arXiv subjects

Yizhou Zhou

Publications and source records attributed to Yizhou Zhou.

44 records · Page 3Linked to original sources

arXiv2021

Data-driven discovery of multiscale chemical reactions governed by the law of mass action

In this paper, we propose a data-driven method to discover multiscale chemical reactions governed by the law of mass action. First, we use a single matrix to represent the stoichiometric coefficients for both the reactants and products in a system without catalysis reactions. The negative entries in the matrix denote the stoichiometric coefficients for the reactants and the positive ones for the products. Second, we find that the conventional optimization methods usually get stuck in the local minima and could not find the true solution in learning the multiscale chemical reactions. To overcome this difficulty, we propose a partial-parameters-freezing (PPF) technique to progressively determine the network parameters by using the fact that the stoichiometric coefficients are integers. With such a technique, the dimension of the searching space is gradually reduced in the training process and the global mimina can be eventually obtained. Several numerical experiments including the classical Michaelis-Menten kinetics, the hydrogen oxidation reactions, and the simplified GRI-3.0 mechanism verify the good performance of our algorithm in learning the multiscale chemical reactions. The code is available at \url{https://github.com/JuntaoHuang/multiscale-chemical-reaction}.

physics.chem-ph↗

arXiv2021

Unsupervised Visual Representation Learning by Tracking Patches in Video

Inspired by the fact that human eyes continue to develop tracking ability in early and middle childhood, we propose to use tracking as a proxy task for a computer vision system to learn the visual representations. Modelled on the Catch game played by the children, we design a Catch-the-Patch (CtP) game for a 3D-CNN model to learn visual representations that would help with video-related tasks. In the proposed pretraining framework, we cut an image patch from a given video and let it scale and move according to a pre-set trajectory. The proxy task is to estimate the position and size of the image patch in a sequence of video frames, given only the target bounding box in the first frame. We discover that using multiple image patches simultaneously brings clear benefits. We further increase the difficulty of the game by randomly making patches invisible. Extensive experiments on mainstream benchmarks demonstrate the superior performance of CtP against other video pretraining methods. In addition, CtP-pretrained features are less sensitive to domain gaps than those trained by a supervised action recognition task. When both trained on Kinetics-400, we are pleasantly surprised to find that CtP-pretrained representation achieves much higher action classification accuracy than its fully supervised counterpart on Something-Something dataset. Code is available online: github.com/microsoft/CtP.

cs.CV↗

arXiv2021

VAE^2: Preventing Posterior Collapse of Variational Video Predictions in the Wild

Predicting future frames of video sequences is challenging due to the complex and stochastic nature of the problem. Video prediction methods based on variational auto-encoders (VAEs) have been a great success, but they require the training data to contain multiple possible futures for an observed video sequence. This is hard to be fulfilled when videos are captured in the wild where any given observation only has a determinate future. As a result, training a vanilla VAE model with these videos inevitably causes posterior collapse. To alleviate this problem, we propose a novel VAE structure, dabbed VAE-in-VAE or VAE$^2$. The key idea is to explicitly introduce stochasticity into the VAE. We treat part of the observed video sequence as a random transition state that bridges its past and future, and maximize the likelihood of a Markov Chain over the video sequence under all possible transition states. A tractable lower bound is proposed for this intractable objective function and an end-to-end optimization algorithm is designed accordingly. VAE$^2$ can mitigate the posterior collapse problem to a large extent, as it breaks the direct dependence between future and observation and does not directly regress the determinate future provided by the training data. We carry out experiments on a large-scale dataset called Cityscapes, which contains videos collected from a number of urban cities. Results show that VAE$^2$ is capable of predicting diverse futures and is more resistant to posterior collapse than the other state-of-the-art VAE-based approaches. We believe that VAE$^2$ is also applicable to other stochastic sequence prediction problems where training data are lack of stochasticity.

cs.CV↗

arXiv2020

Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows

In this work, we develop a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the Conservation-dissipation Formalism of irreversible thermodynamics. As governing equations for non-equilibrium flows in one dimension, the learned PDEs are parameterized by fully-connected neural networks and satisfy the conservation-dissipation principle automatically. In particular, they are hyperbolic balance laws and Galilean invariant. The training data are generated from a kinetic model with smooth initial data. Numerical results indicate that the learned PDEs can achieve good accuracy in a wide range of Knudsen numbers. Remarkably, the learned dynamics can give satisfactory results with randomly sampled discontinuous initial data and Sod's shock tube problem although it is trained only with smooth initial data.

