Latent Reciprocity Network for Neural Operators Nov 2025 – Dec 2025

GitHub Repository

  • Implemented LRN-FNO with a global reproducibility framework and fine-grained loss balancing architecture ($\lambda_{NSE}$), establishing a stable performance floor across three physical regimes.
  • Achieved consistent improvements over vanilla FNO: +10.55% on Darcy Flow (0.1498 $\rightarrow$ 0.1340), +9.09% on Navier–Stokes (0.2276 $\rightarrow$ 0.2070), and +3.42% on Burgers 2D (0.0146 $\rightarrow$ 0.0141).

Physics-Informed Neural Transformer Operator with Geometry Variant (PINTO-G) Oct 2025 – Present

GitHub Repository

  • Developing a hybrid framework that integrates the Physics-Informed Neural Transformer Operator (PINTO) with Geometry-Informed Neural Operator (GNO) architectures.
  • Aims to enhance spatial reasoning and physical consistency, improving generalization across diverse geometries and boundary conditions by combining transformer-based attention with geometry-aware operator learning.

Study on Latent Space Behaviour of Fourier Neural Operator Aug 2025 – Sept 2025

GitHub Repository

  • Introduced latent-space regularization and loss functions within the Fourier Neural Operator to enhance feature learning and convergence stability.
  • Achieved relative error reductions of 13.70% on Burgers’, 11.25% on Darcy flow, and 18.84% on Navier–Stokes ($128\times128$), demonstrating consistent accuracy improvements.

Wavelet Variant of Graph-Informed Neural Operator May 2025 – Aug 2025

GitHub Repository

  • Designed a modified version of the Geometry-Informed Neural Operator (GINO) by integrating a wavelet-based layer in place of the linear transformer within the FNO architecture.
  • Achieved improved performance, recording a relative error of around 2% for the transient case.

Fractional PINNs for solving Time-Fractional Burgers–Huxley July 2024 – May 2025

GitHub Repository

  • Implemented a Physics-Informed Neural Network (PINN) framework extended with fractional derivatives to solve the time-fractional Burgers–Huxley equation.
  • Incorporated fractional-order operators in the loss formulation to accurately capture memory effects and non-local temporal dynamics.
  • Validated the effectiveness of fractional PINNs for nonlinear fractional PDEs with stable convergence and accurate solution profiles.