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Recent advances in video diffusion models have enabled realistic and controllable human image animation with temporal coherence. Although generating reasonable results, existing methods often overlook the need for regional supervision in crucial areas such as the face and hands, and neglect the explicit modeling for motion blur, leading to unrealistic low-quality synthesis. To address these limitations, we first leverage regional supervision for detailed regions to enhance face and hand faithfulness. Second, we model the motion blur explicitly to further improve the appearance quality. Third, we explore novel training strategies for high-resolution human animation to improve the overall fidelity. Experimental results demonstrate that our proposed method outperforms state-of-the-art approaches, achieving significant improvements upon the strongest baseline by more than 21.0% and 57.4% in terms of reconstruction precision (L1) and perceptual quality (FVD) on HumanDance dataset. Code and model will be made available.

Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered.

We propose X-Portrait, an innovative conditional diffusion model tailored for generating expressive and temporally coherent portrait animation. Specifically, given a single portrait as appearance reference, we aim to animate it with motion derived from a driving video, capturing both highly dynamic and subtle facial expressions along with wide-range head movements. As its core, we leverage the generative prior of a pre-trained diffusion model as the rendering backbone, while achieve fine-grained head pose and expression control with novel controlling signals within the framework of ControlNet. In contrast to conventional coarse explicit controls such as facial landmarks, our motion control module is learned to interpret the dynamics directly from the original driving RGB inputs. The motion accuracy is further enhanced with a patch-based local control module that effectively enhance the motion attention to small-scale nuances like eyeball positions. Notably, to mitigate the identity leakage from the driving signals, we train our motion control modules with scaling-augmented cross-identity images, ensuring maximized disentanglement from the appearance reference modules. Experimental results demonstrate the universal effectiveness of X-Portrait across a diverse range of facial portraits and expressive driving sequences, and showcase its proficiency in generating captivating portrait animations with consistently maintained identity characteristics., Comment: SIGGRAPH 2024

The generation of emotional talking faces from a single portrait image remains a significant challenge. The simultaneous achievement of expressive emotional talking and accurate lip-sync is particularly difficult, as expressiveness is often compromised for the accuracy of lip-sync. As widely adopted by many prior works, the LSTM network often fails to capture the subtleties and variations of emotional expressions. To address these challenges, we introduce DREAM-Talk, a two-stage diffusion-based audio-driven framework, tailored for generating diverse expressions and accurate lip-sync concurrently. In the first stage, we propose EmoDiff, a novel diffusion module that generates diverse highly dynamic emotional expressions and head poses in accordance with the audio and the referenced emotion style. Given the strong correlation between lip motion and audio, we then refine the dynamics with enhanced lip-sync accuracy using audio features and emotion style. To this end, we deploy a video-to-video rendering module to transfer the expressions and lip motions from our proxy 3D avatar to an arbitrary portrait. Both quantitatively and qualitatively, DREAM-Talk outperforms state-of-the-art methods in terms of expressiveness, lip-sync accuracy and perceptual quality., Comment: Project Page at https://magic-research.github.io/dream-talk/

We present DiffPortrait3D, a conditional diffusion model that is capable of synthesizing 3D-consistent photo-realistic novel views from as few as a single in-the-wild portrait. Specifically, given a single RGB input, we aim to synthesize plausible but consistent facial details rendered from novel camera views with retained both identity and facial expression. In lieu of time-consuming optimization and fine-tuning, our zero-shot method generalizes well to arbitrary face portraits with unposed camera views, extreme facial expressions, and diverse artistic depictions. At its core, we leverage the generative prior of 2D diffusion models pre-trained on large-scale image datasets as our rendering backbone, while the denoising is guided with disentangled attentive control of appearance and camera pose. To achieve this, we first inject the appearance context from the reference image into the self-attention layers of the frozen UNets. The rendering view is then manipulated with a novel conditional control module that interprets the camera pose by watching a condition image of a crossed subject from the same view. Furthermore, we insert a trainable cross-view attention module to enhance view consistency, which is further strengthened with a novel 3D-aware noise generation process during inference. We demonstrate state-of-the-art results both qualitatively and quantitatively on our challenging in-the-wild and multi-view benchmarks.

