Neural ODEs and Neural PDEs
A unified, rigorous formulation of Neural ODEs and Neural PDEs.
dani2442's Blog
Recent content on dani2442's Blog
Latest posts
Hamilton-Jacobi-Bellman Equation: Reinforcement Learning and Diffusion Models
Why the HJB is Bellman's equation in continuous time, why continuous time matters, and how to solve the resulting control problem with neural policy iteration.
The Linear Quadratic control problem in Infinite-dimensions
Why the HJB is Bellman's equation in continuous time, why continuous time matters, and how to solve the resulting control problem with neural policy iteration.
Harmonic Analysis: Peter-Weyl Theorem and Machine Learning
An overview of the Peter-Weyl theorem and its applications in machine learning.
Industries destined to collapse
Supply compounds forever, but demand (attention) doesn't.
Notes on Generalization Theory
Generalization bounds and theory for machine learning models.
Neo Hospitals
The future of healthcare in the age of AI.
Space Piracy
Why piracy is likely to move to orbit, and how to defend against it.
Creativity in the Age of AI: The curse of knowledge
When answers get cheap, originality becomes scarce
Fusion Energy Simulation: Tokamak
Notes on Tokamak transport PDEs.
Talk at Workshop in Palermo (Italy)
Workshop: 'The Mathematics of Scientific Machine Learning and Digital Twins'
Self-Attention, Kernel Methods and G-Metric Spaces
An introduction to Higher-Order Attention, Kernel Methods, and G-Metric Spaces.
The Importance of (Good) Metrics
We live surrounded by metrics
Gaussian Processes
Math and Code
Low-Earth Orbit
Analysis and Predictions
Prediction Markets
Analysis, Predictions and Experiments
Analog computing in LLMs
Analog computing AI
Physics-Informed Neural Networks
Introduction to Physics-Informed Neural Networks
Functional Principal Component Analysis
Introduction to Functional PCA.
Differentiable programming for gradient-based control and optimization in physical systems
Optimization using Differntiable Programming and Neural ODEs.
Traffic Flow Dynamics
Introduction to Traffic Flow Dynamics.
Nonlinear Functional Analysis: Bifurcation Theory
Introduction to Bifurcation Theory from simple eigenvalues.
About
Hi, this is Daniel López Montero. I will upload notes, projects and some thoughts on topics I am interested in. I am a PhD student of Mathematics researching in Machine Learning, and like to program, read and play football, basketball and padel in my spare time.