Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix the input layer weights with random values and use Moore-Penrose generalized inverse for the output layer weights. The framework is effective, but it easily suffers from overfitting noisy data and lacks uncertainty quantification for the solution under noise scenarios.To this end, we develop the Bayesian physics-informed extreme learning machine (BPIELM) to solve both forward and inverse linear PDE problems with noisy data in a unified framework. In our framework, a prior probability distribution is introduced in the output layer for extreme learning machine with physic laws and the Bayesian method is used to estimate the posterior of parameters. Besides, for inverse PDE problems, problem parameters considered as new output layer weights are unified in a framework with forward PDE problems. Finally, we demonstrate BPIELM considering both forward problems, including Poisson, advection, and diffusion equations, as well as inverse problems, where unknown problem parameters are estimated. The results show that, compared with PIELM, BPIELM quantifies uncertainty arising from noisy data and provides more accurate predictions. In addition, BPIELM is considerably cheaper than PINN in terms of the computational cost.
Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite the success of PINNs in accurately solving a wide variety of PDEs, the method still requires improvements in terms of computational efficiency. One possible improvement idea is to optimize the generation of training point sets. Residual-based adaptive sampling and quasi-uniform sampling approaches have been each applied to improve the training effects of PINNs, respectively. To benefit from both methods, we propose the Residual-based Adaptive Node Generation (RANG) approach for efficient training of PINNs, which is based on a variable density nodal distribution method for RBF-FD. The method is also enhanced by a memory mechanism to further improve training stability. We conduct experiments on three linear PDEs and three nonlinear PDEs with various node generation methods, through which the accuracy and efficiency of the proposed method compared to the predominant uniform sampling approach is verified numerically.
Micro-expression recognition (MER) is valuable because the involuntary nature of micro-expressions (MEs) can reveal genuine emotions. Most works recognize MEs by taking RGB videos or images as input. In fact, the activated facial regions in ME images are very small and the subtle motion can be easily submerged in the unrelated information. Facial landmarks are a low-dimensional and compact modality, which leads to much lower computational cost and can potentially concentrate more on ME-related features. However, the discriminability of landmarks for MER is not clear. Thus, this paper explores the contribution of facial landmarks and constructs a new framework to efficiently recognize MEs with sole facial landmark information. Specially, we design a separate structure module to separately aggregate the spatial and temporal information in the geometric movement graph based on facial landmarks, and a Geometric Two-Stream Graph Network is constructed to aggregate the low-order geometric information and high-order semantic information of facial landmarks. Furthermore, two core components are proposed to enhance features. Specifically, a semantic adjacency matrix can automatically model the relationship between nodes even long-distance nodes in a self-learning fashion; and an Adaptive Action Unit loss is introduced to guide the learning process such that the learned features are forced to have a synchronized pattern with facial action units. Notably, this work tackles MER only utilizing geometric features, processed based on a graph model, which provides a new idea with much higher efficiency to promote MER. The experimental results demonstrate that the proposed method can achieve competitive or even superior performance with a significantly reduced computational cost, and facial landmarks can significantly contribute to MER and are worth further study for efficient ME analysis.
Emotional support conversation aims at reducing the emotional distress of the help-seeker, which is a new and challenging task. It requires the system to explore the cause of help-seeker's emotional distress and understand their psychological intention to provide supportive responses. However, existing methods mainly focus on the sequential contextual information, ignoring the hierarchical relationships with the global cause and local psychological intention behind conversations, thus leads to a weak ability of emotional support. In this paper, we propose a Global-to-Local Hierarchical Graph Network to capture the multi-source information (global cause, local intentions and dialog history) and model hierarchical relationships between them, which consists of a multi-source encoder, a hierarchical graph reasoner, and a global-guide decoder. Furthermore, a novel training objective is designed to monitor semantic information of the global cause. Experimental results on the emotional support conversation dataset, ESConv, confirm that the proposed GLHG has achieved the state-of-the-art performance on the automatic and human evaluations.
