Rahul Manavalan

I work on variational formulations, their associated optimization flows, and structure-preserving numerical algorithms for problems in scientific computing and inverse problems.

Broadly, my interests span:

  • Scientific Computing
  • Mathematical Physics
  • Numerical Analysis
  • Uncertainty quantification
  • Inverse Problems

For more details, visit:

Research Publications Blog

Selected research directions

Flow-based solvers

How can one derive and classify iterative solvers for solving linear algebraic systems and saddle point systems as discretizations of continuous dynamical systems?

Kernel methods

How can one construct RBF kernels that exactly satisfy Dirichlet and Neumann boundary conditions?

Inverse Problems and PDEs

How can PDEs that arise from inverse problems be used to obtain theoretical guarantees on the numerical methods that solve the corresponding inverse problems?

Recent news

(July 2026) New preprint: Our paper on Krylov smoothers for solving linear systems is on arxiv.

Latest blog posts

Numerical analysis

Gradient Flows for Linear Solvers

A short note on viewing classical iterative methods as discretized flows.

 Dynamical systems

Nonlinear RKHS Regression as a Flow

Sketching a dissipative PDE viewpoint for nonlinear regression.
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