparison, Transolver results in errors of 0.116 and 0.121 for the same metrics, indicating that RETO achieves precision enhancements of 23\% and 19\%, respectively. For comprehensive comparison, the surface pressure and velocity errors for AB-UBT are 0.102 and 0.124, while RegDGCNN yields 0.235 and 0.312, respectively. Information-theoretical analysis shows that the entropy peak of RETO at 0.35 is significantly lower than that of Transolver at 0.75 under $10^4$ resolution, indicating a focused attentional mechanism capable of preserving localized gradients against global diffusion.

eess.IV↗

arXiv2026

Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence

Accurate and efficient prediction of three-dimensional (3D) wall-bounded turbulent flows poses a significant challenge for machine learning methods, particularly in scenarios where flow field data are limited. Physics-informed neural operator (PINO) combines neural operator and physics constraint methods, and shows great potential for solving a wide range of partial differential equations. Nevertheless, the multi-scale vortex structures in wall-bounded turbulence make it difficult for most existing PINO methods to make stable and accurate long-term predictions at high Reynolds numbers. To address this challenge, we develop the large-eddy simulation nets (LESnets) that integrates large-eddy simulation (LES) equations into the factorized Fourier neural operator (F-FNO) for wall-bounded turbulence. The LESnets framework does not rely on labeled data for training, which enables it to generate temporal solutions over flexible time horizons during the training process. Moreover, the law of the wall is integrated into the LESnets framework through a wall model for the physics-informed loss, thus enabling reliable simulations of wall-bounded turbulence at high Reynolds number using coarse grids. The proposed LESnets methods are demonstrated in turbulent channel flows at three friction Reynolds numbers: 180, 590, and 1000. Numerical experiments show that the performance of the LESnets in terms of prediction accuracy and efficiency is comparable to that of two data-driven models, namely the implicit U-Net enhanced Fourier neural operator (IUFNO) and F-FNO. Meanwhile, the LESnets model achieves prediction accuracy comparable to traditional LES methods while offering a higher computational efficiency. Thus, the LESnets model demonstrates strong potential for efficient and long-term prediction of wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2026

Stable Fine-Time-Step Long-Horizon Turbulence Prediction with a Multi-Stepsize Mixture-of-Experts Neural Operator

Neural operators have been increasingly used as data-driven surrogates for time-marching predictions of turbulent flows. However, long-horizon autoregressive prediction is sensitive to error accumulation and the choice of prediction interval. Excessively small time increments may increase temporal redundancy and lengthen rollouts, which can degrade the stability of neural operators in turbulence forecasting. This work pursues a unified objective: stable long-horizon autoregressive prediction at fine temporal resolution for three-dimensional turbulence. We propose a multi-stepsize mixture-of-experts (Ms-MoE) neural operator built on an implicit factorized Transformer (IFactFormer) backbone. The model conditions on a requested relative stride and uses a time-step router to activate scale-specific routed experts together with a shared expert, yielding a single architecture that represents a family of stride-parameterized time-advancement operators. We evaluate the approach on forced homogeneous isotropic turbulence (HIT) and turbulent channel flow using filtered direct numerical simulation datasets. Relative to sampling intervals used in previous studies, we construct training datasets with up to 20 times finer temporal resolution and report long-horizon autoregressive rollouts using qualitative time-slice comparisons and long-time-averaged statistics. Ms-MoE-IFactFormer yields more stable long-horizon rollouts and improved agreement with long-time-averaged statistics on both HIT and turbulent channel flow, suggesting potential for stable time-marching at fine temporal resolution in more complex turbulent flows.

physics.flu-dyn↗

arXiv2026

Physics-Informed Transformer operator for the prediction of three-dimensional turbulence

