林得勝

Supervising Autoencoders with Manifold Learning Embeddings: Out-of-Sample Extension and Interpretable Latent Spaces

應用數學系

降維、流形學習、自動編碼器、監督式自動編碼器、樣本外擴展、可解釋潛在空間、Dimensionality Reduction、Manifold Learning、Autoencoder、Supervised Autoencoder、Out-of-Sample Extension、Interpretable Latent Space

Ultraspherical Spectral Methods for the Poisson and Biharmonic Equations in Polar Geometry

應用數學系

超球譜方法、極座標系、矩陣條件數、快速泊松求解器、雙調和方程、Ultraspherical spectral method、Polar coordinates、Matrix conditioning、Fast Poisson solver、Biharmonic equation

A Unified Framework for Classifying Steady-State Distribution Modes in Self-Regulated Gene Networks

應用數學系・共同指導：蔡志強

基因表現網路、啟動子轉換、穩態分布、噪音誘導的雙峰現象、化學主方程、遞迴關係、gene expression network、promoter transitions、steady-state distribution、Noise-induced bimodality、chemical master equation、recursive relations

Physics-Informed Neural Networks for Solving PDEs in Unbounded Domains and with Self-Similar Singularities

應用數學系

物理訊息神經網路、無界域、Poisson 方程、自相似奇異性、Burgers 方程、Physics-Informed Neural Networks、Unbounded Domain、Poisson Equation、Self-Similar Singularity、Burgers' Equation

A Correction Function-Based Neural Network Method for solving Interface Problem

應用數學系數學建模與科學計算

神經網路、有限差分法、修正函數法、橢圓介面問題、斯托克斯介面問題、沉浸介面法、Neural Networks、Finite difference method、Correction function method、Elliptic interface problem、Stokes interface problem、Immersed Interface Method

Exploring Architectural Modifications in Vision Transformer

應用數學系數學建模與科學計算

Vision Transformer、自注意力機制、數學分析、圖片分類、函數擬合、Self-attention、Mathematical Analysis、Image Classifying、Function Fitting

In-depth Analysis of Generative Models: Novel Perspectives through Manifold Learning

應用數學系數學建模與科學計算

擴散模型、生成式AI、流形學習、擴散圖降維、Diffusion Models、Manifold Learning、Diffusion Maps、Generative AI、Dimension Reduction

Solving Elliptic Partial Differential Equations using Ritz method and Physics-Informed Neural Networks

應用數學系數學建模與科學計算

橢圓偏微分方程、李茲法、物理信息神經網路、泊松方程式、格林函數、Elliptic Partial Differential Equations、The Ritz method、PINNs、Poisson equation、Green's function

BE-PINN and ND-PINN for boundary layer problems and biharmonic equations

應用數學系數學建模與科學計算

物理訊息神經網路、水平集方法、邊界層問題、有限差分法、雙調和方程、Physics Informed Neural Networks、level set method、boundary layer problems、finite difference method、bihramonic equations

Approximating high-dimensional functions with neural networks

應用數學系數學建模與科學計算

深度學習、人工神經網路、Deep Learning、Artificial Neural Networks

Anomaly Detection via Manifold Learning

應用數學系所

異常檢測、流形學習、擴散映射、局部線性嵌入、譜聚類、Anomaly detection、Manifold learning、Diffusion map、Locally linear embedding、Spectral clustering

Operator learning with neural network - Based on DeepONet and cubic spline interpolation

應用數學系所

神經網路、三次樣條插值法、深度學習、近似函數、算子學習、Neural Network、Cubic Spline Interpolation、Deep Learning、Approximation、Operator Learning

A Strategy for Incremental Learning

應用數學系數學建模與科學計算碩士班

增量式學習、災難性遺忘、物體辨識、多項式擬合、Incremental learning、Catastrophic forgetting、Object detection、Curve fitting

Using the Neural ODE family to predict the number of confirmed cases in Taiwan

應用數學系所

深度學習、神經常微分方程、殘差網路、時間序列模型、伴隨靈敏度法、Deep Learning、Neural Ordinary Differential Equations、Residual Networks、Time Series Models、Adjoint Sensitivity Method

Local Landmark Extension via Anisotropic Diffusion Maps

應用數學系所

非線性降維、流形學習、擴散映射、Dimensionality reduction、Manifold learning、Diffusion maps

Operator learning with neural network - A direct construction

應用數學系所

神經網路、微分矩陣、算子學習、值譜法、Lagrange插值法、近似、Neural Network、Differential Matrix、Operator learning、Spectral Method、Lagrange interpolation、Approximation

Online Updating Method for Dimensionality Reduction Algorithms

應用數學系數學建模與科學計算碩士班

降維演算法、擴散映射、Roseland演算法、Johnson Lindenstrauss引理、降維演算法的即時更新方法、dimensionality reduction algorithms、Diffusion Maps、Roseland、Johnson Lindenstrauss Lemma

Waveforms of Arterial Blood Pressure Using Manifold Learning

應用數學系所

動脈血壓波形、主成分分析、擴散映射、Arterial blood pressure、Principal component analysis、Diffusion maps

Numerical simulation of solutions of Cahn-Hilliard equation on a disk

應用數學系數學建模與科學計算碩士班

Cahn-Hilliard、泊松方程、雙調和方程、四階擴散方程、有限差分法、克蘭克－尼科爾森方法、反向尤拉法、Poisson、Biharmonic、Fourth order diffusion、Finite centered difference method、Crank-Nicolson method、Backward Euler method

Spectral method for modified Poisson-Boltzmann equation on different geometries

應用數學系所

譜方法、切比雪夫點、切比雪夫-傅立葉演算法、修正泊松-玻爾茲曼方程、電雙層、Spectral method、Chebyshev points、Chebyshev-Fourier Algorithm、MPB equation、Electrical double layer

Formulation and applications of spectral approximations

應用數學系數學建模與科學計算碩士班

譜配置、譜微分矩陣、譜積分矩陣、Collocation、Spectral differentiation matrix、Spectral integration matrix ii

The spreading of an invasive species in one-dimensional heterogeneous environments

應用數學系所

族群動態、物種擴散、反應擴散平流模型、入侵物種、嵌入邊界法、固定邊界法、Population dynamics、Spreading、Reaction-diffusion-advection equation、Invasive species、Immersed boundary Method、Boundary immobilization method

Echo Labeling for Room Shape Estimation Achieved by Alternating Coordinate Descent, Quasi-Newton and Trust-region Methods

應用數學系數學建模與科學計算碩士班・共同指導：劉奕汶

房間形狀估計、回聲標記、room shape estimation、echo labeling

Galerkin Method for Partial Differential Equations in One Dimension

應用數學系數學建模與科學計算碩士班

有限元素法、伽遼金方法、Finite element method、Galerkin method

Pulse transit time of pressure waves in blood vessels

應用數學系所

血液壓力波、行進時間、波方程、樑方程、pressure waves、pulse transit time、wave equation、beam equation