Learning Dynamical Transport without Data

Overview

Explore dynamical transport algorithms for generative modeling without data, focusing on sampling from target distributions using unnormalized log-likelihood functions, with applications in physics, chemistry, and Bayesian inference.

Syllabus

• Introduction to Dynamical Transport
Overview of dynamical transport algorithms
Importance in generative modeling
• Sampling from Target Distributions
Unnormalized log-likelihood functions
Challenges of sampling without direct data
• Theoretical Foundations
Mathematical formulation of dynamical transport
Key principles of stochastic differential equations (SDEs)
Introduction to measure transport and transformation
• Methods and Techniques
Langevin dynamics
Hamiltonian Monte Carlo (HMC)
Normalizing flows
Score-based generative models
• Applications in Physics
Phase space sampling
Quantum systems and path integrals
• Applications in Chemistry
Molecular dynamics for reaction pathways
Importance sampling in chemical systems
• Applications in Bayesian Inference
Prior distribution sampling
Posterior estimation without data
• Computational Aspects
Numerical integration techniques
Efficient computation strategies
• Case Studies
Real-world examples from physics
Chemical systems simulations
Bayesian inference scenarios
• Conclusion
Recap of key concepts
Future perspectives in dynamical transport
• Project and Assessment
Design and implement a dynamical transport model for a chosen application
Evaluation based on accuracy, efficiency, and innovation

Subjects

Computer Science