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Chanwoo Kim

Publications and source records attributed to Chanwoo Kim.

At least 91 records · Page 5Linked to original sources
arXiv2021

Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection

We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by the recent framework in [30], we consider the Navier-Stokes-Fourier system with no-slip boundary conditions as an intermediary approximation and develop a Hilbert-type expansion of the Boltzmann equation around the global Maxwellian that allows the nontrivial heat transfer by convection in the limit. To justify our expansion and the limit, a new direct estimate of the heat flux and its derivatives in the Navier-Stokes-Fourier system is established adopting a recent Green's function approach in the study of the inviscid limit.

math.AP↗
arXiv2021

Regularity of Stationary Boltzmann equation in Convex Domains

Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex domains such as a disk or sphere. In this paper we answer this question in the affirmative by constructing the $C^{1,β}$ solutions away from the grazing boundary, for any $β<1$, to the stationary Boltzmann equation with the non-isothermal diffuse boundary condition in strictly convex domains, as long as a smooth wall temperature has small fluctuation pointwisely.

math.AP↗
arXiv2021

Damping of kinetic transport equation with diffuse boundary condition

We prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as $t^{-3}$ when the domain is any general strictly convex subset of $\mathbb{R}^3$ with the smooth boundary of the diffuse boundary condition. We prove the theorem by establishing a novel $L^1$-$L^\infty$ framework via stochastic cycles.

math.AP↗
arXiv2021

Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^\infty$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^\infty$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate.

math.AP↗
arXiv2020

Incompressible Euler limit from Boltzmann equation with Diffuse Boundary Condition for Analytic data

A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open question in the affirmative when the initial data of fluid are well-prepared in a real analytic space, in 3D half space. As a key of this advance we capture the Navier-Stokes equations of $$\textit{viscosity} \sim \frac{\textit{Knudsen number}}{\textit{Mach number}}$$ satisfying the no-slip boundary condition, as an $\textit{intermediary}$ approximation of the Euler equations through a new Hilbert-type expansion of Boltzmann equation with the diffuse reflection boundary condition. Aiming to justify the approximation we establish a novel quantitative $L^p$-$L^\infty$ estimate of the Boltzmann perturbation around a local Maxwellian of such viscous approximation, along with the commutator estimates and the integrability gain of the hydrodynamic part in various spaces; we also establish direct estimates of the Navier-Stokes equations in higher regularity with the aid of the initial-boundary and boundary layer weights using a recent Green's function approach. The incompressible Euler limit follows as a byproduct of our framework.

math.AP↗
arXiv2020

Data Efficient Direct Speech-to-Text Translation with Modality Agnostic Meta-Learning

End-to-end Speech Translation (ST) models have several advantages such as lower latency, smaller model size, and less error compounding over conventional pipelines that combine Automatic Speech Recognition (ASR) and text Machine Translation (MT) models. However, collecting large amounts of parallel data for ST task is more difficult compared to the ASR and MT tasks. Previous studies have proposed the use of transfer learning approaches to overcome the above difficulty. These approaches benefit from weakly supervised training data, such as ASR speech-to-transcript or MT text-to-text translation pairs. However, the parameters in these models are updated independently of each task, which may lead to sub-optimal solutions. In this work, we adopt a meta-learning algorithm to train a modality agnostic multi-task model that transfers knowledge from source tasks=ASR+MT to target task=ST where ST task severely lacks data. In the meta-learning phase, the parameters of the model are exposed to vast amounts of speech transcripts (e.g., English ASR) and text translations (e.g., English-German MT). During this phase, parameters are updated in such a way to understand speech, text representations, the relation between them, as well as act as a good initialization point for the target ST task. We evaluate the proposed meta-learning approach for ST tasks on English-German (En-De) and English-French (En-Fr) language pairs from the Multilingual Speech Translation Corpus (MuST-C). Our method outperforms the previous transfer learning approaches and sets new state-of-the-art results for En-De and En-Fr ST tasks by obtaining 9.18, and 11.76 BLEU point improvements, respectively.

cs.CL↗
arXiv2020

Small energy masking for improved neural network training for end-to-end speech recognition