In this work, we propose MagicPose, a diffusion-based model for 2D human pose and facial expression retargeting. Specifically, given a reference image, we aim to generate a person's new images by controlling the poses and facial expressions while keeping the identity unchanged. To this end, we propose a two-stage training strategy to disentangle human motions and appearance (e.g., facial expressions, skin tone and dressing), consisting of (1) the pre-training of an appearance-control block and (2) learning appearance-disentangled pose control. Our novel design enables robust appearance control over generated human images, including body, facial attributes, and even background. By leveraging the prior knowledge of image diffusion models, MagicPose generalizes well to unseen human identities and complex poses without the need for additional fine-tuning. Moreover, the proposed model is easy to use and can be considered as a plug-in module/extension to Stable Diffusion. The code is available at: https://github.com/Boese0601/MagicDance, Comment: Accepted by ICML 2024. MagicPose and MagicDance are the same project. Website:https://boese0601.github.io/magicdance/ Code:https://github.com/Boese0601/MagicDance

We study the problem of 3D-aware full-body human generation, aiming at creating animatable human avatars with high-quality textures and geometries. Generally, two challenges remain in this field: i) existing methods struggle to generate geometries with rich realistic details such as the wrinkles of garments; ii) they typically utilize volumetric radiance fields and neural renderers in the synthesis process, making high-resolution rendering non-trivial. To overcome these problems, we propose GETAvatar, a Generative model that directly generates Explicit Textured 3D meshes for animatable human Avatar, with photo-realistic appearance and fine geometric details. Specifically, we first design an articulated 3D human representation with explicit surface modeling, and enrich the generated humans with realistic surface details by learning from the 2D normal maps of 3D scan data. Second, with the explicit mesh representation, we can use a rasterization-based renderer to perform surface rendering, allowing us to achieve high-resolution image generation efficiently. Extensive experiments demonstrate that GETAvatar achieves state-of-the-art performance on 3D-aware human generation both in appearance and geometry quality. Notably, GETAvatar can generate images at 512x512 resolution with 17FPS and 1024x1024 resolution with 14FPS, improving upon previous methods by 2x. Our code and models will be available., Comment: Accepted by ICCV2023. Project Page: https://getavatar.github.io/

Deep learning (DL) has gained popularity in recent years as an effective tool for classifying the current health and predicting the future of industrial equipment. However, most DL models have black-box components with an underlying structure that is too complex to be interpreted and explained to human users. This presents significant challenges when deploying these models for safety-critical maintenance tasks, where non-technical personnel often need to have complete trust in the recommendations these models give. To address these challenges, we utilize a convolutional neural network (CNN) with Gradient-weighted Class Activation Mapping (Grad-CAM) activation map visualizations to form an interpretable DL method for classifying bearing faults. After the model training process, we apply Grad-CAM to identify a training sample's feature importance and to form a library of diagnosis knowledge (or health library) containing training samples with annotated feature maps. During the model evaluation process, the proposed approach retrieves prediction basis samples from the health library according to the similarity of the feature importance. The proposed method can be easily applied to any CNN model without modifying the model architecture, and our experimental results show that this method can select prediction basis samples that are intuitively and physically meaningful, improving the model's trustworthiness for human users.

We present OmniAvatar, a novel geometry-guided 3D head synthesis model trained from in-the-wild unstructured images that is capable of synthesizing diverse identity-preserved 3D heads with compelling dynamic details under full disentangled control over camera poses, facial expressions, head shapes, articulated neck and jaw poses. To achieve such high level of disentangled control, we first explicitly define a novel semantic signed distance function (SDF) around a head geometry (FLAME) conditioned on the control parameters. This semantic SDF allows us to build a differentiable volumetric correspondence map from the observation space to a disentangled canonical space from all the control parameters. We then leverage the 3D-aware GAN framework (EG3D) to synthesize detailed shape and appearance of 3D full heads in the canonical space, followed by a volume rendering step guided by the volumetric correspondence map to output into the observation space. To ensure the control accuracy on the synthesized head shapes and expressions, we introduce a geometry prior loss to conform to head SDF and a control loss to conform to the expression code. Further, we enhance the temporal realism with dynamic details conditioned upon varying expressions and joint poses. Our model can synthesize more preferable identity-preserved 3D heads with compelling dynamic details compared to the state-of-the-art methods both qualitatively and quantitatively. We also provide an ablation study to justify many of our system design choices.

