Explorations in mathematics, computation, AI, and the philosophy of science.
Exploring how classical numerical schemes complement modern deep learning approaches for solving PDEs, and why the marriage of both is the future.
Read More →My thoughts on integrating quantum-inspired algorithms into traditional numerical schemes and the potential paradigm shift it could bring.
Read More →A deep dive into why entropy-stable schemes are crucial for handling degenerate parabolic equations and ensuring physically meaningful solutions.
Read More →How reinforcement learning can automatically tune numerical viscosity parameters, outperforming hand-crafted approaches in complex flows.
Read More →Reflections on how tools like ChatGPT are changing the classroom, and how we can leverage them rather than fear them.
Read More →A personal journey tracing the evolution of PDE solvers from classical finite difference methods to cutting-edge neural operator architectures.
Read More →The delicate balance between capturing shocks accurately while avoiding oscillations — a problem that has fascinated me for years.
Coming Soon →Why conservation form matters in numerical schemes, and how violating it can lead to catastrophic results in simulations.
Coming Soon →Investigating whether genetic algorithms and neural architecture search can discover novel numerical methods that humans haven't thought of yet.
Coming Soon →