Skip to main content
Back to top
Ctrl
+
K
Advanced Scientific Machine Learning
Functional Programming
A Primer on Functional Programming
Just in Time Compilation
Vectorization
Pseudo Random Numbers without Side Effects
Typing Systems, Pytrees, and Models
Typing Systems and why We Care
Python Type Annotations
Haskell Type System
Pytrees to represent model parameters
Differentiable Programming
Numerical Differentiation
Symbolic Differentiation
Automatic Differentiation
Autograd with JAX
Local Sensitivity Analysis of ODEs and PDEs
Local Sensitivity Analysis for Ordinary Differential Equations
Differentiating the Solution of Ordinary Differential Equations
Example: The Duffing Oscillator
Example: Lorenz System
Beyond Local Sensitivity Analysis: The Fokker-Planck Equation
Uncertainty Propagation using Polynomial Chaos
Required Functional Analysis
Symbolic Construction of Polynomial Chaos for Uniform Random Variables
Symbolic Construction of Polynomial Chaos for Gaussian Random Variables
Numerical Estimation of Orthogonal Polynomials
Using Polynomial Chaos to Propagate Uncertainty through an ODE
Polynomial Chaos in Many Dimensions
Uncertainty Propagation in Dynamical Systems
Optimization for Scientific Machine Learning
Basics of Optimization Problems
Gradient Descent
Gradient Descent with Momentum
Optax
- Optimizers in JAX
Stochastic Gradient Descent
Optimization Algorithms with Adaptive Learning Rates
Second-order Methods for Optimization
Initialization of Neural Network Parameters
Physics Informed Neural Networks (PINNs)
Physics-Informed Neural Networks (PINNs) - Forward Problems
Spectral Bias of Neural Networks
Energy Functionals
Solving Parametric Problems using Physics-informed Neural Networks
Proper Orthogonal Decomposition
Singular Value Decomposition
Connection Between SVD and Principal Component Analysis (PCA)
Proper Orthogonal Decomposition
Learning non-linear dynamics from data
Sparsity Promoting Regularization (L1-regularization or Lasso regression)
Sparse Identification of Nonlinear Dynamics
SINDy - Example 2: Lorenz system
Dynamic Mode Decomposition
DMD Example
Homework Problems
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Search
Error
Please activate JavaScript to enable the search functionality.
Ctrl
+
K