About
A short biography
I am Carl D. Lund, a MSc student in Engineering Physics specialising in Computation and Simulation. My interests lie with finding novel ways of solving high-dimensional problems, often with inspiration from disparate fields that have already achieved high mathematical maturity. I enjoy bridging the gap between current applications and potential implementations, generalising scientific principles for a deeper understanding.
My work primarily spans Scientific Machine Learning (SciML), High-Performance Computing (HPC), and Stochastic Mathematics. I focus on exploring theoretical mathematics, how it might have been implemented previously, sometimes in unseeming fields, and then finding computational methods to implement solutions to problems efficiently, building systems capable of high-performance production execution.
I care about architectural rigor, writing that explains rather than posturing, and tools that respect the reader.
Open to Collaboration
I am currently open to research positions, engineering internships, and technical collaborations pertinent to Scientific Machine Learning and High-Performance Computing.
Scientific Machine Learning
Investigating methods to embed known physical laws and stochastic dynamics into neural architectures to solve continuous-time problems.
- — Universal Stochastic PDEs (USPDEs)
- — Weak SINDy for analytical discovery
- — Physics-Informed Neural Networks (PINNs)
- — Fourier Neural Operators (FNOs)
Quantitative Finance
Applying theoretical physics frameworks to model the adversarial, non-stationary microstructure of financial markets.
- — Optimal Control & HJB Equations
- — Limit Order Book Stochastic Modelling
- — Volatility Surfaces via Gaussian Processes
- — Random Matrix Theory
Computational Neuroscience
Exploring bio-computation and neural topologies to bridge the gap between high-level biological modelling and physical execution.
- — Topological Data Analysis (TDA)
- — PDE-Driven Spiking Neural Networks
- — Geometric Deep Learning
- — String-Theoretic Optimisation (STONE)
High-Performance Computing
Building modular, memory-safe infrastructures capable of sub-millisecond data transport and highly concurrent scientific simulation.
- — Rust (Memory-safe control planes)
- — Julia (SciML, DifferentialEquations.jl)
- — Zero-copy pipelines (Apache Arrow, ZMQ)
- — Unified Memory architectures (MLX, Metal)