Junichi Koganemaru

I am a mathematician by training and was most recently a Postdoctoral Associate in the Department of Mathematical Sciences at Carnegie Mellon University, the same department where I completed my Ph.D. under the supervision of Professor Ian Tice.

My research focuses on the rigorous analysis of nonlinear partial differential equations coming from physics, specifically on the free-boundary Navier-Stokes equations modeling incompressible fluids.

Background

Experience

Postdoctoral Associate

Carnegie Mellon University

Department of Mathematical Sciences

2023 – 2025

Research Mentor

Carnegie Mellon University

SEMS (Summer Experiences in the Mathematical Sciences)

Topic: Physics-informed neural networks (PINNs)

Summer 2024

Mathematical Finance Summer Undergraduate Research Program (MFSURP)

Topic: Options pricing

Summer 2022

Ph.D. Researcher

Carnegie Mellon University

Department of Mathematical Sciences

2017 – 2023

Education

Ph.D. in Mathematics

Carnegie Mellon University

Advised by Prof. Ian Tice

2017 – 2023

B.A. with Honors in Mathematics

New York University

2013 – 2017

Projects

PINNs for Options Pricing

Physics-informed neural network approaches to PDE-based pricing problems, connecting PDE analysis with ML-based numerical methods.

PDEs PyTorch scientific ML quant finance
GitHub →

Research

My research focuses on the rigorous analysis of nonlinear partial differential equations.

Research Areas

Partial Differential Equations Functional Analysis Mathematical Fluid Dynamics

Selected Publications

2024

Traveling wave solutions to the free boundary incompressible Navier-Stokes equations with Navier boundary conditions

J. Koganemaru and I. Tice

Journal of Differential Equations · 57 pp.

2023

Traveling wave solutions to the inclined or periodic free boundary incompressible Navier-Stokes equations

J. Koganemaru and I. Tice

Journal of Functional Analysis · 75 pp.

Talks

2024

Traveling wave solutions to the free boundary incompressible Navier-Stokes equations

Equadiff · Karlstad University, Sweden · June 10–14, 2024

Thesis

2023

Traveling wave solutions to the free boundary incompressible Navier-Stokes equations

Carnegie Mellon University · 272 pp.