arXiv subjects

Jihun Han

Publications and source records attributed to Jihun Han.

13 recordsLinked to original sources

arXiv2025

Processing and Analyzing Real-World Driving Data: Insights on Trips, Scenarios, and Human Driving Behaviors

Analyzing large volumes of real-world driving data is essential for providing meaningful and reliable insights into real-world trips, scenarios, and human driving behaviors. To this end, we developed a multi-level data processing approach that adds new information, segments data, and extracts desired parameters. Leveraging a confidential but extensive dataset (over 1 million km), this approach leads to three levels of in-depth analysis: trip, scenario, and driving. The trip-level analysis explains representative properties observed in real-world trips, while the scenario-level analysis focuses on scenario conditions resulting from road events that reduce vehicle speed. The driving-level analysis identifies the cause of driving regimes for specific situations and characterizes typical human driving behaviors. Such analyses can support the design of both trip- and scenario-based tests, the modeling of human drivers, and the establishment of guidelines for connected and automated vehicles.

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arXiv2024

Energy Efficient Automated Driving as a GNEP: Vehicle-in-the-loop Experiments

In this paper, a multi-agent motion planning problem is studied aiming to minimize energy consumption of connected automated vehicles (CAVs) in lane change scenarios. We model this interactive motion planning as a generalized Nash equilibrium problem and formalize how vehicle-to-vehicle intention sharing enables solution of the game between multiple CAVs as an optimal control problem for each agent, to arrive at a generalized Nash equilibrium. The method is implemented via model predictive control (MPC) and compared with an advanced baseline MPC which utilizes unilateral predictions of other agents' future states. A ROS-based in-the-loop testbed is developed: the method is first evaluated in software-in-the-loop and then vehicle-in-the-loop experiments are conducted. Experimental results demonstrate energy and travel time benefits of the presented method in interactive lane change maneuvers.

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arXiv2024

Robust Fourier Neural Networks

Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that introducing a simple diagonal layer after the Fourier embedding layer makes the network more robust to measurement noise, effectively prompting it to learn sparse Fourier features. We provide theoretical justifications for this Fourier feature learning, leveraging recent developments in diagonal networks and implicit regularization in neural networks. Under certain conditions, our proposed approach can also learn functions that are noisy mixtures of nonlinear functions of Fourier features. Numerical experiments validate the effectiveness of our proposed architecture, supporting our theory.

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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.

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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.

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arXiv2023

An analysis of the derivative-free loss method for solving PDEs

This study analyzes the derivative-free loss method to solve a certain class of elliptic PDEs and fluid problems using neural networks. The approach leverages the Feynman-Kac formulation, incorporating stochastic walkers and their averaged values. We investigate how the time interval associated with the Feynman-Kac representation and the walker size influence computational efficiency, trainability, and sampling errors. Our analysis shows that the training loss bias scales proportionally with the time interval and the spatial gradient of the neural network, while being inversely proportional to the walker size. Moreover, we demonstrate that the time interval must be sufficiently long to enable effective training. These results indicate that the walker size can be chosen as small as possible, provided it satisfies the optimal lower bound determined by the time interval. Finally, we present numerical experiments that support our theoretical findings.

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arXiv2023

Weighted inhomogeneous regularization for inverse problems with indirect and incomplete measurement data

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's characteristics, such as sparsity or smoothness. Inhomogeneous regularization, which incorporates a spatially varying exponent $p$ in the standard $\ell_p$-norm-based framework, has been used to recover signals with spatially varying features. This study introduces weighted inhomogeneous regularization, an extension of the standard approach incorporating a novel exponent design and spatially varying weights. The proposed exponent design mitigates misclassification when distinct characteristics are spatially close, while the weights address challenges in recovering regions with small-scale features that are inadequately captured by traditional $\ell_p$-norm regularization. Numerical experiments, including synthetic image reconstruction and the recovery of sea ice data from incomplete wave measurements, demonstrate the effectiveness of the proposed method.

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arXiv2022

Energy-Efficient Driving in Connected Corridors via Minimum Principle Control: Vehicle-in-the-Loop Experimental Verification in Mixed Fleets

Connected and automated vehicles (CAVs) can plan and actuate control that explicitly considers performance, system safety, and actuation constraints in a manner more efficient than their human-driven counterparts. In particular, eco-driving is enabled through connected exchange of information from signalized corridors that share their upcoming signal phase and timing (SPaT). This is accomplished in the proposed control approach, which follows first principles to plan a free-flow acceleration-optimal trajectory through green traffic light intervals by Pontryagin's Minimum Principle in a feedback manner. Urban conditions are then imposed from exogeneous traffic comprised of a mixture of human-driven vehicles (HVs) - as well as other CAVs. As such, safe disturbance compensation is achieved by implementing a model predictive controller (MPC) to anticipate and avoid collisions by issuing braking commands as necessary. The control strategy is experimentally vetted through vehicle-in-the-loop (VIL) of a prototype CAV that is embedded into a virtual traffic corridor realized through microsimulation. Up to 36% fuel savings are measured with the proposed control approach over a human-modelled driver, and it was found connectivity in the automation approach improved fuel economy by up to 26% over automation without. Additionally, the passive energy benefits realizable for human drivers when driving behind downstream CAVs are measured, showing up to 22% fuel savings in a HV when driving behind a small penetration of connectivity-enabled automated vehicles.

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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.

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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.

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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.

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arXiv2020

A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks

We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic representation of the PDE in the spirit of the Feynman-Kac formula. The solution is given by an expectation of a martingale process driven by a Brownian motion. As Brownian walkers explore the domain, the deep neural network is iteratively trained using a form of reinforcement learning. Our method is a 'Derivative-Free Loss Method' since it does not require the explicit calculation of the derivatives of the neural network with respect to the input neurons in order to compute the training loss. The advantages of our method are showcased in a series of test problems: a corner singularity problem, an interface problem, and an application to a chemotaxis population model.

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arXiv2015

The Intrinsic Bounds on the Risk Premium of Markovian Pricing Kernels

The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and lower bounds on the risk premium of an asset based on the market prices of options. One of the key assumptions to achieve this goal is that the market is Markovian. Under this assumption, we can transform the problem of finding the bounds into a second-order differential equation. We then obtain upper and lower bounds on the risk premium by analyzing the differential equation.

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