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Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-by-element construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-by-element approach implies reasonably low training costs.

While the voxel-based methods have achieved promising results for multi-person 3D pose estimation from multi-cameras, they suffer from heavy computation burdens, especially for large scenes. We present Faster VoxelPose to address the challenge by re-projecting the feature volume to the three two-dimensional coordinate planes and estimating X, Y, Z coordinates from them separately. To that end, we first localize each person by a 3D bounding box by estimating a 2D box and its height based on the volume features projected to the xy-plane and z-axis, respectively. Then for each person, we estimate partial joint coordinates from the three coordinate planes separately which are then fused to obtain the final 3D pose. The method is free from costly 3D-CNNs and improves the speed of VoxelPose by ten times and meanwhile achieves competitive accuracy as the state-of-the-art methods, proving its potential in real-time applications.

Differentiable renderers provide a direct mathematical link between an object's 3D representation and images of that object. In this work, we develop an approximate differentiable renderer for a compact, interpretable representation, which we call Fuzzy Metaballs. Our approximate renderer focuses on rendering shapes via depth maps and silhouettes. It sacrifices fidelity for utility, producing fast runtimes and high-quality gradient information that can be used to solve vision tasks. Compared to mesh-based differentiable renderers, our method has forward passes that are 5x faster and backwards passes that are 30x faster. The depth maps and silhouette images generated by our method are smooth and defined everywhere. In our evaluation of differentiable renderers for pose estimation, we show that our method is the only one comparable to classic techniques. In shape from silhouette, our method performs well using only gradient descent and a per-pixel loss, without any surrogate losses or regularization. These reconstructions work well even on natural video sequences with segmentation artifacts. Project page: //leonidk.github.io/fuzzy-metaballs

Image-based volumetric humans using pixel-aligned features promise generalization to unseen poses and identities. Prior work leverages global spatial encodings and multi-view geometric consistency to reduce spatial ambiguity. However, global encodings often suffer from overfitting to the distribution of the training data, and it is difficult to learn multi-view consistent reconstruction from sparse views. In this work, we investigate common issues with existing spatial encodings and propose a simple yet highly effective approach to modeling high-fidelity volumetric humans from sparse views. One of the key ideas is to encode relative spatial 3D information via sparse 3D keypoints. This approach is robust to the sparsity of viewpoints and cross-dataset domain gap. Our approach outperforms state-of-the-art methods for head reconstruction. On human body reconstruction for unseen subjects, we also achieve performance comparable to prior work that uses a parametric human body model and temporal feature aggregation. Our experiments show that a majority of errors in prior work stem from an inappropriate choice of spatial encoding and thus we suggest a new direction for high-fidelity image-based human modeling. //markomih.github.io/KeypointNeRF

Object reconstruction from 3D point clouds has achieved impressive progress in the computer vision and computer graphics research field. However, reconstruction from time-varying point clouds (a.k.a. 4D point clouds) is generally overlooked. In this paper, we propose a new network architecture, namely RFNet-4D, that jointly reconstruct objects and their motion flows from 4D point clouds. The key insight is that simultaneously performing both tasks via learning spatial and temporal features from a sequence of point clouds can leverage individual tasks, leading to improved overall performance. To prove this ability, we design a temporal vector field learning module using unsupervised learning approach for flow estimation, leveraged by supervised learning of spatial structures for object reconstruction. Extensive experiments and analyses on benchmark dataset validated the effectiveness and efficiency of our method. As shown in experimental results, our method achieves state-of-the-art performance on both flow estimation and object reconstruction while performing much faster than existing methods in both training and inference. Our code and data are available at //github.com/hkust-vgd/RFNet-4D