While substantial progresses have been made in automated 2D portrait stylization, admirable 3D portrait stylization from a single user photo remains to be an unresolved challenge. One primary obstacle here is the lack of high quality stylized 3D training data. In this paper, we propose a novel framework \emph{AgileGAN3D} that can produce 3D artistically appealing and personalized portraits with detailed geometry. New stylization can be obtained with just a few (around 20) unpaired 2D exemplars. We achieve this by first leveraging existing 2D stylization capabilities, \emph{style prior creation}, to produce a large amount of augmented 2D style exemplars. These augmented exemplars are generated with accurate camera pose labels, as well as paired real face images, which prove to be critical for the downstream 3D stylization task. Capitalizing on the recent advancement of 3D-aware GAN models, we perform \emph{guided transfer learning} on a pretrained 3D GAN generator to produce multi-view-consistent stylized renderings. In order to achieve 3D GAN inversion that can preserve subject's identity well, we incorporate \emph{multi-view consistency loss} in the training of our encoder. Our pipeline demonstrates strong capability in turning user photos into a diverse range of 3D artistic portraits. Both qualitative results and quantitative evaluations have been conducted to show the superior performance of our method. Code and pretrained models will be released for reproduction purpose.

Synthesis and reconstruction of 3D human head has gained increasing interests in computer vision and computer graphics recently. Existing state-of-the-art 3D generative adversarial networks (GANs) for 3D human head synthesis are either limited to near-frontal views or hard to preserve 3D consistency in large view angles. We propose PanoHead, the first 3D-aware generative model that enables high-quality view-consistent image synthesis of full heads in $360^\circ$ with diverse appearance and detailed geometry using only in-the-wild unstructured images for training. At its core, we lift up the representation power of recent 3D GANs and bridge the data alignment gap when training from in-the-wild images with widely distributed views. Specifically, we propose a novel two-stage self-adaptive image alignment for robust 3D GAN training. We further introduce a tri-grid neural volume representation that effectively addresses front-face and back-head feature entanglement rooted in the widely-adopted tri-plane formulation. Our method instills prior knowledge of 2D image segmentation in adversarial learning of 3D neural scene structures, enabling compositable head synthesis in diverse backgrounds. Benefiting from these designs, our method significantly outperforms previous 3D GANs, generating high-quality 3D heads with accurate geometry and diverse appearances, even with long wavy and afro hairstyles, renderable from arbitrary poses. Furthermore, we show that our system can reconstruct full 3D heads from single input images for personalized realistic 3D avatars., Comment: CVPR 2023. Project Page:https://sizhean.github.io/panohead

Unsupervised generation of 3D-aware clothed humans with various appearances and controllable geometries is important for creating virtual human avatars and other AR/VR applications. Existing methods are either limited to rigid object modeling, or not generative and thus unable to generate high-quality virtual humans and animate them. In this work, we propose AvatarGen, the first method that enables not only geometry-aware clothed human synthesis with high-fidelity appearances but also disentangled human animation controllability, while only requiring 2D images for training. Specifically, we decompose the generative 3D human synthesis into pose-guided mapping and canonical representation with predefined human pose and shape, such that the canonical representation can be explicitly driven to different poses and shapes with the guidance of a 3D parametric human model SMPL. AvatarGen further introduces a deformation network to learn non-rigid deformations for modeling fine-grained geometric details and pose-dependent dynamics. To improve the geometry quality of the generated human avatars, it leverages the signed distance field as geometric proxy, which allows more direct regularization from the 3D geometric priors of SMPL. Benefiting from these designs, our method can generate animatable 3D human avatars with high-quality appearance and geometry modeling, significantly outperforming previous 3D GANs. Furthermore, it is competent for many applications, e.g., single-view reconstruction, re-animation, and text-guided synthesis/editing. Code and pre-trained model will be available at http://jeff95.me/projects/avatargen.html., Comment: First two authors contributed equally. Our code and models will be available at http://jeff95.me/projects/avatargen.html. arXiv admin note: substantial text overlap with arXiv:2208.00561

We focus on the task of estimating a physically plausible articulated human motion from monocular video. Existing approaches that do not consider physics often produce temporally inconsistent output with motion artifacts, while state-of-the-art physics-based approaches have either been shown to work only in controlled laboratory conditions or consider simplified body-ground contact limited to feet. This paper explores how these shortcomings can be addressed by directly incorporating a fully-featured physics engine into the pose estimation process. Given an uncontrolled, real-world scene as input, our approach estimates the ground-plane location and the dimensions of the physical body model. It then recovers the physical motion by performing trajectory optimization. The advantage of our formulation is that it readily generalizes to a variety of scenes that might have diverse ground properties and supports any form of self-contact and contact between the articulated body and scene geometry. We show that our approach achieves competitive results with respect to existing physics-based methods on the Human3.6M benchmark, while being directly applicable without re-training to more complex dynamic motions from the AIST benchmark and to uncontrolled internet videos., Comment: Accepted to CVPR 2022

