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This paper presents a motion data augmentation scheme incorporating motion synthesis encouraging diversity and motion correction imposing physical plausibility. This motion synthesis consists of our modified Variational AutoEncoder (VAE) and Inverse Kinematics (IK). In this VAE, our proposed sampling-near-samples method generates various valid motions even with insufficient training motion data. Our IK-based motion synthesis method allows us to generate a variety of motions semi-automatically. Since these two schemes generate unrealistic artifacts in the synthesized motions, our motion correction rectifies them. This motion correction scheme consists of imitation learning with physics simulation and subsequent motion debiasing. For this imitation learning, we propose the PD-residual force that significantly accelerates the training process. Furthermore, our motion debiasing successfully offsets the motion bias induced by imitation learning to maximize the effect of augmentation. As a result, our method outperforms previous noise-based motion augmentation methods by a large margin on both Recurrent Neural Network-based and Graph Convolutional Network-based human motion prediction models. The code is available at //github.com/meaten/MotionAug.

This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an ''infinitely'' deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially provided solution. $\Psi$-GNN is trained using a ''physics-informed'' loss, and the training process is stable by design, and insensitive to its initialization. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, $\Psi$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

Sentiment transfer aims at revising the input text to satisfy a given sentiment polarity while retaining the original semantic content. The nucleus of sentiment transfer lies in precisely separating the sentiment information from the content information. Existing explicit approaches generally identify and mask sentiment tokens simply based on prior linguistic knowledge and manually-defined rules, leading to low generality and undesirable transfer performance. In this paper, we view the positions to be masked as the learnable parameters, and further propose a novel AM-ST model to learn adaptive task-relevant masks based on the attention mechanism. Moreover, a sentiment-aware masked language model is further proposed to fill in the blanks in the masked positions by incorporating both context and sentiment polarity to capture the multi-grained semantics comprehensively. AM-ST is thoroughly evaluated on two popular datasets, and the experimental results demonstrate the superiority of our proposal.

We set out the novel bottom up procedure to aggregate or cluster cells with small frequency counts together, in a two way classification while maintaining dependence in the table. The procedure is model free. It combines cells in a table into clusters based on independent log odds ratios. We use this procedure to build a set of statistically efficient and robust imputation cells, for the imputation of missing values of a continuous variable using a pair classification variables. A nice feature of the procedure is it forms aggregation groups homogeneous with respect to the cell response mean. Using a series of simulation studies, we show IlocA only groups together independent cells and does so in a consistent and credible way. While imputing missing data, we show IlocAs generates close to an optimal number of imputation cells. For ignorable non-response the resulting imputed means are accurate in general. With non-ignorable missingness results are consistent with those obtained elsewhere. We close with a case study applying our method to imputing missing building energy performance data

Grid-free Monte Carlo methods based on the \emph{walk on spheres (WoS)} algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain, nor approximating functions in a finite basis. Such methods hence avoid aliasing in the solution, and evade the many challenges of mesh generation. Yet for problems with complex geometry, practical grid-free methods have been largely limited to basic Dirichlet boundary conditions. This paper introduces the \emph{walk on stars (WoSt)} method, which solves linear elliptic PDEs with arbitrary mixed Neumann and Dirichlet boundary conditions. The key insight is that one can efficiently simulate reflecting Brownian motion (which models Neumann conditions) by replacing the balls used by WoS with \emph{star-shaped} domains; we identify such domains by locating the closest visible point on the geometric silhouette. Overall, WoSt retains many attractive features of other grid-free Monte Carlo methods, such as progressive evaluation, trivial parallel implementation, and logarithmic scaling relative to geometric complexity.

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the problems of maintaining geometric features and choosing a reasonable implicit degree. The present paper has two contributions. We first introduce a new regularization constraint(called the weak gradient constraint) for both polynomial and non-polynomial curves, which efficiently possesses shape preserving. We then propose two adaptive algorithms of approximate implicitization for polynomial and non-polynomial curves respectively, which find the ``optimal'' implicit degree based on the behavior of the weak gradient constraint. More precisely, the idea is gradually increasing the implicit degree, until there is no obvious improvement in the weak gradient loss of the outputs. Experimental results have shown the effectiveness and high quality of our proposed methods.

This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a mathematical formulation and a numerical treatment that can be used both to carry out transient simulations, and to compute steady solutions -- for any flow admitting them. In the literature on numerical towing tank in fact, steady and unsteady fully nonlinear potential flow solvers are characterized by different mathematical formulations. The kinematic and dynamic fully nonlinear free surface boundary conditions are discussed, and in particular it is proven that the kinematic free surface boundary condition, written in semi-Lagrangian form, can be manipulated to derive an alternative non penetration boundary condition by all means identical to the one used on the surface of floating bodies or on the basin bottom. The simplified mathematical problem obtained is discretized over space and time via Boundary Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme, respectively. The results confirm that the solver implemented is able to solve steady potential flow problems just by eliminating null time derivatives in the unsteady formulation. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.

Bokeh rendering is a popular and effective technique used in photography to create an aesthetically pleasing effect. It is widely used to blur the background and highlight the subject in the foreground, thereby drawing the viewer's attention to the main focus of the image. In traditional digital single-lens reflex cameras (DSLRs), this effect is achieved through the use of a large aperture lens. This allows the camera to capture images with shallow depth-of-field, in which only a small area of the image is in sharp focus, while the rest of the image is blurred. However, the hardware embedded in mobile phones is typically much smaller and more limited than that found in DSLRs. Consequently, mobile phones are not able to capture natural shallow depth-of-field photos, which can be a significant limitation for mobile photography. To address this challenge, in this paper, we propose a novel method for bokeh rendering using the Vision Transformer, a recent and powerful deep learning architecture. Our approach employs an adaptive depth calibration network that acts as a confidence level to compensate for errors in monocular depth estimation. This network is used to supervise the rendering process in conjunction with depth information, allowing for the generation of high-quality bokeh images at high resolutions. Our experiments demonstrate that our proposed method outperforms state-of-the-art methods, achieving about 24.7% improvements on LPIPS and obtaining higher PSNR scores.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Solving continuous Partially Observable Markov Decision Processes (POMDPs) is challenging, particularly for high-dimensional continuous action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver, called Adaptive Discretization using Voronoi Trees (ADVT). It uses Monte Carlo Tree Search in combination with an adaptive discretization of the action space as well as optimistic optimization to efficiently sample high-dimensional continuous action spaces and compute the best action to perform. Specifically, we adaptively discretize the action space for each sampled belief using a hierarchical partition called Voronoi tree, which is a Binary Space Partitioning that implicitly maintains the partition of a cell as the Voronoi diagram of two points sampled from the cell. ADVT uses the estimated diameters of the cells to form an upper-confidence bound on the action value function within the cell, guiding the Monte Carlo Tree Search expansion and further discretization of the action space. This enables ADVT to better exploit local information with respect to the action value function, allowing faster identification of the most promising regions in the action space, compared to existing solvers. Voronoi trees keep the cost of partitioning and estimating the diameter of each cell low, even in high-dimensional spaces where many sampled points are required to cover the space well. ADVT additionally handles continuous observation spaces, by adopting an observation progressive widening strategy, along with a weighted particle representation of beliefs. Experimental results indicate that ADVT scales substantially better to high-dimensional continuous action spaces, compared to state-of-the-art methods.