BI-GreenNet: Learning Green's functions by boundary integral network

Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following three folds. Firstly, compared with the original PDE, the dimension of Green's function is doubled, making it impossible to be handled by traditional mesh-based methods. Secondly, Green's function usually contains singularities which increase the difficulty to get a good approximation. Lastly, the computational domain may be very complex or even unbounded. To override these problems, we leverage the fundamental solution, boundary integral method and neural networks to develop a new method for computing Green's function with high accuracy in this paper. We focus on Green's function of Poisson and Helmholtz equations in bounded domains, unbounded domains. We also consider Poisson equation and Helmholtz domains with interfaces. Extensive numerical experiments illustrate the efficiency and the accuracy of our method for solving Green's function. In addition, we also use the Green's function calculated by our method to solve a class of PDE, and also obtain high-precision solutions, which shows the good generalization ability of our method on solving PDEs.

M2N: Mesh Movement Networks for PDE Solvers

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.

FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis

Denoising diffusion probabilistic models (DDPMs) have recently achieved leading performances in many generative tasks. However, the inherited iterative sampling process costs hindered their applications to speech synthesis. This paper proposes FastDiff, a fast conditional diffusion model for high-quality speech synthesis. FastDiff employs a stack of time-aware location-variable convolutions of diverse receptive field patterns to efficiently model long-term time dependencies with adaptive conditions. A noise schedule predictor is also adopted to reduce the sampling steps without sacrificing the generation quality. Based on FastDiff, we design an end-to-end text-to-speech synthesizer, FastDiff-TTS, which generates high-fidelity speech waveforms without any intermediate feature (e.g., Mel-spectrogram). Our evaluation of FastDiff demonstrates the state-of-the-art results with higher-quality (MOS 4.28) speech samples. Also, FastDiff enables a sampling speed of 58x faster than real-time on a V100 GPU, making diffusion models practically applicable to speech synthesis deployment for the first time. We further show that FastDiff generalized well to the mel-spectrogram inversion of unseen speakers, and FastDiff-TTS outperformed other competing methods in end-to-end text-to-speech synthesis. Audio samples are available at \url{https://FastDiff.github.io/}.

Modeling Temporal-Modal Entity Graph for Procedural Multimodal Machine Comprehension

Procedural Multimodal Documents (PMDs) organize textual instructions and corresponding images step by step. Comprehending PMDs and inducing their representations for the downstream reasoning tasks is designated as Procedural MultiModal Machine Comprehension (M3C). In this study, we approach Procedural M3C at a fine-grained level (compared with existing explorations at a document or sentence level), that is, entity. With delicate consideration, we model entity both in its temporal and cross-modal relation and propose a novel Temporal-Modal Entity Graph (TMEG). Specifically, graph structure is formulated to capture textual and visual entities and trace their temporal-modal evolution. In addition, a graph aggregation module is introduced to conduct graph encoding and reasoning. Comprehensive experiments across three Procedural M3C tasks are conducted on a traditional dataset RecipeQA and our new dataset CraftQA, which can better evaluate the generalization of TMEG.

Deep Algebraic Fitting for Multiple Circle Primitives Extraction from Raw Point Clouds

The shape of circle is one of fundamental geometric primitives of man-made engineering objects. Thus, extraction of circles from scanned point clouds is a quite important task in 3D geometry data processing. However, existing circle extraction methods either are sensitive to the quality of raw point clouds when classifying circle-boundary points, or require well-designed fitting functions when regressing circle parameters. To relieve the challenges, we propose an end-to-end Point Cloud Circle Algebraic Fitting Network (Circle-Net) based on a synergy of deep circle-boundary point feature learning and weighted algebraic fitting. First, we design a circle-boundary learning module, which considers local and global neighboring contexts of each point, to detect all potential circle-boundary points. Second, we develop a deep feature based circle parameter learning module for weighted algebraic fitting, without designing any weight metric, to avoid the influence of outliers during fitting. Unlike most of the cutting-edge circle extraction wisdoms, the proposed classification-and-fitting modules are originally co-trained with a comprehensive loss to enhance the quality of extracted circles.Comparisons on the established dataset and real-scanned point clouds exhibit clear improvements of Circle-Net over SOTAs in terms of both noise-robustness and extraction accuracy. We will release our code, model, and data for both training and evaluation on GitHub upon publication.

BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis

Diffusion probabilistic models (DPMs) and their extensions have emerged as competitive generative models yet confront challenges of efficient sampling. We propose a new bilateral denoising diffusion model (BDDM) that parameterizes both the forward and reverse processes with a schedule network and a score network, which can train with a novel bilateral modeling objective. We show that the new surrogate objective can achieve a lower bound of the log marginal likelihood tighter than a conventional surrogate. We also find that BDDM allows inheriting pre-trained score network parameters from any DPMs and consequently enables speedy and stable learning of the schedule network and optimization of a noise schedule for sampling. Our experiments demonstrate that BDDMs can generate high-fidelity audio samples with as few as three sampling steps. Moreover, compared to other state-of-the-art diffusion-based neural vocoders, BDDMs produce comparable or higher quality samples indistinguishable from human speech, notably with only seven sampling steps (143x faster than WaveGrad and 28.6x faster than DiffWave). We release our code at https://github.com/tencent-ailab/bddm.