Although existing face anti-spoofing (FAS) methods achieve high accuracy in intra-domain experiments, their effects drop severely in cross-domain scenarios because of poor generalization. Recently, multifarious techniques have been explored, such as domain generalization and representation disentanglement. However, the improvement is still limited by two issues: 1) It is difficult to perfectly map all faces to a shared feature space. If faces from unknown domains are not mapped to the known region in the shared feature space, accidentally inaccurate predictions will be obtained. 2) It is hard to completely consider various spoof traces for disentanglement. In this paper, we propose a Feature Generation and Hypothesis Verification framework to alleviate the two issues. Above all, feature generation networks which generate hypotheses of real faces and known attacks are introduced for the first time in the FAS task. Subsequently, two hypothesis verification modules are applied to judge whether the input face comes from the real-face space and the real-face distribution respectively. Furthermore, some analyses of the relationship between our framework and Bayesian uncertainty estimation are given, which provides theoretical support for reliable defense in unknown domains. Experimental results show our framework achieves promising results and outperforms the state-of-the-art approaches on extensive public datasets., Comment: Accepted by AAAI 2022

We present neural radiance fields for rendering and temporal (4D) reconstruction of humans in motion (H-NeRF), as captured by a sparse set of cameras or even from a monocular video. Our approach combines ideas from neural scene representation, novel-view synthesis, and implicit statistical geometric human representations, coupled using novel loss functions. Instead of learning a radiance field with a uniform occupancy prior, we constrain it by a structured implicit human body model, represented using signed distance functions. This allows us to robustly fuse information from sparse views and generalize well beyond the poses or views observed in training. Moreover, we apply geometric constraints to co-learn the structure of the observed subject -- including both body and clothing -- and to regularize the radiance field to geometrically plausible solutions. Extensive experiments on multiple datasets demonstrate the robustness and the accuracy of our approach, its generalization capabilities significantly outside a small training set of poses and views, and statistical extrapolation beyond the observed shape.

We present imGHUM, the first holistic generative model of 3D human shape and articulated pose, represented as a signed distance function. In contrast to prior work, we model the full human body implicitly as a function zero-level-set and without the use of an explicit template mesh. We propose a novel network architecture and a learning paradigm, which make it possible to learn a detailed implicit generative model of human pose, shape, and semantics, on par with state-of-the-art mesh-based models. Our model features desired detail for human models, such as articulated pose including hand motion and facial expressions, a broad spectrum of shape variations, and can be queried at arbitrary resolutions and spatial locations. Additionally, our model has attached spatial semantics making it straightforward to establish correspondences between different shape instances, thus enabling applications that are difficult to tackle using classical implicit representations. In extensive experiments, we demonstrate the model accuracy and its applicability to current research problems., Comment: ICCV 2021

3D ED is an effective technique to determine the structures of submicron- or nano-sized crystals. In this paper, we implemented energy-filtered 3D ED using a Gatan Energy Filter (GIF) in both selected area electron diffraction mode and micro/nanoprobe mode. We explained the setup in detail, which improves the accessibility of energy-filtered 3D ED experiments as more electron microscopes are equipped with a GIF than an in-column filter. We also proposed a crystal tracking method in STEM mode using live HAADF image stream. This method enables us to collect energy-filtered 3D ED datasets in STEM mode with a larger tilt range without foregoing any frames. In order to compare the differences between energy-filtered 3D ED and normal 3D ED data, three crystalline samples have been studied in detail. We observed that the final R1 will improve 20% to 30% for energy-filtered datasets compared with unfiltered datasets and the structure became more reasonable. We also discussed the possible reasons that lead to the improvement.

