arXiv subjects

Yoonsang Lee

Publications and source records attributed to Yoonsang Lee.

At least 37 records · Page 2Linked to original sources

arXiv2024

AmbigDocs: Reasoning across Documents on Different Entities under the Same Name

Different entities with the same name can be difficult to distinguish. Handling confusing entity mentions is a crucial skill for language models (LMs). For example, given the question "Where was Michael Jordan educated?" and a set of documents discussing different people named Michael Jordan, can LMs distinguish entity mentions to generate a cohesive answer to the question? To test this ability, we introduce a new benchmark, AmbigDocs. By leveraging Wikipedia's disambiguation pages, we identify a set of documents, belonging to different entities who share an ambiguous name. From these documents, we generate questions containing an ambiguous name and their corresponding sets of answers. Our analysis reveals that current state-of-the-art models often yield ambiguous answers or incorrectly merge information belonging to different entities. We establish an ontology categorizing four types of incomplete answers and automatic evaluation metrics to identify such categories. We lay the foundation for future work on reasoning across multiple documents with ambiguous entities.

cs.CL↗

arXiv2024

Crafting In-context Examples according to LMs' Parametric Knowledge

In-context learning can improve the performances of knowledge-rich tasks such as question answering. In such scenarios, in-context examples trigger a language model (LM) to surface information stored in its parametric knowledge. We study how to better construct in-context example sets, based on whether the model is aware of the in-context examples. We identify 'known' examples, where models can correctly answer from their parametric knowledge, and 'unknown' ones. Our experiments show that prompting with 'unknown' examples decreases the performance, potentially as it encourages hallucination rather than searching for its parametric knowledge. Constructing an in-context example set that presents both known and unknown information performs the best across diverse settings. We perform analysis on three multi-answer question answering datasets, which allows us to further study answer set ordering strategies based on the LM's knowledge of each answer. Together, our study sheds light on how to best construct in-context example sets for knowledge-rich tasks.

cs.CL↗

arXiv2024

Utilizing Motion Matching with Deep Reinforcement Learning for Target Location Tasks

We present an approach using deep reinforcement learning (DRL) to directly generate motion matching queries for long-term tasks, particularly targeting the reaching of specific locations. By integrating motion matching and DRL, our method demonstrates the rapid learning of policies for target location tasks within minutes on a standard desktop, employing a simple reward design. Additionally, we propose a unique hit reward and obstacle curriculum scheme to enhance policy learning in environments with moving obstacles.

cs.GR↗

arXiv2024

Stochastic approach for elliptic problems in perforated domains

A wide range of applications in science and engineering involve a PDE model in a domain with perforations, such as perforated metals or air filters. Solving such perforated domain problems suffers from computational challenges related to resolving the scale imposed by the geometries of perforations. We propose a neural network-based mesh-free approach for perforated domain problems. The method is robust and efficient in capturing various configuration scales, including the averaged macroscopic behavior of the solution that involves a multiscale nature induced by small perforations. The new approach incorporates the derivative-free loss method that uses a stochastic representation or the Feynman-Kac formulation. In particular, we implement the Neumann boundary condition for the derivative-free loss method to handle the interface between the domain and perforations. A suite of stringent numerical tests is provided to support the proposed method's efficacy in handling various perforation scales.

math.NA↗

arXiv2024

A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations

Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is well known that the commonly used Gaussian distribution assumption introduces biases for state variables that admit discontinuous profiles, which are prevalent in nonlinear partial differential equations. This investigation designs a new structurally informed non-Gaussian prior that exploits statistical information from the simulated state variables. In particular, we construct a new weighting matrix based on the second moment of the gradient information of the state variable to replace the prior covariance matrix used for model/data compromise in the ETKF data assimilation framework. We further adapt our weighting matrix to include information in discontinuity regions via a clustering technique. Our numerical experiments demonstrate that this new approach yields more accurate estimates than those obtained using ETKF on shallow water equations, even when ETKF is enhanced with inflation and localization techniques.

math.NA↗

arXiv2024

Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13

We give a list of minimal grid diagrams of the 13 crossing prime nonalternating knots which have arc index 13. There are 9,988 prime knots with crossing number 13. Among them 4,878 are alternating and have arc index 15. Among the other nonalternating knots, 49, 399, 1,412 and 3,250 have arc index 10, 11, 12, and 13, respectively. We used the Dowker-Thistlethwaite code of the 3,250 knots provided by the program Knotscape to generate spanning trees of the corresponding knot diagrams to obtain minimal arc presentations in the form of grid diagrams.

