Goal
The overall goal of this course is to bring you to where the current literature is regarding the use of Digital Twins to
- monitor physical systems from indirect measurements
- assess uncertainty
- control the system
The course will start with introducing topics from traditional Data Assimilation (DA) and Bayesian inference and will make it through to the latest developments in Differential Programming (DP), Simulation-Based Inference (SBI), recursive Bayesian Inference (RBI), and learned RBI through the use of Generative AI.
Course outline
- Introduction
- welcome
- overview Digital Twins
- Inverse Problems
- ill-posedness
- Tikhonov regularization
- General Formulation
- Discrepancy principle
- Cross-validation
- Basic Data Assimilation
- introduction
- adjoint state method
- variational data assimilation
Statistical Inverse Problems
- differential programming
- reverse-mode = adjoint state
- Advanced Data Assimilation
- Neural Density Estimation
- generative Networks
- Normalizing Flows
- conditional Normalizing Flows
- Simulation-based inference
- introduction scientific ML
- Bayesian inference
- Surrogate Modeling
- Fourier Neural Operators FNOs
Learned Data Assimilation