Data-driven turbulence prediction methods often face challenges related to data dependency and lack of physical interpretability. In this paper, we propose a physics-informed Transformer operator (PITO) and its implicit variant (PIITO) for predicting three-dimensional (3D) turbulence, which are developed based on the vision Transformer (ViT) architecture with an appropriate patch size. Given the current flow field, the Transformer operator computes its prediction for the next time step. By embedding the large-eddy simulation (LES) equations into the loss function, PITO and PIITO can learn solution operators without using labeled data. Furthermore, PITO can automatically learn the subgrid scale (SGS) coefficient using a single set of flow data during training. Both PITO and PIITO exhibit excellent stability and accuracy on the predictions of various statistical properties and flow structures for the situation of long-term extrapolation exceeding 25 times the training horizon in decaying homogeneous isotropic turbulence (HIT), and outperform the physics-informed Fourier neural operator (PIFNO). Furthermore, PITO exhibits a remarkable accuracy on the predictions of forced HIT where PIFNO fails. Notably, PITO and PIITO reduce GPU memory consumption by 79.5% and 91.3% while requiring only 31.5% and 3.1% of the parameters, respectively, compared to PIFNO. Moreover, both PITO and PIITO models are much faster compared to traditional LES method.

physics.flu-dyn↗

arXiv2025

Integrating Fourier Neural Operator with Diffusion Model for Autoregressive Predictions of Three-dimensional Turbulence

Accurately autoregressive prediction of three-dimensional (3D) turbulence has been one of the most challenging problems for machine learning approaches. Diffusion models have demonstrated high accuracy in predicting two-dimensional (2D) turbulence, but their applications in 3D turbulence are relatively limited. To achieve reliable autoregressive predictions of 3D turbulence, we propose the DiAFNO model which integrates the implicit adaptive Fourier neural operator (IAFNO) with diffusion model. IAFNO can effectively capture the global frequency and structural features, which is crucial for global consistent reconstructions of the denoising process in diffusion models. Furthermore, based on conditional generation from diffusion models, we design an autoregressive framework in DiAFNO to achieve long-term stable predictions of 3D turbulence. The proposed DiAFNO model is systematically trained and tested separately with fixed hyperparameters in several types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT) at Taylor Reynolds number 100, decaying HIT at initial Taylor Reynolds number at 100 and turbulent channel flow at friction Reynolds numbers 395 and 590 with case-specific training at each Reynolds number. The results in the \textit{a posteriori} tests demonstrate that DiAFNO exhibits a significantly higher prediction accuracy in most of the analyzed statistics (such as the velocity spectra, the root-mean-square (RMS) values of both velocity and vorticity, and Reynolds stresses), as compared to the elucidated diffusion model (EDM) and the traditional large-eddy simulation (LES) using dynamic Smagorinsky model (DSM). Although DiAFNO is not optimal in certain statistics, its overall performance is substantially better than all baseline models (EDM and DSM). Ignoring training costs, the well-trained DiAFNO achieves higher inference efficiency than EDM and LES with DSM.

physics.flu-dyn↗

arXiv2025

Uncertainty quantification and stability of neural operators for prediction of three-dimensional turbulence

Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine learning (SciML) models, such as Fourier Neural Operators (FNO), show promise in solving PDEs, but are typically limited to one-step-ahead predictions and often fail over long time horizons, especially in 3D turbulence. This study proposes a framework to assess the reliability of neural operator models in turbulent flows. Using three-dimensional forced homogeneous isotropic turbulence (HIT) as a benchmark, we evaluate models in terms of uncertainty quantification (UQ), error propagation, and sensitivity to initial perturbations. Statistical tools such as error distribution analysis and autocorrelation functions (ACF) are used to assess predictive robustness and temporal coherence. Our proposed model, the factorized-implicit FNO (F-IFNO), improves long-term stability and accuracy by incorporating implicit factorization into the prediction process. It outperforms conventional LES and other FNO-based models in balancing accuracy, stability, and efficiency. The results highlight the importance of prediction constraints, time interval selection, and UQ in developing robust neural operator frameworks for turbulent systems.

physics.flu-dyn↗

arXiv2025

Machine-learning-based simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator framework

Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator (HUFNO) framework. The newly proposed HUFNO model integrates the strengths of both the convolutional neural network (CNN) and Fourier neural operator (FNO) in a novel way that the FNO is applied in the periodic directions of the flow field while the non-periodicity is handled by the CNN-based U-Net framework. In the numerical tests, compared to the original FNO and the U-Net framework, the HUFNO model shows a higher accuracy in the predictions of the velocity field and Reynolds stresses. Further numerical experiments in the LES show that the HUFNO framework outperforms the traditional Smagorinsky (SMAG) model and the wall-adapted local eddy-viscosity (WALE) model in the predictions of the turbulence statistics, the energy spectrum, the invariant characteristics of velocity gradients, the wall stresses and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions, Reynolds number and hill shapes, underscoring its great potentials for the fast prediction of strongly separated turbulent flows over curved boundaries.

physics.flu-dyn↗

arXiv2025

An Implicit Adaptive Fourier Neural Operator for Long-term Predictions of Three-dimensional Turbulence

Long-term prediction of three-dimensional (3D) turbulent flows is one of the most challenging problems for machine learning approaches. Although some existing machine learning approaches such as implicit U-net enhanced Fourier neural operator (IUFNO) have been proven to be capable of achieving stable long-term predictions for turbulent flows, their computational costs are usually high. In this paper, we use the adaptive Fourier neural operator (AFNO) as the backbone to construct a model that can predict 3D turbulence. Furthermore, we employ the implicit iteration to our constructed AFNO and propose the implicit adaptive Fourier neural operator (IAFNO). IAFNO is systematically tested in three types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT), temporally evolving turbulent mixing layer and turbulent channel flow. The numerical results demonstrate that IAFNO is more accurate than IUFNO and the traditional large-eddy simulation using dynamic Smagorinsky model (DSM), while exhibiting greater stability compared to IUFNO. Meanwhile, the AFNO model exhibits instability in numerical simulations. Moreover, the training efficiency of IAFNO is 4 times higher than that of IUFNO, and the number of parameters and GPU memory occupation of IAFNO are only 1/80 and 1/3 of IUFNO, respectively in HIT. In other tests, the improvements are slightly lower but still considerable. These improvements mainly come from patching and self-attention in 3D space. Besides, the well-trained IAFNO is significantly faster than the DSM. The code (and datasets) of the current work can be accessed at https://github.com/yuchi-richard-jiang/IAFNO.

physics.flu-dyn↗

arXiv2024

Implicit factorized transformer approach to fast prediction of turbulent channel flows

Transformer neural operators have recently become an effective approach for surrogate modeling of systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers $\text{Re}_{\tau}\approx 180,395,590$, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods. By analyzing the attention kernels, we elucidate the reasons why IFactFormer-m converges faster and achieves a stable and accurate long-term prediction compared to IFactFormer-o. Code and data are available at: https://github.com/huiyu-2002/IFactFormer-m.

physics.flu-dyn↗

arXiv2024

LESnets (Large-Eddy Simulation nets): Physics-informed neural operator for large-eddy simulation of turbulence

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and shows great potential in a variety of partial differential equations. In this work, we employ physics-informed neural operator, encoding the large-eddy simulation (LES) equations directly into the neural operator for simulating three-dimensional incompressible turbulent flows. We develop the LESnets (Large-Eddy Simulation nets) by adding large-eddy simulation equations to two different data-driven models, including Fourier neural operator (FNO) and implicit Fourier neural operator (IFNO) without using label data. Notably, by leveraging only PDE constraints to learn the spatio-temporal dynamics, LESnets models retain the computational efficiency of data-driven approaches while obviating the necessity for data. Meanwhile, using LES equations as PDE constraints makes it possible to efficiently predict complex turbulence at coarse grids. We investigate the performance of the LESnets models with two standard three-dimensional turbulent flows: decaying homogeneous isotropic turbulence and temporally evolving turbulent mixing layer. In the numerical experiments, the LESnets models show similar accuracy as compared to traditional large-eddy simulation and data-driven models including FNO and IFNO, and exhibits a robust generalization ability to unseen regime of flow fields. By integrating a single set of flow data, the LESnets models can automatically learn the coefficient of the subgrid scale (SGS) model during the training of the neural operator. Moreover, the well-trained LESnets models are significantly faster than traditional LES, and exhibits comparable computational efficiency to the data-driven FNO and IFNO models.

