Neural Hybrid Differential Equations and Adjoint Sensitivity Analysis

Project summary In this project, we have implemented state-of-the-art sensitivity tools for chaotic dynamical systems, continuous adjoint sensitivity methods for hybrid differential equations, as well as a high level API for automatic differentiation.

AbstractDifferentiation.jl for AD-backend agnostic code

Differentiable programming (∂P), i.e., the ability to differentiate general computer program structures, has enabled the efficient combination of existing packages for scientific computation and machine learning1. The Julia2 language is well suited for ∂P, see also Chris' article3 for a detailed examination.

Sensitivity Analysis of Hybrid Differential Equations

In this post, we discuss sensitivity analysis of differential equations with state changes caused by events triggered at defined moments, for example reflections, bounces off a wall or other sudden forces.

Shadowing Methods for Forward and Adjoint Sensitivity Analysis of Chaotic Systems

In this post, we dig into sensitivity analysis of chaotic systems. Chaotic systems are dynamical, deterministic systems that are extremely sensitive to small changes in the initial state or the system parameters.

Neural Hybrid Differential Equations

I am delighted that I have been awarded my second GSoC stipend this year. I look forward to carrying out the ambitious project scope with my mentors Chris Rackauckas, Moritz Schauer, Yingbo Ma, and Mohamed Tarek.

High weak order solvers and adjoint sensitivity analysis for stochastic differential equations

Project summary In this project, we have implemented new promising tools within the SciML organization which are relevant for tasks such as optimal control or parameter estimation for stochastic differential equations.

High weak order SDE solvers

This post summarizes our new high weak order methods for the SciML ecosystem, as implemented within the Google Summer of Code 2020 project. After an introductory part highlighting the differences between the strong and the weak approximation for stochastic differential equations, we look into the convergence and performance properties of a few representative new methods in case of a non-commutative noise process.

GSoC 2020: High weak order SDE solvers and their utility in neural SDEs

First and foremost, I would like to thank my mentors Chris Rackauckas, Moritz Schauer, and Yingbo Ma for their willingness to supervise me in this Google Summer of Code project. Although we are still at the very beginning of the project, we already had plenty of very inspiring discussion.