Research

My research develops numerical algorithms and machine-learning models for partial-differential-equation-based physics, and implements them in parallel software that runs at scale. The application areas are fusion and high-energy-density plasmas, atmospheric flows, compressible aerodynamics, and epidemiology.

Scientific machine learning

Simulation data and solvers for machine-learning studies

Most of my involvement in machine learning has been from the physics side. I supply the solvers and generate the training data that the learned models are built on, and co-author the resulting papers.

• HyPar provided the electrostatic plasma simulations behind local reduced-order models built by physics-informed decomposition of the solution manifold (Comput. Phys. Commun., 2026), and the earlier latent-space dynamics identification work (GPLaSDI, Comput. Methods Appl. Mech. Eng., 2024).
• The super-droplet microphysics capability I developed in ERF generated the training data for data-driven reduced-order modeling of warm-rain microphysics, led by Emily de Jong (JGR: Machine Learning and Computation, 2026).

Learned denoisers for particle-in-cell data

This is early-stage exploratory work, begun in 2026. It is not published and the results so far are preliminary.

Particle-in-cell methods represent a plasma by a finite sample of macroparticles. Grid quantities deposited from that sample carry Monte-Carlo noise that decays only as the inverse square root of the particle count. Accuracy therefore costs particles, and particles dominate memory and compute. We are examining whether a neural denoiser trained on paired low- and high-particle-count snapshots can reduce that cost. The work compares conditioned U-Net, diffusion, and local convolutional architectures, with physics-informed terms in the training objective.

Numerical methods

• High-resolution finite-difference and finite-volume methods for hyperbolic conservation laws (SIAM J. Sci. Comput. 2012; Numer. Methods Partial Differ. Equ. 2026).
• Nonlinear, non-oscillatory compact schemes. The CRWENO family couples compact reconstruction with weighted essentially non-oscillatory limiting, giving higher spectral resolution at a given formal order (SIAM J. Sci. Comput. 2012; J. Sci. Comput. 2014; AIAA J. 2014).
• Multi-stage implicit and implicit-explicit (IMEX) time integration for multiscale systems, including characteristic-based flux partitioning for low-Mach-number and gravity-stratified flows (SIAM J. Sci. Comput. 2016; ICOSAHOM 2014, Springer LNCSE).
• Multirate and extrapolated multirate methods for adaptive-mesh-refinement solvers.
• Well-balanced discretizations that preserve hydrostatic balance to machine precision (AIAA J. 2016; AIAA 2015-2889).
• Preconditioning and nonlinear solver design for stiff multiphysics systems (AIAA 2022-1108).

Particle-based methods

• Super-droplet cloud microphysics, including ice processes, coupled to a performance-portable atmospheric solver.
• Fully implicit, exactly energy- and charge-conserving particle-in-cell algorithms for dense plasmas, with Monte-Carlo Coulomb collisions (J. Comput. Phys. 2022; J. Comput. Phys. 2023; J. Comput. Phys. 2024; Phys. Rev. E 2025).
• Agent-based epidemiological models, where each agent carries an individual disease and behaviour state.

Plasma simulation

• Continuum gyrokinetic and drift-kinetic modeling of the tokamak edge, on mapped multi-block grids with high-order finite-volume discretization (J. Comput. Phys. 2018a; J. Comput. Phys. 2018b; Phys. Plasmas 2024; Phys. Plasmas 2025).
• Semi-implicit time integration of the Vlasov-Fokker-Planck system, treating the stiff collisional and parallel-streaming terms implicitly (AIAA 2017-4016; J. Sci. Comput. 2018; Phys. Plasmas 2025).
• Multifluid models for interpenetrating, counterstreaming plasmas in inertial confinement fusion (Comput. Fluids 2019; IEEE Trans. Plasma Sci. 2019; Phys. Plasmas 2021).
• Nonlinear hydrodynamics with photochemistry, for plasma-based and gaseous optical elements (Phys. Plasmas 2025; Phys. Rev. Applied 2026).

High-performance computing

• Scalable implementation of nonlinear compact schemes, which require solving distributed tridiagonal systems at every reconstruction. Our iterative substructuring approach removed the serial bottleneck and demonstrated scaling on DOE leadership-class platforms (SIAM J. Sci. Comput. 2015).
• GPU-accelerated direct numerical simulation of compressible turbulent flows (Comput. Fluids 2023).
• Performance-portable implementations over AMReX, and distributed multi-GPU training for the machine-learning work.

Earlier research

• Derivation, analysis, and parallel implementation of the CRWENO schemes (Ph.D., University of Maryland; adviser James Baeder) (thesis; SIAM J. Sci. Comput. 2012).
• Time integrators and a matrix format in PETSc, contributed 2013–2015 and still part of the library:
  • TSGLEE — general linear methods with global error estimation, which carry an error estimate in the solution vector rather than reconstructing it from a step-doubling or embedded pair (implementation, extension to diagonally implicit methods).
  • MATKAIJ — a matrix format for I ⊗ S + J ⊗ T with S and T small and dense and J sparse. This is the structure of the stage system in an implicit Runge-Kutta method, so storing it this way avoids forming the full Kronecker product (format, example solving an IRK stage system).
  • Dormand-Prince and Bogacki-Shampine embedded Runge-Kutta schemes, with the default changed to the embedded RK3BS so that adaptive stepping works without extra configuration (commit).
  • Extrapolated stage-predictor initial guesses for ARKIMEX, which cut Newton iterations on stiff problems (commit).
  • The Hull et al. (1972) non-stiff and stiff ODE test suite as TS example 31 (commit).
  (all PETSc commits)
• Semi-implicit and multirate time integration in NUMA, a non-hydrostatic atmospheric model.
• A three-dimensional incompressible Navier-Stokes solver with immersed boundaries, applied to vortex-ring and wall interactions and to rotorcraft wake modeling (AIAA 2010-5030; AIAA J. 2012).
• Probability density function methods for power systems with uncertain input (SIAM/ASA J. Uncertain. Quantif. 2015).
• High-order ENO and WENO schemes for ideal magnetohydrodynamics, and the effect of non-convexity on scheme convergence (M.Tech., IIT Bombay; adviser Avijit Chatterjee) (thesis).
• Finite-volume time-domain solution of Maxwell's equations, used to predict the radar cross-section of low-observable aircraft (seminar).