Ritoban Roy-Chowdhury

I am a undergraduate student double majoring in Computer Science and Mathematics at the University of California, San Diego. I do research advised by Albert Chern at the Center for Visual Computing, working on Computer Graphics, particularly structure-preserving fluid simulation algorithms.

In Summer 2025, I interned at Sandia National Labs working on research on scientific machine learning for dissipative systems described by Onsager's Variational Principle, like the Cahn-Hilliard equations applied to modelling block copolymers. I was supported by the M2dt: Multifaceted Mathematics for Predictive Digital Twins project, and was advised by Anthony Gruber, Irina Tezaur, and Nathan Urban.

Previously, in high school and my first year of college, I worked at the University of California, Riverside with Tamar Shinar and Craig Schroeder, on interpolation algorithms for divergence and curl free vector fields, as well as geometric machine learning algorithms for reconstructing surfaces from point clouds.

Email: rroychowdhury-at-ucsd-dot-edu

CV  /  GitHub  /  Google Scholar  /  LinkedIn

Research

I'm interested in mathematical applications of computing -- scientific computing, physics simulations, geometry processing algorithms, and machine learning. I'm passionate about beautiful mathematical ideas, sharing them with other people, developing algorithms that use them, and using that to build interesting programs.

I'm particularly excited when I can bring ideas from pure mathematics and apply them to computational problems with a physical flavor. Recently, that's often meant differential geometry and the calculus of variations applied to fluid simulation and other partial differential equations. But I'm curious about and have explored mathematics both with a more analytic flavor (optimal transport, functional analysis, ergodic theory) as well as algebro-geometric (complex differential geometry, sheaf and cohomology theory, characteristic classes) -- and I hope to apply them to interesting computational problems in the future!

Vakonomic Fluids

We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms. It is well known that encoding diffeomorphisms and their infinitesimal generators through a discretized Koopman representation places a nonholonomic constraint on discrete velocities, for which there is no consensus on a variational treatment. We show that taking the vakonomic perspective, as opposed to the usual perspective of Lagrange-d’Alembert, yields discrete fluid trajectories that remain geodesics on a (sub-)Riemannian manifold. In particular, the resulting vakonomic dynamics are Lie–Poisson and their solutions admit a discrete relabeling symmetry, leading to machine-precision satisfaction of Casimir invariants along with a discrete analogue of Kelvin’s Circulation Theorem. Using an efficient momentum map representation based on low-rank Clebsch variables, we show that these vakonomic fluids behave stably and consistently even at low grid resolutions, leading to increased robustness and physical realism in the long term.

Flexible and Stable Dynamics Discovery with Onsager's Variational Principle

Variational principles specify the dynamics of a physical system via the extremization of associated functional data. Onsager’s variational principle (OVP), which characterizes dissipation-dominated phenomena such as phase separation, admits an unconditionally energy-stable time discretization through the minimization of a Rayleighan functional combining free energy and dissipative effects. The present work considers the case where one or more parts of this functional are empirically approximated or otherwise uncertain. To address this, a novel variational discretization of OVP is introduced which recovers previous work as a special case, and a learning problem is formulated which identifies uncertain terms in the free energy and dissipation potential from observable data. It is shown that the resulting OVP-based models connect directly to previous work in terms of proximal methods, Sobolev and Wasserstein gradient flows, while remaining provably energy-stable under arbitrarily long rollouts. The approach is illustrated on examples including Allen-Cahn, Fokker-Planck, and Cahn-Hilliard system models, where the effects of bulk free-energy densities, nonlocal potentials, and nonstandard boundary conditions are effectively learned with model classes consisting of polynomials, shallow neural networks, and spectral convolution kernels.

Fluid Implicit Particles on Coadjoint Oribts

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. Using a discrete Hamiltonian formulation we achieve energy and Casimir preservation; formally, the flow evolves on infinite-dimensional coadjoint orbits. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions.

Higher order divergence-free and curl-free interpolation on MAC grids

Building on our prior divergence-free interpolation paper, (1) we design a divergence-free interpolation scheme that preserves the discrete flux, (2) we adapt the general construction of divergence-free fields into a general construction for curl-free fields, (3) we extend the framework to a more general class of finite difference discretizations, and (4) we use this flexibility to construct fourth-order accurate interpolation schemes for the divergence-free case and the curl-free case.

Local divergence-free polynomial interpolation on MAC grids

In discretizations of partial differential equations, diveregence free vector fields are often obtained by solving a linear system, resulting in a discrete approximation of the continuous field that is discretely divergence-free. For many applications, such as tracing particles, this discrete field must then be extended to the entire region using interpolation. In this paper, we construct approximation schemes with the property that discretely divergence-free data interpolates to an analytically divergence-free vector field. Our solution is remarkably simple, compared to previous approaches, being local, piecewise polynomial, and $C^0$ or $C^1$ continuous, even at cell boundaries.

Projects

Rendering Fractals with Raymarching

Extends the path tracer from CSE 167 to support ray marching. Ray marching allows one to render any geometry described by a signed distance function (SDF), by taking steps along rays of size determined by the SDF. By constructing repeating SDFs, we can very efficiently render fractals or other duplicated geometries, like the Menger Sponge shown on the left, or manipulate geometry (such as by extruding or rounding corners) simply by processing the SDF.

Triton Trails

A React/Typescript web app that displays hiking trails in the San Diego area, and lets users create accounts, create new trails, and write reviews. The backend is implemented as an Express.js server with an SQLite database, using Sequelize as an ORM. The maps are displayed with Leaflet and the OSRM API.

Vortex Particle Simulator

A fluid simulator implementing the vortex particle method, written in Rust. Vortex particles are simulated by an RK4 time integrator, and the dye is advected by a 4th order semi-Lagrangian advection. I had a lot of fun messing with mixing in various color spaces.

Finite Element Elasticity Simulator

Simulates an elastic body, using a piecewise-linear finite element discretization on a triangle mesh. The code is written in Rust, and implements backward Euler time integration, using an incremental potential formulation for the update, which is a minimization problem solved with gradient descent.

Fluid Simulator

A physics simulator written in Rust, implementing the Smoothed Particle Hydrodynamics algorithm for fluids, and the Material Point Method for simulating elastic objects, as well as snow (as in the Frozen movies!).

Firework Renderer

A 3D physically-based path tracing renderer written in Rust; originally based on the “Raytracing in One Weekend” book series, but with several features from the PBR Book impelemented as well. Features multi-threading and BVH acceleration, and supports rendering triangle meshes, HDR environment maps, volumetrics, mathematical primitives like conic sections, procedural textures like Perlin Noise, scenes exported as YAML files, and more!

Design and source code from Leonid Keselman's website