3D object detection is an important task in computer vision. Most existing methods require a large number of high-quality 3D annotations, which are expensive to collect. Especially for outdoor scenes, the problem becomes more severe due to the sparseness of the point cloud and the complexity of urban scenes. Semi-supervised learning is a promising technique to mitigate the data annotation issue. Inspired by this, we propose a novel semi-supervised framework based on pseudo-labeling for outdoor 3D object detection tasks. We design the Adaptive Class Confidence Selection module (ACCS) to generate high-quality pseudo-labels. Besides, we propose Holistic Point Cloud Augmentation (HPCA) for unlabeled data to improve robustness. Experiments on the KITTI benchmark demonstrate the effectiveness of our method., Comment: Accepted at International Conference on Image Processing (ICIP 2021)

Machine learning classification techniques have been used widely to recognize the feasible design domain and discover hidden patterns in engineering design. An accurate classification model needs a large dataset; however, generating a large dataset is costly for complex simulation-based problems. After training by a small dataset, surrogate models can generate a large pseudo dataset efficiently. Errors, however, may be introduced by surrogate modeling. This paper investigates the mutual effect of a large pseudo dataset and surrogate modeling uncertainty. Four widely used methods, i.e., Naive Bayes classifier, support vector machine, random forest regression, and artificial neural network for classification, are studied on four benchmark problems. Kriging is used as the basic surrogate model method. The results show that a large pseudo dataset improves the classification accuracy, which depends on both design problems and classification algorithms. Except for the Naive Bayes, the other three methods are recommended for using pseudo data to improve classification performance. Also, a wind turbine design problem is used to illustrate the effect of the pseudo dataset on feasible subspace recognition. The large pseudo dataset improves the recognized subspace bound greatly, which can be reproduced by classification models well except for the Naive Bayes classifier. Under the uncertainty of surrogate modeling, the random forest presents high robustness to recognize the feasible design domain bound, while the artificial neural network demonstrates a high sensitivity to uncertainty with the recognized bound deteriorated., Comment: 28 pages, 14 figures, 6 tables

To relieve the computational cost of design evaluations using expensive finite element simulations, surrogate models have been widely applied in computer-aided engineering design. Machine learning algorithms (MLAs) have been implemented as surrogate models due to their capability of learning the complex interrelations between the design variables and the response from big datasets. Typically, an MLA regression model contains model parameters and hyperparameters. The model parameters are obtained by fitting the training data. Hyperparameters, which govern the model structures and the training processes, are assigned by users before training. There is a lack of systematic studies on the effect of hyperparameters on the accuracy and robustness of the surrogate model. In this work, we proposed to establish a hyperparameter optimization (HOpt) framework to deepen our understanding of the effect. Four frequently used MLAs, namely Gaussian Process Regression (GPR), Support Vector Machine (SVM), Random Forest Regression (RFR), and Artificial Neural Network (ANN), are tested on four benchmark examples. For each MLA model, the model accuracy and robustness before and after the HOpt are compared. The results show that HOpt can generally improve the performance of the MLA models in general. HOpt leads to few improvements in the MLAs accuracy and robustness for complex problems, which are featured by high-dimensional mixed-variable design space. The HOpt is recommended for the design problems with intermediate complexity. We also investigated the additional computational costs incurred by HOpt. The training cost is closely related to the MLA architecture. After HOpt, the training cost of ANN and RFR is increased more than that of the GPR and SVM. To sum up, this study benefits the selection of HOpt method for the different types of design problems based on their complexity., Comment: 43 pages, 15 figures,8 tables, Accepted by the Computer-aided design

Monocular 3D human pose and shape estimation is challenging due to the many degrees of freedom of the human body and thedifficulty to acquire training data for large-scale supervised learning in complex visual scenes. In this paper we present practical semi-supervised and self-supervised models that support training and good generalization in real-world images and video. Our formulation is based on kinematic latent normalizing flow representations and dynamics, as well as differentiable, semantic body part alignment loss functions that support self-supervised learning. In extensive experiments using 3D motion capture datasets like CMU, Human3.6M, 3DPW, or AMASS, as well as image repositories like COCO, we show that the proposed methods outperform the state of the art, supporting the practical construction of an accurate family of models based on large-scale training with diverse and incompletely labeled image and video data.

A DigitalMicrograph script InsteaDMatic has been developed to facilitate rapid automated continuous rotation electron diffraction (cRED) data acquisition. The script coordinates microscope functions, such as stage rotation, camera functions relevant for data collection, and stores the experiment metadata. The script is compatible with any microscope that can be controlled by DigitalMicrograph and has been tested on both JEOL and Thermo Fisher Scientific microscopes. A proof-of-concept has been performed through employing InsteaDMatic for data collection and structure determination of a ZSM-5 zeolite. The influence of illumination settings and electron dose rate on the quality of diffraction data, unit cell determination and structure solution has been investigated in order to optimize the data acquisition procedure.

