I'm a research scientist developing software and numerical algorithms for simulation, control, and design of complex physical systems. My interests range 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.

You can see examples of my work at pkarnakov.com, reach me on social media LinkedIn, Twitter/X, and watch some of my simulation videos on YouTube.

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

Demos

Poisson	Wave	Heat

Distributed multiphysics solver 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.

Videos and demos

Foaming	Electrolysis	Drops	Gallery

Automatic differentiation framework in C++ with GPU support through OpenCL.

Game with particles and portals. Written in C++ with OpenGL and SDL2. There is a web version.

Description and screenshots

You can connect particles to create ropes, run them through portals, and manipulate with the mouse. The accel button couples the gravity vector with measurements from an accelerometer (if supported).

Native	Web

Visual materials for a class on numerical methods that I lectured in 2022.

Sound of the wave equation. Code | Slide

The forcing signal excites certain frequencies of an oscillator. Videos with (loud) sound:

Forcing	Response

Prototype operating system in x86 assembly.