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Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

Wind turbine wake modelling is of crucial importance to accurate resource assessment, to layout optimisation, and to the operational control of wind farms. This work proposes a surrogate model for the representation of wind turbine wakes based on a state-of-the-art graph representation learning method termed a graph neural network. The proposed end-to-end deep learning model operates directly on unstructured meshes and has been validated against high-fidelity data, demonstrating its ability to rapidly make accurate 3D flow field predictions for various inlet conditions and turbine yaw angles. The specific graph neural network model employed here is shown to generalise well to unseen data and is less sensitive to over-smoothing compared to common graph neural networks. A case study based upon a real world wind farm further demonstrates the capability of the proposed approach to predict farm scale power generation. Moreover, the proposed graph neural network framework is flexible and highly generic and as formulated here can be applied to any steady state computational fluid dynamics simulations on unstructured meshes., Comment: 20 pages, 12 figures

Materials that are capable of extracting gold from complex sources, especially electronic waste (e-waste) with high efficiency are needed for gold resource sustainability and effective e-waste recycling. However, it remains challenging to achieve high extraction capacity to trace amount of gold, and precise selectivity to gold over a wide range of complex co-existing elements. Here we report a reduced graphene oxide (rGO) material that has an ultrahigh extraction capacity for trace amounts of gold (1,850 mg/g and 1,180 mg/g to 10 ppm and 1 ppm gold). The excellent gold extraction behavior is accounted to the graphene areas and oxidized regions of rGO. The graphene areas spontaneously reduce gold ions to metallic gold, and the oxidized regions provide a good dispersibility so that efficient adsorption and reduction of gold ions by the graphene area can be realized. The rGO is also highly selective to gold ions. By controlling the protonation process of the functional groups on the oxidized regions of rGO, it shows an exclusive gold extraction without adsorption of 14 co-existing elements seen in e-waste. These discoveries are further exploited in highly efficient, continuous gold recycling from e-waste with good scalability and economic viability, as exemplified by extracting gold from e-waste using a rGO membrane based flow-through process.

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., Comment: 27 pages, 14 figures

Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion, and thus struggle if applied to fluid motion estimation directly. Further, optical flow methods only focus on two consecutive frames without utilising historical temporal information, while the fluid motion (velocity field) can be considered a continuous trajectory constrained by time-dependent partial differential equations (PDEs). This discrepancy has the potential to induce physically inconsistent estimations. Here we propose an unsupervised learning based prediction-correction scheme for fluid flow estimation. An estimate is first given by a PDE-constrained optical flow predictor, which is then refined by a physical based corrector. The proposed approach outperforms optical flow methods and shows competitive results compared to existing supervised learning based methods on a benchmark dataset. Furthermore, the proposed approach can generalize to complex real-world fluid scenarios where ground truth information is effectively unknowable. Finally, experiments demonstrate that the physical corrector can refine flow estimates by mimicking the operator splitting method commonly utilised in fluid dynamical simulation., Comment: published at ICML 2022

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.

Mediation analysis assesses the extent to which the exposure affects the outcome indirectly through a mediator and the extent to which it operates directly through other pathways. As the most popular method in empirical mediation analysis, the Baron-Kenny approach estimates the indirect and direct effects of the exposure on the outcome based on linear structural equation models. However, when the exposure and the mediator are not randomized, the estimates may be biased due to unmeasured confounding among the exposure, mediator, and outcome. Building on Cinelli and Hazlett (2020), we derive general omitted-variable bias formulas in linear regressions with vector responses and regressors. We then use the formulas to develop a sensitivity analysis method for the Baron-Kenny approach to mediation in the presence of unmeasured confounding. To ensure interpretability, we express the sensitivity parameters to correspond to the natural factorization of the joint distribution of the direct acyclic graph for mediation analysis. They measure the partial correlation between the unmeasured confounder and the exposure, mediator, outcome, respectively. With the sensitivity parameters, we propose a novel measure called the "robustness value for mediation" or simply the "robustness value", to assess the robustness of results based on the Baron-Kenny approach with respect to unmeasured confounding. Intuitively, the robustness value measures the minimum value of the maximum proportion of variability explained by the unmeasured confounding, for the exposure, mediator and outcome, to overturn the results of the point estimate or confidence interval for the direct and indirect effects. Importantly, we prove that all our sensitivity bounds are attainable and thus sharp.

Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the solution is not well-resolved, whilst reducing unnecessary resolution elsewhere. However, mesh movement methods, such as the Monge-Ampere method, require the solution of auxiliary equations, which can be extremely expensive especially when the mesh is adapted frequently. In this paper, we propose to our best knowledge the first learning-based end-to-end mesh movement framework for PDE solvers. Key requirements of learning-based mesh movement methods are alleviating mesh tangling, boundary consistency, and generalization to mesh with different resolutions. To achieve these goals, we introduce the neural spline model and the graph attention network (GAT) into our models respectively. While the Neural-Spline based model provides more flexibility for large deformation, the GAT based model can handle domains with more complicated shapes and is better at performing delicate local deformation. We validate our methods on stationary and time-dependent, linear and non-linear equations, as well as regularly and irregularly shaped domains. Compared to the traditional Monge-Ampere method, our approach can greatly accelerate the mesh adaptation process, whilst achieving comparable numerical error reduction.