In this paper, we present a Small Energy Masking (SEM) algorithm, which masks inputs having values below a certain threshold. More specifically, a time-frequency bin is masked if the filterbank energy in this bin is less than a certain energy threshold. A uniform distribution is employed to randomly generate the ratio of this energy threshold to the peak filterbank energy of each utterance in decibels. The unmasked feature elements are scaled so that the total sum of the feature values remain the same through this masking procedure. This very simple algorithm shows relatively 11.2 % and 13.5 % Word Error Rate (WER) improvements on the standard LibriSpeech test-clean and test-other sets over the baseline end-to-end speech recognition system. Additionally, compared to the input dropout algorithm, SEM algorithm shows relatively 7.7 % and 11.6 % improvements on the same LibriSpeech test-clean and test-other sets. With a modified shallow-fusion technique with a Transformer LM, we obtained a 2.62 % WER on the LibriSpeech test-clean set and a 7.87 % WER on the LibriSpeech test-other set.

eess.AS↗
arXiv2020

Attention based on-device streaming speech recognition with large speech corpus

In this paper, we present a new on-device automatic speech recognition (ASR) system based on monotonic chunk-wise attention (MoChA) models trained with large (> 10K hours) corpus. We attained around 90% of a word recognition rate for general domain mainly by using joint training of connectionist temporal classifier (CTC) and cross entropy (CE) losses, minimum word error rate (MWER) training, layer-wise pre-training and data augmentation methods. In addition, we compressed our models by more than 3.4 times smaller using an iterative hyper low-rank approximation (LRA) method while minimizing the degradation in recognition accuracy. The memory footprint was further reduced with 8-bit quantization to bring down the final model size to lower than 39 MB. For on-demand adaptation, we fused the MoChA models with statistical n-gram models, and we could achieve a relatively 36% improvement on average in word error rate (WER) for target domains including the general domain.

eess.AS↗
arXiv2019

Improved Multi-Stage Training of Online Attention-based Encoder-Decoder Models

In this paper, we propose a refined multi-stage multi-task training strategy to improve the performance of online attention-based encoder-decoder (AED) models. A three-stage training based on three levels of architectural granularity namely, character encoder, byte pair encoding (BPE) based encoder, and attention decoder, is proposed. Also, multi-task learning based on two-levels of linguistic granularity namely, character and BPE, is used. We explore different pre-training strategies for the encoders including transfer learning from a bidirectional encoder. Our encoder-decoder models with online attention show 35% and 10% relative improvement over their baselines for smaller and bigger models, respectively. Our models achieve a word error rate (WER) of 5.04% and 4.48% on the Librispeech test-clean data for the smaller and bigger models respectively after fusion with long short-term memory (LSTM) based external language model (LM).

eess.AS↗
arXiv2019

end-to-end training of a large vocabulary end-to-end speech recognition system

In this paper, we present an end-to-end training framework for building state-of-the-art end-to-end speech recognition systems. Our training system utilizes a cluster of Central Processing Units(CPUs) and Graphics Processing Units (GPUs). The entire data reading, large scale data augmentation, neural network parameter updates are all performed "on-the-fly". We use vocal tract length perturbation [1] and an acoustic simulator [2] for data augmentation. The processed features and labels are sent to the GPU cluster. The Horovod allreduce approach is employed to train neural network parameters. We evaluated the effectiveness of our system on the standard Librispeech corpus [3] and the 10,000-hr anonymized Bixby English dataset. Our end-to-end speech recognition system built using this training infrastructure showed a 2.44 % WER on test-clean of the LibriSpeech test set after applying shallow fusion with a Transformer language model (LM). For the proprietary English Bixby open domain test set, we obtained a WER of 7.92 % using a Bidirectional Full Attention (BFA) end-to-end model after applying shallow fusion with an RNN-LM. When the monotonic chunckwise attention (MoCha) based approach is employed for streaming speech recognition, we obtained a WER of 9.95 % on the same Bixby open domain test set.

eess.AS↗
arXiv2019

power-law nonlinearity with maximally uniform distribution criterion for improved neural network training in automatic speech recognition

In this paper, we describe the Maximum Uniformity of Distribution (MUD) algorithm with the power-law nonlinearity. In this approach, we hypothesize that neural network training will become more stable if feature distribution is not too much skewed. We propose two different types of MUD approaches: power function-based MUD and histogram-based MUD. In these approaches, we first obtain the mel filterbank coefficients and apply nonlinearity functions for each filterbank channel. With the power function-based MUD, we apply a power-function based nonlinearity where power function coefficients are chosen to maximize the likelihood assuming that nonlinearity outputs follow the uniform distribution. With the histogram-based MUD, the empirical Cumulative Density Function (CDF) from the training database is employed to transform the original distribution into a uniform distribution. In MUD processing, we do not use any prior knowledge (e.g. logarithmic relation) about the energy of the incoming signal and the perceived intensity by a human. Experimental results using an end-to-end speech recognition system demonstrate that power-function based MUD shows better result than the conventional Mel Filterbank Cepstral Coefficients (MFCCs). On the LibriSpeech database, we could achieve 4.02 % WER on test-clean and 13.34 % WER on test-other without using any Language Models (LMs). The major contribution of this work is that we developed a new algorithm for designing the compressive nonlinearity in a data-driven way, which is much more flexible than the previous approaches and may be extended to other domains as well.