physics.flu-dyn↗

arXiv2024

Prediction of three-dimensional chemically reacting compressible turbulence based on implicit U-Net enhanced Fourier neural operator

The accurate and fast prediction of long-term dynamics of turbulence presents a significant challenge for both traditional numerical simulations and machine learning methods. In recent years, the emergence of neural operators has provided a promising approach to address this issue. The implicit U-Net enhanced Fourier neural operator (IU-FNO) has successfully demonstrated long-term stable predictions for three-dimensional incompressible turbulence. In this study, we extend this method to the three-dimensional chemically reacting compressible turbulence. Numerical results show that the IU-FNO model predicts flow dynamics significantly faster than the traditional dynamic Smagorinsky model (DSM) used in large eddy simulation (LES). In terms of prediction accuracy, the IU-FNO framework outperforms the traditional DSM in predicting the energy spectra of velocity, temperature, and density, the probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of temperature. Therefore, the IU-FNO represents a highly promising approach for predicting chemically reacting compressible turbulence.

physics.flu-dyn↗

arXiv2024

A Priori Error Estimation of Physics-Informed Neural Networks Solving Allen--Cahn and Cahn--Hilliard Equations

Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome this, we employ a novel loss function, Residuals-weighted Region Activation Evaluation (Residuals-RAE), featuring a { pre-training weight update scheme}. { Unlike conventional self-adaptive PINNs where weights evolve simultaneously with network parameters, Residuals-RAE-PINNs computes weights from current residuals before each training step and holds them constant during gradient updates. We establish weight convergence under standard neural network optimization assumptions, which justifies analyzing the converged network with constant weights.} Based on this theoretical framework, we derive the error estimation for PINNs with Residuals-RAE when solving AC and CH equations. {The analysis is aligned with Monte-Carlo sampling for the discretization of integrals, consistent with the numerical experiments.} Numerical experiments on one- and two-dimensional AC and CH systems confirm our theoretical results. Additionally, our analysis reveals that feedforward neural networks with two hidden layers and the tanh activation function bound the approximation errors of the solution, its temporal derivative, and the nonlinear term, constrained by the training loss and the number of collocation points.

math.NA↗

arXiv2023

Parameter Identification for Partial Differential Equations with Spatiotemporal Varying Coefficients

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the resolution of the parameter inverse problem from the observed spatiotemporal data a challenging endeavor. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural network, encompassing a sub-network, as our methodology for parameter identification, and a finite mixture model approach to detect regions of probable parameter variations. Through our scheme, we can precisely ascertain the unknown varying parameters of the complex multi-state system, thereby accomplishing the inversion of the varying parameters. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers' equation with time-varying parameters and the 2D wave equation with a space-varying parameter.

cs.LG↗

arXiv2022

Automatic Depression Detection: An Emotional Audio-Textual Corpus and a GRU/BiLSTM-based Model

Depression is a global mental health problem, the worst case of which can lead to suicide. An automatic depression detection system provides great help in facilitating depression self-assessment and improving diagnostic accuracy. In this work, we propose a novel depression detection approach utilizing speech characteristics and linguistic contents from participants' interviews. In addition, we establish an Emotional Audio-Textual Depression Corpus (EATD-Corpus) which contains audios and extracted transcripts of responses from depressed and non-depressed volunteers. To the best of our knowledge, EATD-Corpus is the first and only public depression dataset that contains audio and text data in Chinese. Evaluated on two depression datasets, the proposed method achieves the state-of-the-art performances. The outperforming results demonstrate the effectiveness and generalization ability of the proposed method. The source code and EATD-Corpus are available at https://github.com/speechandlanguageprocessing/ICASSP2022-Depression.

eess.AS↗