The inherent slow imaging speed of Magnetic Resonance Image (MRI) has spurred the development of various acceleration methods, typically through heuristically undersampling the MRI measurement domain known as k-space. Recently, deep neural networks have been applied to reconstruct undersampled k-space data and have shown improved reconstruction performance. While most of these methods focus on designing novel reconstruction networks or new training strategies for a given undersampling pattern, e.g., Cartesian undersampling or Non-Cartesian sampling, to date, there is limited research aiming to learn and optimize k-space sampling strategies using deep neural networks. This work proposes a novel optimization framework to learn k-space sampling trajectories by considering it as an Ordinary Differential Equation (ODE) problem that can be solved using neural ODE. In particular, the sampling of k-space data is framed as a dynamic system, in which neural ODE is formulated to approximate the system with additional constraints on MRI physics. In addition, we have also demonstrated that trajectory optimization and image reconstruction can be learned collaboratively for improved imaging efficiency and reconstruction performance. Experiments were conducted on different in-vivo datasets (e.g., brain and knee images) acquired with different sequences. Initial results have shown that our proposed method can generate better image quality in accelerated MRI than conventional undersampling schemes in Cartesian and Non-Cartesian acquisitions.
Semantic segmentation (SS) aims to classify each pixel into one of the pre-defined classes. This task plays an important role in self-driving cars and autonomous drones. In SS, many works have shown that most misclassified pixels are commonly near object boundaries with high uncertainties. However, existing SS loss functions are not tailored to handle these uncertain pixels during training, as these pixels are usually treated equally as confidently classified pixels and cannot be embedded with arbitrary low distortion in Euclidean space, thereby degenerating the performance of SS. To overcome this problem, this paper designs a "Hyperbolic Uncertainty Loss" (HyperUL), which dynamically highlights the misclassified and high-uncertainty pixels in Hyperbolic space during training via the hyperbolic distances. The proposed HyperUL is model agnostic and can be easily applied to various neural architectures. After employing HyperUL to three recent SS models, the experimental results on Cityscapes and UAVid datasets reveal that the segmentation performance of existing SS models can be consistently improved.
In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis followed. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.
Story Ending Generation (SEG) is a challenging task in natural language generation. Recently, methods based on Pre-trained Language Models (PLM) have achieved great prosperity, which can produce fluent and coherent story endings. However, the pre-training objective of PLM-based methods is unable to model the consistency between story context and ending. The goal of this paper is to adopt contrastive learning to generate endings more consistent with story context, while there are two main challenges in contrastive learning of SEG. First is the negative sampling of wrong endings inconsistent with story contexts. The second challenge is the adaptation of contrastive learning for SEG. To address these two issues, we propose a novel Contrastive Learning framework for Story Ending Generation (CLSEG), which has two steps: multi-aspect sampling and story-specific contrastive learning. Particularly, for the first issue, we utilize novel multi-aspect sampling mechanisms to obtain wrong endings considering the consistency of order, causality, and sentiment. To solve the second issue, we well-design a story-specific contrastive training strategy that is adapted for SEG. Experiments show that CLSEG outperforms baselines and can produce story endings with stronger consistency and rationality.
Intention, emotion and action are important elements in human activities. Modeling the interaction process between individuals by analyzing the relationships between these elements is a challenging task. However, previous work mainly focused on modeling intention and emotion independently, and neglected of exploring the mutual relationships between intention and emotion. In this paper, we propose a RelAtion Interaction Network (RAIN), consisting of Intention Relation Module and Emotion Relation Module, to jointly model mutual relationships and explicitly integrate historical intention information. The experiments on the dataset show that our model can take full advantage of the intention, emotion and action between individuals and achieve a remarkable improvement over BERT-style baselines. Qualitative analysis verifies the importance of the mutual interaction between the intention and emotion.