eess.AS↗
arXiv2019

Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition. The construction is based on an $L^{2}$-$L^{\infty}$ framework with a novel \textit{nonlinear-normed energy estimate} of a distribution function in weighted $W^{1,p}$-spaces and a $C^{2,δ}$-estimate of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.

math.AP↗
arXiv2019

Efficient Implementation of the Room Simulator for Training Deep Neural Network Acoustic Models

In this paper, we describe how to efficiently implement an acoustic room simulator to generate large-scale simulated data for training deep neural networks. Even though Google Room Simulator in [1] was shown to be quite effective in reducing the Word Error Rates (WERs) for far-field applications by generating simulated far-field training sets, it requires a very large number of Fast Fourier Transforms (FFTs) of large size. Room Simulator in [1] used approximately 80 percent of Central Processing Unit (CPU) usage in our CPU + Graphics Processing Unit (GPU) training architecture [2]. In this work, we implement an efficient OverLap Addition (OLA) based filtering using the open-source FFTW3 library. Further, we investigate the effects of the Room Impulse Response (RIR) lengths. Experimentally, we conclude that we can cut the tail portions of RIRs whose power is less than 20 dB below the maximum power without sacrificing the speech recognition accuracy. However, we observe that cutting RIR tail more than this threshold harms the speech recognition accuracy for rerecorded test sets. Using these approaches, we were able to reduce CPU usage for the room simulator portion down to 9.69 percent in CPU/GPU training architecture. Profiling result shows that we obtain 22.4 times speed-up on a single machine and 37.3 times speed up on Google's distributed training infrastructure.

cs.SD↗
arXiv2017

Decay of the Boltzmann equation with the specular boundary condition in non-convex cylindrical domains

A basic question about the existence and stability of the Boltzmann equation in general non-convex domain with the specular reflection boundary condition has been widely open. In this paper, we consider cylindrical domains whose cross sections are general non-convex analytic planar domain. We establish the global-wellposedness and asymptotic stability of the Boltzmann equation with the specular reflection boundary condition in such domains. Our method consists of sharp classification of billiard trajectories which bounce infinitely many times or hit the boundary tangentially at some moment, and a delicate construction of an $\e$-tubular neighborhood of such trajectories. Analyticity of the boundary is crucially used. Away from such $\e$-tubular neighborhood, we control the number of bounces of trajectories and its' distance from singular sets in a uniform fashion. The worst case, sticky grazing set, can be excluded by cutting off small portion of the temporal integration. Finally we apply a method of \cite{KimLee} by the authors and achieve a pointwise estimate of the Boltzmann solutions.

math.AP↗
arXiv2016

The Boltzmann equation with specular boundary condition in convex domains

We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the long standing open problem after an announcement of [20] in 1977.

math.AP↗
arXiv2016

Dynamics and stability of surfactant-driven surface waves

In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants resides on the free surface and evolves in time with the fluid. The surfactants dynamics couple to the fluid dynamics by adjusting the surface tension coefficient on the interface and also through tangential Marangoni stresses caused by gradients in surfactant concentration. We prove that small perturbations of equilibria give rise to global-in-time solutions in an appropriate functional space, and we prove that the solutions return to equilibrium exponentially fast. In particular this proves the asymptotic stability of equilibria.

math.AP↗
arXiv2016

Stationary solutions to the Boltzmann equation in the Hydrodynamic limit

Despite its conceptual and practical importance, the rigorous derivation of the steady incompressible Navier-Stokes-Fourier system from the Boltzmann theory has been {an} outstanding {open problem} for general domains in 3D. We settle this open question in {the} affirmative, in the presence of a small external field and a small boundary temperature variation for the diffuse boundary condition. We employ a recent quantitative $L^{2}-L^{\infty }$ approach with new $L^{6}$ estimates for the hydrodynamic part $\mathbf{P}f$ of the distribution function. Our results also imply the validity of Fourier law in the hydrodynamical limit, and our method {leads to {asymptotical} stability of steady Boltzmann solutions as well as the derivation of the {unsteady} Navier-Stokes Fourier system}.

math.AP↗