Undergraduate Researcher in Computational Mathematics & Scientific Machine Learning at the Department of Mathematics, University of Delhi.

Investigating the intersection of geometric deep learning, numerical PDEs, high-dimensional stochastic control, and high-performance scientific computing. Research emphasizes exact mathematical invariants (symplectic conservation, parameter null-space decoupling, hard boundary constraints) and bare-metal computational efficiency.

Portfolio • ORCID (0009-0009-1973-7532) • LinkedIn • Email

• cpa-shnn — Symplectic Hamiltonian Neural Networks for multi-body celestial mechanics. Formulates separable kinetic-Coriolis splitting and Arnold extended contact phase spaces across 6 chaotic gravitational systems, achieving up to $126.4\times$ Fourier error collapse.
• eit-neural-surrogate-inversion — Deep shape inversion in Electrical Impedance Tomography (EIT). Resolves Calderón logarithmic ill-posedness via stochastic directional JVP supervision on $\mathbb{S}^{63}$, bounding peak VRAM to $342.8,\mathrm{MB}$ with a $56.8\times$ wall-clock speedup. (Under review at IEEE Transactions on Computational Imaging; DOI: 10.5281/zenodo.22096368).
• pinn-fluid-formulations — Formulation-induced failure modes in high-$Re$ incompressible fluid PINNs. Analyzes operator diffusion in continuous $\psi-\omega$ representations due to absence of discrete Thom stencils, and proves Helmholtz-Hodge projection recovery in $\psi-p$.

• as-pinn — Adaptive $N$-Subspace PINN. Autonomous parameter-space Adaptive Mesh Refinement (AMR) using vectorized per-sample Gram alignment profiling (torch.func.vmap) with exact zero-disruption cleavage invariance. Validated across 9 canonical PDEs with $725.6\times$ loss reduction on high-frequency Helmholtz.
• null-space-pinn — Decoupling boundary-PDE gradient conflicts via orthogonal direct-sum parameter subspaces ($\Theta_0 \oplus \Theta_1$) blended with a $C^2$ Quintic Hermite seam operator. (DOI: 10.5281/zenodo.22132799).
• as-vit-multitask — Adaptive Subspace Vision Transformers. Tracks inter-task Gram matrix negative eigenvalues to dynamically route latent expert subspaces using Partition of Unity (PoU) gating, eliminating multi-task negative transfer on NYUv2.

• Deep-EEP-PINN — High-dimensional American basket option pricing up to $d=50$ assets (1,225 correlations). Computes diffusion operator via directional autograd trace contraction in $\mathcal{O}(d)$ linear complexity and $<3,\mathrm{GB}$ VRAM, validated against 100K-path Longstaff-Schwartz Monte Carlo.
• PINN-Bayesian-Posterior-Fidelity — Diagnostic framework quantifying Bayesian posterior distortion under neural surrogate approximations using the 1-Wasserstein Bayesian Fidelity Ratio (BFR) normalized by empirical MCMC noise floors.
• Lid-Driven-Cavity-FDM-Solver — High-resolution 2D incompressible Navier-Stokes solver on dense $251 \times 251$ meshes ($Re=1000$). Peaceman-Rachford ADI vorticity transport with Red-Black SOR Chebyshev acceleration. (DOI: 10.5281/zenodo.18312938).
• BRSDK — Real-time telemetry extraction framework operating inside the 2000Hz Vehicle Lua physics thread of BeamNG.drive/tech. Features pre-allocated static ring buffers, zero-allocation hot path, and RFC 8259 JSON metadata sidecars. (DOI: 10.5281/zenodo.21729606).

• Languages: Python (3.11+), C++20, Lua / LuaJIT, Bash, LaTeX
• Deep Learning & Autograd: PyTorch (custom autograd, torch.func.vmap, forward-mode AD, JVPs), JAX, CUDA
• Scientific Computing & HPC: NumPy, SciPy, OpenMP, CMake, Finite Difference Methods (ADI, Red-Black SOR), Symplectic Verlet Integration
• Systems & Simulation: Linux, Git/GitHub, Docker, BeamNG.tech JBeam Continuum Physics

• Email: kartikeysingh525@protonmail.com
• Portfolio: kartikeyagangwar.github.io
• ORCID: 0009-0009-1973-7532
• LinkedIn: kartikey-singh-2a3434329
• Zenodo: Kartikey Singh on Zenodo