Recent advanced studies have spent considerable human efforts on optimizing network architectures for stereo matching but hardly achieved both high accuracy and fast inference speed. To ease the workload in network design, neural architecture search (NAS) has been applied with great success to various sparse prediction tasks, such as image classification and object detection. However, existing NAS studies on the dense prediction task, especially stereo matching, still cannot be efficiently and effectively deployed on devices of different computing capabilities. To this end, we propose to train an elastic and accurate network for stereo matching (EASNet) that supports various 3D architectural settings on devices with different computing capabilities. Given the deployment latency constraint on the target device, we can quickly extract a sub-network from the full EASNet without additional training while the accuracy of the sub-network can still be maintained. Extensive experiments show that our EASNet outperforms both state-of-the-art human-designed and NAS-based architectures on Scene Flow and MPI Sintel datasets in terms of model accuracy and inference speed. Particularly, deployed on an inference GPU, EASNet achieves a new SOTA 0.73 EPE on the Scene Flow dataset with 100 ms, which is 4.5$\times$ faster than LEAStereo with a better quality model.

We present a new Integrated Finite Element Neural Network framework (I-FENN), with the objective to accelerate the numerical solution of nonlinear computational mechanics problems. We leverage the swift predictive capability of neural networks (NNs) and we embed them inside the finite element stiffness function, to compute element-level state variables and their derivatives within a nonlinear, iterative numerical solution. This process is conducted jointly with conventional finite element methods that involve shape functions: the NN receives input data that resembles the material point deformation and its output is used to construct element-level field variables such as the element Jacobian matrix and residual vector. Here we introduce I-FENN to the continuum damage analysis of quasi-brittle materials, and we establish a new non-local gradient-based damage framework which operates at the cost of a local damage approach. First, we develop a physics informed neural network (PINN) to resemble the non-local gradient model and then we train the neural network offline. The network learns to predict the non-local equivalent strain at each material point, as well as its derivative with respect to the local strain. Then, the PINN is integrated in the element stiffness definition and conducts the local to non-local strain transformation, whereas the two PINN outputs are used to construct the element Jacobian matrix and residual vector. This process is carried out within the nonlinear solver, until numerical convergence is achieved. The resulting method bears the computational cost of the conventional local damage approach, but ensures mesh-independent results and a diffused non-local strain and damage profile. As a result, the proposed method tackles the vital drawbacks of both the local and non-local gradient method, respectively being the mesh-dependence and additional computational cost.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids (in Lagrangian descriptions). Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities. It is a potential alternative approach to understanding complex fluid mechanics, such as turbulence, that are difficult to model using traditional methods of mathematical physics.

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our first contribution is to formulate geometric perception as an optimization problem that jointly optimizes the feature descriptor and the geometric models given a large corpus of visual measurements (e.g., images, point clouds). Under this optimization formulation, we show that two important streams of research in vision, namely robust model fitting and deep feature learning, correspond to optimizing one block of the unknown variables while fixing the other block. This analysis naturally leads to our second contribution -- the SGP algorithm that performs alternating minimization to solve the joint optimization. SGP iteratively executes two meta-algorithms: a teacher that performs robust model fitting given learned features to generate geometric pseudo-labels, and a student that performs deep feature learning under noisy supervision of the pseudo-labels. As a third contribution, we apply SGP to two perception problems on large-scale real datasets, namely relative camera pose estimation on MegaDepth and point cloud registration on 3DMatch. We demonstrate that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.

In this paper, we present an accurate and scalable approach to the face clustering task. We aim at grouping a set of faces by their potential identities. We formulate this task as a link prediction problem: a link exists between two faces if they are of the same identity. The key idea is that we find the local context in the feature space around an instance (face) contains rich information about the linkage relationship between this instance and its neighbors. By constructing sub-graphs around each instance as input data, which depict the local context, we utilize the graph convolution network (GCN) to perform reasoning and infer the likelihood of linkage between pairs in the sub-graphs. Experiments show that our method is more robust to the complex distribution of faces than conventional methods, yielding favorably comparable results to state-of-the-art methods on standard face clustering benchmarks, and is scalable to large datasets. Furthermore, we show that the proposed method does not need the number of clusters as prior, is aware of noises and outliers, and can be extended to a multi-view version for more accurate clustering accuracy.