math.GT↗

arXiv2024

Learning Human-like Locomotion Based on Biological Actuation and Rewards

We propose a method of learning a policy for human-like locomotion via deep reinforcement learning based on a human anatomical model, muscle actuation, and biologically inspired rewards, without any inherent control rules or reference motions. Our main ideas involve providing a dense reward using metabolic energy consumption at every step during the initial stages of learning and then transitioning to a sparse reward as learning progresses, and adjusting the initial posture of the human model to facilitate the exploration of locomotion. Additionally, we compared and analyzed differences in learning outcomes across various settings other than the proposed method.

cs.GR↗

arXiv2024

Adaptive Tracking of a Single-Rigid-Body Character in Various Environments

Since the introduction of DeepMimic [Peng et al. 2018], subsequent research has focused on expanding the repertoire of simulated motions across various scenarios. In this study, we propose an alternative approach for this goal, a deep reinforcement learning method based on the simulation of a single-rigid-body character. Using the centroidal dynamics model (CDM) to express the full-body character as a single rigid body (SRB) and training a policy to track a reference motion, we can obtain a policy that is capable of adapting to various unobserved environmental changes and controller transitions without requiring any additional learning. Due to the reduced dimension of state and action space, the learning process is sample-efficient. The final full-body motion is kinematically generated in a physically plausible way, based on the state of the simulated SRB character. The SRB simulation is formulated as a quadratic programming (QP) problem, and the policy outputs an action that allows the SRB character to follow the reference motion. We demonstrate that our policy, efficiently trained within 30 minutes on an ultraportable laptop, has the ability to cope with environments that have not been experienced during learning, such as running on uneven terrain or pushing a box, and transitions between learned policies, without any additional learning.

cs.RO↗

arXiv2024

Performance-Based Biped Control using a Consumer Depth Camera

We present a technique for controlling physically simulated characters using user inputs from an off-the-shelf depth camera. Our controller takes a real-time stream of user poses as input, and simulates a stream of target poses of a biped based on it. The simulated biped mimics the user's actions while moving forward at a modest speed and maintaining balance. The controller is parameterized over a set of modulated reference motions that aims to cover the range of possible user actions. For real-time simulation, the best set of control parameters for the current input pose is chosen from the parameterized sets of pre-computed control parameters via a regression method. By applying the chosen parameters at each moment, the simulated biped can imitate a range of user actions while walking in various interactive scenarios.

cs.GR↗

arXiv2023

Learning In-between Imagery Dynamics via Physical Latent Spaces

We present a framework designed to learn the underlying dynamics between two images observed at consecutive time steps. The complex nature of image data and the lack of temporal information pose significant challenges in capturing the unique evolving patterns. Our proposed method focuses on estimating the intermediary stages of image evolution, allowing for interpretability through latent dynamics while preserving spatial correlations with the image. By incorporating a latent variable that follows a physical model expressed in partial differential equations (PDEs), our approach ensures the interpretability of the learned model and provides insight into corresponding image dynamics. We demonstrate the robustness and effectiveness of our learning framework through a series of numerical tests using geoscientific imagery data.

cs.LG↗

arXiv2022

Designing Neural Networks for Hyperbolic Conservation Laws

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form network (CFN) in which the network learns the flux function of the unknown system. Our numerical examples demonstrate that the CFN yields significantly better prediction accuracy than what is obtained using a standard non-conservative form network, even when it is enhanced with constraints to promote conservation. In particular, solutions obtained using the CFN consistently capture the correct shock propagation speed without introducing non-physical oscillations into the solution. They are furthermore robust to noisy and sparse observation environments.

math.NA↗

arXiv2022

Improving numerical accuracy for the viscous-plastic formulation of sea ice

Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the most widely accepted model based on the viscous-plastic (VP) formulation introduced by Hibler in 1979. Due to its highly nonlinear features, this model is intrinsically challenging for computational solvers. In particular, sea ice simulations often significantly differ from satellite observations. This study therefore focuses on improving the numerical accuracy of the VP sea ice model. Since the poor convergence observed in existing numerical simulations stems from the nonlinear nature of the VP formulation, this investigation proposes using the celebrated weighted essentially non-oscillatory (WENO) scheme -- as opposed to the frequently employed centered difference (CD) scheme -- for the spatial derivatives in the VP sea ice model. We then proceed to numerically demonstrate that WENO yields higher-order convergence for smooth solutions, and that furthermore it is able to resolve the discontinuities in the sharp features of sea ice covers -- something that is not possible using CD methods. Finally, our proposed framework integrates a potential function method that utilizes the phase field method to naturally incorporates the physical restrictions of ice thickness and ice concentration in transport equations, resulting in a modified transport equations which includes additional forcing terms. Our method does not require post-processing, thereby avoiding the possible introduction of discontinuities and corresponding negative impact on the solution behavior. Numerical experiments are provided to demonstrate the efficacy of our new methodology.

