Abhinaash Blog

MSc in Mathematics (incoming)

BSc in Computational Mathematics · CGPA 3.25 / 4.00

Thesis

LSTM-Driven Portfolio Optimization on the Nepal Stock Exchange (NEPSE) using Differential Evolution

Supervisor

Dr. Khim Bahadur Khattri

Abstract accepted for oral presentation, 4th International Conference on Applications of Mathematics to Nonlinear Sciences (AMNS-2026)

Undergraduate thesis

• Formulated a mixed-integer nonlinear portfolio optimization problem under real-world market constraints and solved it with Differential Evolution, using a custom decode-and-repair operator to keep integer-lot solutions feasible.
• Combined sector-level LSTM networks with attention for return signals, Ledoit–Wolf shrinkage for covariance estimation, and a penalty-augmented Sharpe ratio objective; ran a systematic sensitivity analysis over the key hyperparameters.

Mathematics seminar project · Code on GitHub

• Applied truncated SVD to lossy greyscale image compression, grounded in the Eckart–Young–Mirsky theorem, and verified its error formula numerically.
• Built a Python (NumPy) compression module and command-line tool with unit tests, choosing the rank by energy retained and PSNR. A 360×360 image is stored with 9× fewer values at 33.5 dB.
• Analysed when the method fails (random noise vs. structured patterns) and compared it with JPEG.

Independent project · Code on GitHub

• Benchmarked PINNs against explicit, implicit and Crank–Nicolson finite-difference schemes for the 1D, 2D and 3D heat equations, comparing accuracy, runtime and memory under coarse discretization.
• Trained PINNs with adaptive GradNorm loss weighting, Latin Hypercube Sampling and Adam/L-BFGS. Finite differences were more accurate; PINNs were faster in 3D.

11-day intensive on AI and machine learning; 226 participants selected from 745 applicants across 35 countries.

Intensive programme on post-quantum cryptography at Kathmandu University, supported by CIMPA.

• Organized a national mathematics Olympiad whose problems feed into Nepal's IMO qualification pathway.
• Coordinated a mathematics hackathon, academic workshops and a national academic conference.