physics.comp-ph↗

arXiv2020

Boundary Conditions for Hyperbolic Relaxation Systems with Characteristic Boundaries of Type II

This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries of type I. Here we focus on the characteristic boundaries of type II, where the boundary is characteristic for the equilibrium system and is non-characteristic for the relaxation system. For this kind of characteristic initial-boundary-value problems (IBVPs), we introduce a three-scale asymptotic expansion to analyze the boundary-layer behaviors of the general multi-dimensional linear relaxation systems. Moreover, we derive the reduced boundary condition under the Generalized Kreiss Condition by resorting to some subtle matrix transformations and the perturbation theory of linear operators. The reduced boundary condition is proved to satisfy the Uniformed Kreiss Condition for characteristic IBVPs. Its validity is shown through an error estimate involving the Fourier-Laplace transformation and an energy method based on the structural stability condition.

math.AP↗

arXiv2020

Boundary Conditions for Hyperbolic Relaxation Systems with Characteristic Boundaries of Type I

This work is concerned with boundary conditions for one-dimensional hyperbolic relaxation systems with characteristic boundaries. We assume that the relaxation system satisfies the structural stability condition proposed by the second author previously and the boundary is characteristic of type I (characteristic for the relaxation system but non-characteristic for the corresponding equilibrium system). For this kind of characteristic initial-boundary-value problems, we propose a modified Generalized Kreiss condition (GKC). This extends the GKC proposed by the second author for the non-characteristic boundaries to the present characteristic case. Under this modified GKC, we derive the reduced boundary condition and verify its validity by combining an energy estimate with the Laplace transform. Moreover, we show the existence of boundary-layers for nonlinear problems.

math.AP↗

arXiv2020

Spatiotemporal Fusion in 3D CNNs: A Probabilistic View

Despite the success in still image recognition, deep neural networks for spatiotemporal signal tasks (such as human action recognition in videos) still suffers from low efficacy and inefficiency over the past years. Recently, human experts have put more efforts into analyzing the importance of different components in 3D convolutional neural networks (3D CNNs) to design more powerful spatiotemporal learning backbones. Among many others, spatiotemporal fusion is one of the essentials. It controls how spatial and temporal signals are extracted at each layer during inference. Previous attempts usually start by ad-hoc designs that empirically combine certain convolutions and then draw conclusions based on the performance obtained by training the corresponding networks. These methods only support network-level analysis on limited number of fusion strategies. In this paper, we propose to convert the spatiotemporal fusion strategies into a probability space, which allows us to perform network-level evaluations of various fusion strategies without having to train them separately. Besides, we can also obtain fine-grained numerical information such as layer-level preference on spatiotemporal fusion within the probability space. Our approach greatly boosts the efficiency of analyzing spatiotemporal fusion. Based on the probability space, we further generate new fusion strategies which achieve the state-of-the-art performance on four well-known action recognition datasets.

cs.CV↗

arXiv2019

Posterior-Guided Neural Architecture Search

The emergence of neural architecture search (NAS) has greatly advanced the research on network design. Recent proposals such as gradient-based methods or one-shot approaches significantly boost the efficiency of NAS. In this paper, we formulate the NAS problem from a Bayesian perspective. We propose explicitly estimating the joint posterior distribution over pairs of network architecture and weights. Accordingly, a hybrid network representation is presented which enables us to leverage the Variational Dropout so that the approximation of the posterior distribution becomes fully gradient-based and highly efficient. A posterior-guided sampling method is then presented to sample architecture candidates and directly make evaluations. As a Bayesian approach, our posterior-guided NAS (PGNAS) avoids tuning a number of hyper-parameters and enables a very effective architecture sampling in posterior probability space. Interestingly, it also leads to a deeper insight into the weight sharing used in the one-shot NAS and naturally alleviates the mismatch between the sampled architecture and weights caused by the weight sharing. We validate our PGNAS method on the fundamental image classification task. Results on Cifar-10, Cifar-100 and ImageNet show that PGNAS achieves a good trade-off between precision and speed of search among NAS methods. For example, it takes 11 GPU days to search a very competitive architecture with 1.98% and 14.28% test errors on Cifar10 and Cifar100, respectively.

cs.LG↗