Refine-Net: Normal Refinement Neural Network for Noisy Point Clouds

Point normal, as an intrinsic geometric property of 3D objects, not only serves conventional geometric tasks such as surface consolidation and reconstruction, but also facilitates cutting-edge learning-based techniques for shape analysis and generation. In this paper, we propose a normal refinement network, called Refine-Net, to predict accurate normals for noisy point clouds. Traditional normal estimation wisdom heavily depends on priors such as surface shapes or noise distributions, while learning-based solutions settle for single types of hand-crafted features. Differently, our network is designed to refine the initial normal of each point by extracting additional information from multiple feature representations. To this end, several feature modules are developed and incorporated into Refine-Net by a novel connection module. Besides the overall network architecture of Refine-Net, we propose a new multi-scale fitting patch selection scheme for the initial normal estimation, by absorbing geometry domain knowledge. Also, Refine-Net is a generic normal estimation framework: 1) point normals obtained from other methods can be further refined, and 2) any feature module related to the surface geometric structures can be potentially integrated into the framework. Qualitative and quantitative evaluations demonstrate the clear superiority of Refine-Net over the state-of-the-arts on both synthetic and real-scanned datasets. Our code is available at https://github.com/hrzhou2/refinenet.

PointAttN: You Only Need Attention for Point Cloud Completion

Point cloud completion referring to completing 3D shapes from partial 3D point clouds is a fundamental problem for 3D point cloud analysis tasks. Benefiting from the development of deep neural networks, researches on point cloud completion have made great progress in recent years. However, the explicit local region partition like kNNs involved in existing methods makes them sensitive to the density distribution of point clouds. Moreover, it serves limited receptive fields that prevent capturing features from long-range context information. To solve the problems, we leverage the cross-attention and self-attention mechanisms to design novel neural network for processing point cloud in a per-point manner to eliminate kNNs. Two essential blocks Geometric Details Perception (GDP) and Self-Feature Augment (SFA) are proposed to establish the short-range and long-range structural relationships directly among points in a simple yet effective way via attention mechanism. Then based on GDP and SFA, we construct a new framework with popular encoder-decoder architecture for point cloud completion. The proposed framework, namely PointAttN, is simple, neat and effective, which can precisely capture the structural information of 3D shapes and predict complete point clouds with highly detailed geometries. Experimental results demonstrate that our PointAttN outperforms state-of-the-art methods by a large margin on popular benchmarks like Completion3D and PCN. Code is available at: https://github.com/ohhhyeahhh/PointAttN

Plan Your Target and Learn Your Skills: Transferable State-Only Imitation Learning via Decoupled Policy Optimization

Recent progress in state-only imitation learning extends the scope of applicability of imitation learning to real-world settings by relieving the need for observing expert actions. However, existing solutions only learn to extract a state-to-action mapping policy from the data, without considering how the expert plans to the target. This hinders the ability to leverage demonstrations and limits the flexibility of the policy. In this paper, we introduce Decoupled Policy Optimization (DePO), which explicitly decouples the policy as a high-level state planner and an inverse dynamics model. With embedded decoupled policy gradient and generative adversarial training, DePO enables knowledge transfer to different action spaces or state transition dynamics, and can generalize the planner to out-of-demonstration state regions. Our in-depth experimental analysis shows the effectiveness of DePO on learning a generalized target state planner while achieving the best imitation performance. We demonstrate the appealing usage of DePO for transferring across different tasks by pre-training, and the potential for co-training agents with various skills.

CandidateDrug4Cancer: An Open Molecular Graph Learning Benchmark on Drug Discovery for Cancer

Anti-cancer drug discoveries have been serendipitous, we sought to present the Open Molecular Graph Learning Benchmark, named CandidateDrug4Cancer, a challenging and realistic benchmark dataset to facilitate scalable, robust, and reproducible graph machine learning research for anti-cancer drug discovery. CandidateDrug4Cancer dataset encompasses multiple most-mentioned 29 targets for cancer, covering 54869 cancer-related drug molecules which are ranged from pre-clinical, clinical and FDA-approved. Besides building the datasets, we also perform benchmark experiments with effective Drug Target Interaction (DTI) prediction baselines using descriptors and expressive graph neural networks. Experimental results suggest that CandidateDrug4Cancer presents significant challenges for learning molecular graphs and targets in practical application, indicating opportunities for future researches on developing candidate drugs for treating cancers.