Ciao! I'm Luca Muscarnera

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I am an HPC Engineering Graduate @ Politecnico di Milano, Italy. I have a strong passion for the intersection of Mathematics and High Performance Computing, with a strong drift towards Machine Learning and Optimization. Currently planning to pursue a PhD to study the Mathematics of Deep Learning.
My dream is to make deep learning less mysterious and help in making it a pervasive technology

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A pervasive view on High Performance Computing

Game of life, running on GPU through WebGL shaders, implemented via gpu.js, real time simulation. Every configuration that you obtain is almost unique, with a probability of appearing \(\approx 10^{-78913.2071}\)

I have a B.Sc. in Computer Engineering (Politecnico di Milano) and in the last two years I decided to specialize also in Mathematics, not as a Minor but rather in the sense of a "Parallel Major".
As you will see, my projects often try to take a little bit from both these amazing subjects.

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How does it work?

Parallel Percolation Simulation, Close to critical phase. Each site is initialized with a certain probability as a hole or a filled cavity, and the percolation model allows to study diffusion of fluid among neighbouring sites. Near to criticality, the model exhibits a non trivial structure (scale free distribution of clusters)

A continuous investigation of the mechanics that governate reality, models and data.
Curiosity drives me, along with the idea of constructing a real understanding.

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Some projects that I had fun making

click the items in the list to find more details...

A Network Theoretical Approach on Drug Discovery
Cache Usage Optimization for Voxel Grids by PCA
Entropy-based latent representation perturbations for kernel regression in a generative framework
ADHD diagnosis as anomaly detection
A surrogate optimization approach for black-box convex optimization

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Some personal projects i'm working on

Algebraic Multigrid heuristics validation
Learning to rank as a maximum likelihood estimation of a non differentiable function
High Performance Montecarlo Simulation for non parametric returns in financial markets
My master thesis

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Some topics I'd love to work on

Deterministic & Stochastic Optimal Control
Protein Folding & Protein Engineering
Parallelization of numerical algorithms & performance sensitive machine learning
Theoretical Mathematics (Functional Analysis,Measure Theory...) for deep learning and Statistical Mechanics approach to Learning
Experimental Machine Learning Algorithms & Experimental Generative Artificial Intelligence
Discrete & Continuous ( \(n- \)derivatives based) global optimization
High Performance Data Structures and algorithms (and heuristics)

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But more in general...

Compressible Navier Stokes
Real time (Forward Euler) finite differences simulation of Compressible Navier Stokes Equation, by means of a stabilized version of the Langtangen numerical scheme. Compressibility allow to model behavior of objects moving throu non-incompressible fluids like air in a more accurate way. Like in the previous figure, simulation is running through shaders, thanks to the gpu.js library. You can move the cylinder, just swiping over the computational domain

What I really enjoy about HPC is the ability of making abstractions real, through the power of simulation and modelling.
I'm always eager to learn something new, and bring it to life using coding and scientific computing as tools, trying to understand always what is the most efficient way (from a computational perspective).

If you want, feel free to reach me though my channels. I am always happy to discuss science and algorithms.

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Thank you for your time.

"Rain over a torus puddle"
Real time simulation of rain on torus \(\mathbb T^2\) world. Randomly, the simulation modifies the computational domain in order to simulate rain creating temporary boundaries inside the region.Position of the impulse follow the distribution \( {\bf x} \sim \mathcal U(\mathbb T^2) \). The toroidal topology allow waves to travel freely from one side to the other.

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