The model of ideal fluid flow around a cylindrical obstacle exhibits a long-established physical picture where originally straight streamlines will be deflected over the whole space by the obstacle. As inspired by transformation optics and metamaterials, recent theories have proposed the concept of fluid cloaking able to recover the straight streamlines as if the obstacle does not exist. However, such a cloak, similar to all previous transformation-optics-based devices, relies on complex metamaterials, being difficult to implement. Here we deploy the theory of scattering cancellation and report on the experimental realization of a fluid-flow cloak without metamaterials. This cloak is realized by engineering the geometry of the fluid channel, which effectively cancels the dipole-like scattering of the obstacle. The cloaking effect is demonstrated via direct observation of the recovered straight streamlines in the fluid flow with injected dyes. Our work sheds new light on conventional fluid control and may find applications in microfluidic devices., Comment: 12 pages, 4 figures

Facial animation is one of the most challenging problems in computer graphics, and it is often solved using linear heuristics like blend-shape rigging. More expressive approaches like physical simulation have emerged, but these methods are very difficult to tune, especially when simulating a real actor's face. We propose to use a simple finite element simulation approach for face animation, and present a novel method for recovering the required simulation parameters in order to best match a real actor's face motion. Our method involves reconstructing a very small number of head poses of the actor in 3D, where the head poses span different configurations of force directions due to gravity. Our algorithm can then automatically recover both the gravity-free rest shape of the face as well as the spatially-varying physical material stiffness such that a forward simulation will match the captured targets as closely as possible. As a result, our system can produce actor-specific, physical parameters that can be immediately used in recent physical simulation methods for faces. Furthermore, as the simulation results depend heavily on the chosen spatial layout of material clusters, we analyze and compare different spatial layouts.

In-depth analyses of existing direct numerical simulations (DNS) data from various sources supported a logical and important classification of generic turbulent boundary layers (TBL), namely Type-A, -B and -C TBL, based on distribution patterns of time-averaged wall-shear stress. Among these types, Type-A TBL and its related law, as represented by the DNS data of turbulence on a zero-pressure-gradient semi-infinite flat-plate, was investigated in terms of analytical formulations of velocity independent on Reynolds ( ) number. With reference to the analysis from von Karman in developing the conventional law-of-the-wall, the current study first physically distinguished the time-averaged local scale used by von Karman from the ensemble-averaged scale defined in the paper, and then derived the governing equations with the -independency under the ensemble-averaged scales. Based on indicator function (IDF) and TBL thickness, the sublayer partitions were rigorously defined. The analytical formulations for entire TBL, namely the complete law-of-the-wall, were established, including the formula in inner, buffer, semi-logarithmic (semi-log) and wake layer. The researches were featured by introducing the general damping and enhancing functions (GDF and GEF) and applying these functions to both linear and logarithmic coordinates. These law formulations were proved uniform and consistent in time-averaged local and ensemble-averaged scales, which were validated by the existing DNS and experiment data. Based on the similarity of relevant properly-scaled governing equations, the law formulations were logically reasoned being applicable to the temperature in Type-A thermal TBL. The findings advance the current understandings of the conventional TBL theory and its well-known foundations of law-of-the-wall.

Systematic study of the existing statistical data from direct numerical simulations (DNS) lead to a logical and important classification of generic turbulent boundary layers (TBL), namely Type A,B and C TBL, based on the distribution patterns of time averaged wall shear stress. Among these three types, Type A and B TBLs are investigated in terms of its universal statistical laws of velocity and temperature with independency on both Reynolds (Re) and Prandtl (Pr) numbers. With reference to the analysis by von Karman in developing the conventional law of the wall for Type A TBL, the current study first physically distinguishes the time averaged local velocity scale from the ensemble averaged velocity scale, and properly defines the TBL temperature scale based on wall heat flux, similar to the well known frictional velocity scale based on wall shear stress. The unified law of the wall formulations are then derived for the inner layer of Type A and B thermal TBLs using these scales. The formulations are constructed by introducing the general damping and enhancing functions in inner layer, and further, these functions are extended to logarithmic coordinate based on the multiscale characteristics of TBL velocity profiles. The validations of the law are conducted both by the DNS guided near wall integration of Type B TBL governing equations, which uncovered the Re and Pr independency mechanisms of the law. The research advances the current understandings of the conventional TBL theory and develop the complete analytical forms of law of the wall for Type A and B TBLs, including inner layer, transition layer, logarithmic layer and wake layer.