01
Machine Learning & Deep Learning
Regression, classification, neural networks, optimisation, model evaluation and practical experimentation.
OSLO · NORWAY
Zejing Wang.
AI meets mathematics.
Master's student in Mathematics for Applications at the University of Oslo, working across machine learning, scientific computing, numerical PDEs, NLP and computational modelling.
PythonPyTorchMachine LearningNumerical PDEsNLPScientific Computing
ACADEMIC DIRECTION
From mathematical structure
to computational models.
My main interest is the intersection of mathematics and computation: understanding a problem analytically, implementing numerical methods, and using machine learning where it can add something meaningful. My current direction is deep learning for conservation laws and scientific computing.
TECHNICAL FOCUS
A broad toolkit with a mathematical core.
I am building depth in numerical mathematics while expanding into modern AI, data-driven methods and high-performance computing.
02
Scientific Computing
Numerical modelling, simulation, numerical stability, approximation and computational experiments for scientific problems.
03
PDEs & Conservation Laws
Hyperbolic PDEs, finite-volume ideas, shocks, rarefactions, entropy conditions and numerical flux functions.
04
Natural Language Processing
Tokenisation, language modelling, sequence labelling, probabilistic methods and neural representations of language.
05
Computer Vision
Developing toward deep-learning methods for image analysis, classification, detection and visual representation.
06
HPC & Software
Strengthening software engineering and performance-oriented computing, with Python as the main language and growing C/C++ skills.
PROJECTS & TECHNICAL WORK
What I have actually worked on.
Research direction, numerical simulation, machine learning, NLP and algorithmic coursework — with the emphasis on implementation and mathematical understanding.
Deep Learning for Numerical Fluxes & Conservation Laws
My master's direction is to study how deep learning can be used to learn or improve numerical flux functions for hyperbolic conservation laws, while retaining the numerical structure needed for stable and physically meaningful computation.
- Finite-volume methods and numerical fluxes for conservation laws.
- Riemann problems, shocks, rarefactions, contacts and entropy conditions.
- Longer-term application direction: systems of conservation laws and the two-dimensional Euler equations.
CFD & Numerical Simulation of Fluid Dynamics
Developed numerical models in Python for one-dimensional hydrodynamics and coupled ion-neutral fluids, with emphasis on understanding the numerical behaviour rather than treating the solver as a black box.
- Studied stability and shock structures in numerical solutions.
- Examined numerical diffusion and compared results with exact solutions.
- Connected physical modelling with numerical discretisation and computational analysis.
Regression & Optimisation for the Runge Function
A machine-learning project on polynomial regression using the Runge function as a controlled test problem, comparing closed-form regression with gradient-based optimisation.
- Implemented OLS, Ridge and Lasso regression with polynomial features.
- Used k-fold cross-validation, MSE and R² to study model complexity and regularisation.
- Implemented and compared Plain GD, Momentum, AdaGrad, RMSProp, Adam and stochastic-gradient approaches.
Language Models, Tokenisation & Sequence Labelling
NLP coursework combining probabilistic language modelling and sequence-labelling methods with practical implementation and model analysis.
- BPE-style tokenisation and text representation.
- N-gram language models with smoothing and backoff ideas.
- POS / sequence modelling with HMMs, CRFs, Viterbi decoding and perceptron-based methods.
Search, Evolutionary Algorithms & Machine Learning
Algorithmic AI coursework focused on how search and learning methods behave under different representations, objective functions and optimisation strategies.
- Compared local search ideas such as hill climbing with population-based evolutionary algorithms.
- Worked with fitness functions, mutation, crossover and selection.
- Connected optimisation choices to exploration, exploitation and generalisation.
Hyperbolic Conservation Laws — Analytical Foundation
A theoretical foundation supporting the scientific-machine-learning direction, with emphasis on the structure of weak solutions and physically relevant solution concepts.
- Riemann problems and Rankine–Hugoniot jump conditions.
- Lax entropy, Kružkov and Oleinik conditions, and vanishing-viscosity ideas.
- Front tracking, characteristic structure, eigenvalues/eigenvectors and genuinely nonlinear versus linearly degenerate fields.
SELECTED COURSEWORK
Mathematics first. Computing on top.
My coursework spans advanced analysis and PDEs, numerical methods, statistics, machine learning, NLP, programming and economics. Current and planned courses are separated from the broader academic foundation below.
Current · Autumn 2026
CurrentFYS-STK4155
Applied Data Analysis and Machine Learning
IN4050
Introduction to Artificial Intelligence and Machine Learning
IN4080
Natural Language Processing
Current work combines statistical learning, neural networks, optimisation, AI algorithms and practical NLP.