During the COVID-19 pandemic, people sought information through digital news platforms. To investigate how to design these platforms to support users' needs in a crisis, we conducted a two-week diary study with 22 participants across the United States. Participants' news-consumption experience followed two stages: in the \textbf{seeking} stage, participants increased their general consumption, motivated by three common informational needs -- specifically, to find, understand and verify relevant news pieces. Participants then moved to the \textbf{sustaining} stage, and coping with the news emotionally became as important as their informational needs. We elicited design ideas from participants and used these to distill six themes for creating digital news platforms that provide better informational and emotional support during a crisis. Thus, we contribute, first, a model of users' needs over time with respect to engaging with crisis news, and second, example design concepts for supporting users' needs in each of these stages., Comment: ACM conference format

Photo collage aims to automatically arrange multiple photos on a given canvas with high aesthetic quality. Existing methods are based mainly on handcrafted feature optimization, which cannot adequately capture high-level human aesthetic senses. Deep learning provides a promising way, but owing to the complexity of collage and lack of training data, a solution has yet to be found. In this paper, we propose a novel pipeline for automatic generation of aspect ratio specified collage and the reinforcement learning technique is introduced in collage for the first time. Inspired by manual collages, we model the collage generation as sequential decision process to adjust spatial positions, orientation angles, placement order and the global layout. To instruct the agent to improve both the overall layout and local details, the reward function is specially designed for collage, considering subjective and objective factors. To overcome the lack of training data, we pretrain our deep aesthetic network on a large scale image aesthetic dataset (CPC) for general aesthetic feature extraction and propose an attention fusion module for structural collage feature representation. We test our model against competing methods on two movie datasets and our results outperform others in aesthetic quality evaluation. Further user study is also conducted to demonstrate the effectiveness.

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants for scalable projection-free optimization. We first propose 1-SFW, the first projection-free method that requires only one sample per iteration to update the optimization variable and yet achieves the best known complexity bounds for convex, non-convex, and monotone DR-submodular settings. Then we move forward to the distributed setting, and develop Quantized Frank-Wolfe (QFW), a general communication-efficient distributed FW framework for both convex and non-convex objective functions. We study the performance of QFW in two widely recognized settings: 1) stochastic optimization and 2) finite-sum optimization. Finally, we propose Black-Box Continuous Greedy, a derivative-free and projection-free algorithm, that maximizes a monotone continuous DR-submodular function over a bounded convex body in Euclidean space., Comment: dissertation

Fuzzing is a technique widely used in vulnerability detection. The process usually involves writing effective fuzz driver programs, which, when done manually, can be extremely labor intensive. Previous attempts at automation leave much to be desired, in either degree of automation or quality of output. In this paper, we propose IntelliGen, a framework that constructs valid fuzz drivers automatically. First, IntelliGen determines a set of entry functions and evaluates their respective chance of exhibiting a vulnerability. Then, IntelliGen generates fuzz drivers for the entry functions through hierarchical parameter replacement and type inference. We implemented IntelliGen and evaluated its effectiveness on real-world programs selected from the Android Open-Source Project, Google's fuzzer-test-suite and industrial collaborators. IntelliGen covered on average 1.08X-2.03X more basic blocks and 1.36X-2.06X more paths over state-of-the-art fuzz driver synthesizers FUDGE and FuzzGen. IntelliGen performed on par with manually written drivers and found 10 more bugs., Comment: 10 pages, 5 figures

Online shopping has become a valuable modern convenience, but blind or low vision (BLV) users still face significant challenges using it, because of: 1) inadequate image descriptions and 2) the inability to filter large amounts of information using screen readers. To address those challenges, we propose Revamp, a system that leverages customer reviews for interactive information retrieval. Revamp is a browser integration that supports review-based question-answering interactions on a reconstructed product page. From our interview, we identified four main aspects (color, logo, shape, and size) that are vital for BLV users to understand the visual appearance of a product. Based on the findings, we formulated syntactic rules to extract review snippets, which were used to generate image descriptions and responses to users' queries. Evaluations with eight BLV users showed that Revamp 1) provided useful descriptive information for understanding product appearance and 2) helped the participants locate key information efficiently.

Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the development of deep learning based methods has inspired new approaches to tackle the PIV problem. These supervised learning based methods are driven by large volumes of data with ground truth training information. However, it is difficult to collect reliable ground truth data in large-scale, real-world scenarios. Although synthetic datasets can be used as alternatives, the gap between the training set-ups and real-world scenarios limits applicability. We present here what we believe to be the first work which takes an unsupervised learning based approach to tackle PIV problems. The proposed approach is inspired by classic optical flow methods. Instead of using ground truth data, we make use of photometric loss between two consecutive image frames, consistency loss in bidirectional flow estimates and spatial smoothness loss to construct the total unsupervised loss function. The approach shows significant potential and advantages for fluid flow estimation. Results presented here demonstrate that our method outputs competitive results compared with classical PIV methods as well as supervised learning based methods for a broad PIV dataset, and even outperforms these existing approaches in some difficult flow cases. Codes and trained models are available at https://github.com/erizmr/UnLiteFlowNet-PIV.

Despite remarkable success in practice, modern machine learning models have been found to be susceptible to adversarial attacks that make human-imperceptible perturbations to the data, but result in serious and potentially dangerous prediction errors. To address this issue, practitioners often use adversarial training to learn models that are robust against such attacks at the cost of higher generalization error on unperturbed test sets. The conventional wisdom is that more training data should shrink the gap between the generalization error of adversarially-trained models and standard models. However, we study the training of robust classifiers for both Gaussian and Bernoulli models under $\ell_\infty$ attacks, and we prove that more data may actually increase this gap. Furthermore, our theoretical results identify if and when additional data will finally begin to shrink the gap. Lastly, we experimentally demonstrate that our results also hold for linear regression models, which may indicate that this phenomenon occurs more broadly., Comment: Accepted to ICML'20. First two authors contributed equally

In this paper, we propose three online algorithms for submodular maximisation. The first one, Mono-Frank-Wolfe, reduces the number of per-function gradient evaluations from $T^{1/2}$ [Chen2018Online] and $T^{3/2}$ [chen2018projection] to 1, and achieves a $(1-1/e)$-regret bound of $O(T^{4/5})$. The second one, Bandit-Frank-Wolfe, is the first bandit algorithm for continuous DR-submodular maximization, which achieves a $(1-1/e)$-regret bound of $O(T^{8/9})$. Finally, we extend Bandit-Frank-Wolfe to a bandit algorithm for discrete submodular maximization, Responsive-Frank-Wolfe, which attains a $(1-1/e)$-regret bound of $O(T^{8/9})$ in the responsive bandit setting., Comment: Accepted by NeurIPS 2019

One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications. However, once we replace the projection operator with a simpler linear program, as is done in the Frank-Wolfe method, both simplicity and stability take a serious hit. The aim of this paper is to bring them back without sacrificing the efficiency. In this paper, we propose the first one-sample stochastic Frank-Wolfe algorithm, called 1-SFW, that avoids the need to carefully tune the batch size, step size, learning rate, and other complicated hyper parameters. In particular, 1-SFW achieves the optimal convergence rate of $\mathcal{O}(1/\epsilon^2)$ for reaching an $\epsilon$-suboptimal solution in the stochastic convex setting, and a $(1-1/e)-\epsilon$ approximate solution for a stochastic monotone DR-submodular maximization problem. Moreover, in a general non-convex setting, 1-SFW finds an $\epsilon$-first-order stationary point after at most $\mathcal{O}(1/\epsilon^3)$ iterations, achieving the current best known convergence rate. All of this is possible by designing a novel unbiased momentum estimator that governs the stability of the optimization process while using a single sample at each iteration.

There is an urgent need for an effective video classification method by means of a small number of samples. The deficiency of samples could be effectively alleviated by generating samples through Generative Adversarial Networks (GAN), but the generation of videos on a typical category remains to be underexplored since the complex actions and the changeable viewpoints are difficult to simulate. In this paper, we propose a generative data augmentation method for temporal stream of the Temporal Segment Networks with the dynamic image. The dynamic image compresses the motion information of video into a still image, removing the interference factors such as the background. Thus it is easier to generate images with categorical motion information using GAN. We use the generated dynamic images to enhance the features, with regularization achieved as well, thereby to achieve the effect of video augmentation. In order to deal with the uneven quality of generated images, we propose a Self-Paced Selection (SPS) method, which automatically selects the high-quality generated samples to be added to the network training. Our method is verified on two benchmark datasets, HMDB51 and UCF101. The experimental results show that the method can improve the accuracy of video classification under the circumstance of sample insufficiency and sample imbalance.

How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this paper, we propose Quantized-Frank-Wolfe (QFW), the first projection-free and communication-efficient algorithm for solving constrained optimization problems at scale. We consider both convex and non-convex objective functions, expressed as a finite-sum or more generally a stochastic optimization problem, and provide strong theoretical guarantees on the convergence rate of QFW. This is accomplished by proposing novel quantization schemes that efficiently compress gradients while controlling the noise variance introduced during this process. Finally, we empirically validate the efficiency of QFW in terms of communication and the quality of returned solution against natural baselines.