Petr Karnakov

Research scientist developing software and numerical algorithms for simulation, control, and design of complex physical systems. Interests ranging from classical numerical methods to data-driven techniques and machine learning, with a focus on software engineering and high-performance computing. List of publications.

Currently working at Harvard University in Cambridge, MA, United States.

Skills

Skills grouped by activities

Programming
C++, Python, JavaScript, OpenGL, Fortran, x86 assembly

High Performance Computing
MPI, OpenMP, OpenCL, CUDA, HDF5, vectorization

Mathematics
Numerical methods, linear algebra, optimization

Machine Learning
TensorFlow, JAX, reinforcement learning, stochastic methods, Bayesian inference

Visualization & Simulation
Matplotlib, ParaView, Ansys Fluent, COMSOL

Development Tools
Git, Unix shell, CMake, Docker, CI/CD

Presentation & Publishing
LaTeX, HTML, Keynote, reveal.js

Research Projects

ODIL

ODIL (Optimizing a DIscrete Loss) is a method and Python framework for solving inverse problems for partial differential equations, which is orders of magnitude faster than PINN (physics-informed neural networks). Article about the method.

Inverse design: body from flow

Demo: Poisson

Demo: Wave

Demo: Heat

Aphros

Distributed multiphysics solver in C++ with MPI for simulating multiphase flow with bubbles and electrochemical reactors. The solver performed the largest simulations of foaming by breakup and mixing of air in water. Article about foam simulations.

Bubble coalescence