PDEs & Advanced Analysis
FoundationMAT4301
Partial Differential Equations
MAT4305
Partial Differential Equations and Sobolev Spaces
MAT4400
Linear Analysis with Applications
MATSP100
Front Tracking for Hyperbolic Conservation Laws
MAT4500
Topology
Numerical & Computational Mathematics
FoundationMAT4110
Introduction to Numerical Analysis
MAT3360
Introduction to Partial Differential Equations
MAT-INF1100
Modelling and Computations
IN1910
Programming for Scientific Applications
Statistics, Data & Risk
FoundationSTK1100
Probability and Statistical Modelling
STK1110
Statistical Methods and Data Analysis
STK2130
Modelling by Stochastic Processes
STK3405
Introduction to Risk and Reliability Analysis
Mathematics & Economics Foundation
BScMAT1100
Calculus
MAT1110
Calculus and Linear Algebra
MAT1120
Linear Algebra
MAT2200
Groups, Rings and Fields
MAT2400
Real Analysis
ECON1210
Microeconomics 1
ECON2220
Microeconomics 2
ECON1310
Macroeconomics
ECON2310
Macroeconomics 2
EXPHIL03
Examen Philosophicum
Planned · 2027
PlannedIN4310
Deep Learning for Image Analysis
IN4200
High-Performance Computing and Numerical Projects
FYS5429
Advanced Machine Learning and Data Analysis for the Physical Sciences
The plan is designed to add computer vision, performance-oriented computing and more advanced machine learning before the main thesis period.
PROFILE
Zejing Wang
Mathematics · Machine Learning · Scientific Computing
DegreeMSc Mathematics for Applications, UiO · 2025–2028
BachelorMathematics and Economics, UiO · 2021–2024
ThesisDeep learning of numerical flux functions for conservation laws
SupervisorProf. Nils Henrik Risebro
I am a Master's student in Mathematics for Applications at the University of Oslo, with a bachelor's degree in Mathematics and Economics. My strongest academic interests are mathematical analysis, partial differential equations, numerical methods and computational modelling, increasingly combined with machine learning and deep learning.
I am particularly interested in work where a strong mathematical model, a numerical implementation and data-driven methods meet. Alongside technical work, I have experience teaching mathematics and taking operational responsibility in student organisations.
PythonPyTorchMATLABRGit / GitHubLaTeXMachine LearningDeep LearningNumerical MethodsPDEsNLPHPC
LanguagesNorwegian · English · Chinese
InterestsScientific ML · numerical simulation · computer vision · NLP · optimisation
EDUCATION & EXPERIENCE
Technical depth plus real responsibility.
My background is not only coursework. I have taught mathematics, managed practical operations for student reading rooms, and represented students at faculty level.
2025 — 2028
MSc Mathematics for Applications · University of Oslo
Graduate studies in applied mathematics with a focus on PDEs, numerical analysis, machine learning and scientific computing.
Master's thesis direction: deep learning of numerical flux functions for conservation laws, finite-volume methods and applications toward two-dimensional Euler equations.
JUN — JUL 2026
Mathematics Teaching · OsloMet
Student assistant / group teacher for TRE1000 and TRE1300.
Teaching and problem-session support in linear algebra, differential equations and calculus.
SEP 2025 — PRESENT
Reading Room Manager · MFU / University of Oslo
Responsible for applications, allocation of reading-room spaces, access follow-up and practical communication.
The role involves coordination, structured follow-up, independent decisions and communication with students and administration.
MAR — SEP 2026
Student Representative · Faculty of Mathematics and Natural Sciences
Represented student interests in dialogue with faculty administration and leadership.
Experience with formal communication, representation and cross-organisational collaboration.
2021 — 2024
BSc Mathematics & Economics · University of Oslo
Combined mathematics, economics, statistics, modelling, risk analysis and quantitative methods.
The degree provides a broad quantitative foundation behind the current shift toward applied mathematics and computing.
ONGOING DEVELOPMENT
Programming & Computational Skills
Python and PyTorch are my main tools for current technical work, supported by MATLAB, R, Git/GitHub and LaTeX.
I am also expanding toward C/C++, computer vision and high-performance computing.
CONTACT
Open to problems
worth solving.
I am interested in internships, part-time roles and technical projects involving machine learning, scientific computing, numerical methods, NLP, computer vision or applied mathematics.
Professional and academic references are available on request.