</> Akshay Thakur

about 00

I'm a PhD candidate in the Department of Aerospace and Mechanical Engineering at the University of Notre Dame, advised by Prof. Matthew J. Zahr in the CAMO Lab. My research sits at the intersection of scientific machine learning, finite element / finite volume methods, and model order reduction. I build numerical methods that combine classical scientific computing with deep learning to solve PDEs more efficiently and reliably.

Right now I'm working on feature-tracking physics-informed neural networks for boundary layers and shocks, and on optimization-based nonlinear discontinuous Galerkin methods that resolve thin layers on coarse meshes. I also contribute to an in-house finite element package written in Julia. I've interned at Synopsys, building foundation models for external aerodynamics, and at Mitsubishi Electric Research Labs, building neural-operator and GNN surrogates for sound propagation. Before Notre Dame, I worked at the CSCCM Lab at IIT Delhi on neural operators and generative surrogates for stochastic PDEs.

Reach me at athakur3@nd.edu. You can also find me on Google Scholar, GitHub, and LinkedIn.

recent 01

• Sep 2026Invited talk on FT-PINN for resolving localized features at the JHU–IITD SMaRT Seminar Series.
• 2026Paper on FT-PINN for boundary layers published in Computer Physics Communications.
• Jun 2026Started a research internship at Synopsys on foundation models for external aerodynamics.
• 2025Scalable h-adaptive probabilistic solver accepted in CMAME.
• Sep 2025Joined MERL (Cambridge, MA) as a research intern working on surrogates for sound propagation.
• Jul 2024Presented ML surrogates for Riemann solvers at WCCM-PANACM 2024, Vancouver.

experience 02

• Research Intern · Synopsys Inc.Jun 2026 – Oct 2026
  Foundation models for external aerodynamics: benchmarking existing models, developing new ones, quantifying uncertainty in their predictions, and designing data-acquisition and training strategies for large-scale aerodynamic datasets.
• Research Intern · Mitsubishi Electric Research Labs, Cambridge MASep 2025 – Feb 2026
  Physics-grounded, scalable surrogate models for sound propagation, built on attention-based neural operators and graph neural networks.
• Graduate Research Assistant · CAMO Lab, Notre DameAug 2023 – present
  PINN methods for boundary layers and shocks, nonlinear DG methods, and neural-network surrogates for Riemann solvers. Contributor to an in-house Julia finite element package; wrote an unstructured finite volume code in PyTorch.
• Graduate Research Assistant · COMSAIL Lab, Notre DameAug 2022 – Aug 2023
  Uncertainty quantification for Fourier neural operator surrogates and their extended variants (M.S. thesis).
• Research Intern · CSCCM Lab, IIT DelhiJul 2021 – Aug 2022
  Multi-fidelity wavelet neural operators for reliability analysis, generative-moment-matching surrogates for stochastic simulators, and capsule-network surrogates for PDEs.

education

• Ph.D., Aerospace & Mechanical Engineering · University of Notre DameAug 2022 – present
• M.S., Mechanical Engineering · University of Notre DameAug 2022 – Aug 2023

research projects 03

CAMO Lab · 2024 – present

FT-PINN: feature tracking in physics-informed neural networks

PINNs struggle with localized features such as thin boundary layers and shocks: the loss is dominated by the smooth bulk, so steep gradients are under-resolved. FT-PINN puts the network on a fixed reference domain and composes it with a trainable coordinate map, optimized jointly with the network weights. Collocation points then concentrate where the solution is steep, with no resampling and no prior knowledge of where the feature is.

• Part I: analytical tensor-product manifolds for boundary layers (advection–diffusion at Pe = 10³, flat plate at Re = 10⁶).
• Part II: RBF deformation manifolds for shocks (Burgers merging and decelerating shocks, Sod shock tube, Euler regular reflection).

paper · boundary layers preprint · shocks (submitted) SMaRT seminar 2026

CAMO Lab · ongoing

Optimization-based nonlinear discontinuous Galerkin (NLDG) for high-Péclet flows

The usual way to resolve thin viscous layers is with highly stretched, anisotropic meshes, which are tedious and fragile to generate. NLDG takes the opposite approach. It keeps coarse, isotropic meshes and enriches the DG approximation space with a nonlinear manifold of trial functions. The nonlinear parameters and the solution coefficients are solved for together through residual minimization, so no a priori knowledge of the layer scale is needed.

in preparation

CAMO Lab · 2023 – 2025

Neural Godunov corrections for approximate Riemann solvers

In finite volume schemes, the exact Godunov flux is accurate but expensive, while approximate Riemann solvers such as Roe are cheap but diffusive near shocks. A bi-fidelity neural network learns the residual between the Godunov and Roe fluxes, which gives a cheap correction with near-Godunov accuracy. It was tested a posteriori inside an unstructured PyTorch FV solver on Burgers' equation and the 2-D shallow water equations.

CAMCoS 2025WCCM 2024 talk

Notre Dame × IIT Delhi · 2024 – 2025

Scalable h-adaptive probabilistic PDE solver

A Gaussian-process-based probabilistic solver that conditions a GP prior on the PDE and boundary conditions, so it quantifies epistemic discretization uncertainty. Solving for the posterior normally costs O(N³); stochastic dual descent (a dual reformulation with randomized coordinate gradients and Nesterov momentum) avoids that. A clustering-based active-learning loop adds collocation points where the posterior variance is highest. The method handles both time-independent and time-dependent systems.

arXiv:2508.09623CMAME (accepted)

CSCCM Lab, IIT Delhi · 2021 – 2024

Multi-fidelity wavelet neural operators for reliability analysis

A low-fidelity WNO learns the coarse solution operator, and a high-fidelity WNO learns the residual correction from a small set of expensive simulations. The resulting surrogate is used for time-independent and time-dependent reliability analysis, including failure probability and first-passage time, on Darcy flow in a notched triangular domain and on the unsteady Allen–Cahn equation.

Prob. Eng. Mech. 2024

COMSAIL Lab · 2022 – 2023

Randomized-prior Fourier neural operators for uncertainty-aware rollout

Deep ensembles tend to give overconfident uncertainty estimates. This project extends randomized prior networks to the Fourier neural operator: each ensemble member pairs a trainable FNO with a fixed, randomly initialized prior FNO. The result is efficient, parallelizable UQ for spatiotemporal rollouts of time-dependent PDEs such as the 2-D Allen–Cahn equation.

M.S. thesis

• Industry: foundation models for external aerodynamics (Synopsys) and attention / GNN surrogates for sound propagation (MERL).
• Earlier work on stochastic surrogates: MD-NOMAD, a mixture-density decoder for stochastic simulators [4]; capsule encoder–decoder networks [6]; and generative-moment-matching surrogates [7].

publications 04

teaching 05