math.NA↗

arXiv2022

A Neural Network Approach for Homogenization of Multiscale Problems

We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a multiscale PDE solution. Compared with other network-based approaches for multiscale problems, the proposed method is free from the design of hand-crafted neural network architecture and the cell problem to calculate the homogenization coefficient. The exploration neighborhood of the Brownian walkers affects the overall learning trajectory. We determine the bounds of micro- and macro-time steps that capture the local heterogeneous and global homogeneous solution behaviors, respectively, through a neural network. The bounds imply that the computational cost of the proposed method is independent of the microscale periodic structure for the standard periodic problems. We validate the efficiency and robustness of the proposed method through a suite of linear and nonlinear multiscale problems with periodic and random field coefficients.

cs.LG↗

arXiv2022

Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural network, the network learns global features corresponding to low-frequency components while high-frequency components are approximated at a much slower rate. For a class of equations in which the solution contains a wide range of scales, the network training process can suffer from slow convergence and low accuracy due to its inability to capture the high-frequency components. In this work, we propose a hierarchical approach to improve the convergence rate and accuracy of the neural network solution to partial differential equations. The proposed method comprises multi-training levels in which a newly introduced neural network is guided to learn the residual of the previous level approximation. By the nature of neural networks' training process, the high-level correction is inclined to capture the high-frequency components. We validate the efficiency and robustness of the proposed hierarchical approach through a suite of linear and nonlinear partial differential equations.

cs.LG↗

arXiv2021

Inhomogenous Regularization with Limited and Indirect Data

For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a suite of regularization of various characteristics depending on the value of p. When there are no explicit features to determine p, a spatially varying inhomogeneous p can be incorporated to apply different regularization characteristics that change over the domain. This study proposes a strategy to design the exponent p when the first and second derivatives of the true signal are not available, such as in the case of indirect and limited measurement data. The proposed method extracts statistical and patch-wise information using multiple reconstructions from a single measurement, which assists in classifying each patch to predefined features with corresponding p values. We validate the robustness and effectiveness of the proposed approach through a suite of numerical tests in 1D and 2D, including a sea ice image recovery from partial Fourier measurement data. Numerical tests show that the exponent distribution is insensitive to the choice of multiple reconstructions.

math.NA↗

arXiv2021

Sampling error correction in ensemble Kalman inversion

Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to capture the correct statistical information in estimating the unknown variable of interest. Still, the ensemble is limited to a size smaller than the unknown variable's dimension for computational efficiency. This study proposes a strategy to correct the sampling error due to a small ensemble size, which improves the performance of the ensemble Kalman inversion. This study validates the efficiency and robustness of the proposed strategy through a suite of numerical tests, including compressive sensing, image deblurring, parameter estimation of a nonlinear dynamical system, and a PDE-constrained inverse problem.

math.NA↗

arXiv2021

$l_p$ regularization for ensemble Kalman inversion

Ensemble Kalman inversion (EKI) is a derivative-free optimization method that lies between the deterministic and the probabilistic approaches for inverse problems. EKI iterates the Kalman update of ensemble-based Kalman filters, whose ensemble converges to a minimizer of an objective function. EKI regularizes ill-posed problems by restricting the ensemble to the linear span of the initial ensemble, or by iterating regularization with early stopping. Another regularization approach for EKI, Tikhonov EKI, penalizes the objective function using the $l_2$ penalty term, preventing overfitting in the standard EKI. This paper proposes a strategy to implement $l_p, 0<p\leq 1,$ regularization for EKI to recover sparse structures in the solution. The strategy transforms a $l_p$ problem into a $l_2$ problem, which is then solved by Tikhonov EKI. The transformation is explicit, and thus the proposed approach has a computational cost comparable to Tikhonov EKI. We validate the proposed approach's effectiveness and robustness through a suite of numerical experiments, including compressive sensing and subsurface flow inverse problems.

math.NA↗

arXiv2020

Understanding the Stability of Deep Control Policies for Biped Locomotion

Achieving stability and robustness is the primary goal of biped locomotion control. Recently, deep reinforce learning (DRL) has attracted great attention as a general methodology for constructing biped control policies and demonstrated significant improvements over the previous state-of-the-art. Although deep control policies have advantages over previous controller design approaches, many questions remain unanswered. Are deep control policies as robust as human walking? Does simulated walking use similar strategies as human walking to maintain balance? Does a particular gait pattern similarly affect human and simulated walking? What do deep policies learn to achieve improved gait stability? The goal of this study is to answer these questions by evaluating the push-recovery stability of deep policies compared to human subjects and a previous feedback controller. We also conducted experiments to evaluate the effectiveness of variants of DRL algorithms.

cs.GR↗