FS
Click on the Slides button above to view the built-in slides feature. Slides can be added in a few ways: Create slides using Hugo Blox Builder’s Slides feature and link using slides parameter in the front matter of the talk file Upload an existing slide deck to static/ and link using url_slides parameter in the front matter of the talk file Embed your slides (e.g. Google Slides) or…
Automatic differentiation (AD) has become ubiquitous throughout scientific computing and deep learning. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability p of being heads, pose a challenge to these systems.…
Control of devices at the quantum level holds enormous potential for current and future applications in the field of quantum information science. However, due to the nonlinear and stochastic nature of quantum systems under continuous observation, analytical solutions to all but the simplest quantum control problems remain unknown. In this project, we present a convex optimization framework to…
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. Possible fields of application for these tools range from model discovery with explicit dosing times in pharmacology, over accurate gradient…
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 learning 1 . The Julia 2 language is well suited for ∂P , see also Chris’ article 3 for a detailed examination. There is already a plethora of examples where ∂P has provided massive…
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. These are described by hybrid differential equations 1 . We highlight differences between explicit 2 and implicit events 3 4 . As a paradigmatic example, we consider a bouncing ball described by…
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. Specifically, the dependence of a chaotic system on its initial conditions is well known as the “butterfly effect”. Chaotic models are encountered in various fields ranging…
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 . This year’s project is embedded within the NumFocus / SciML organization and comprises adjoint sensitivity methods for discontinuities, shadowing methods for chaotic dynamics,…
Conceptually, it is straightforward to determine the time evolution of a quantum system for a fixed initial state given its (time-dependent) Hamiltonian or Lindbladian. Depending on the physical context, the dynamics is described by an ordinary or stochastic differential equation. In quantum state control, which is of paramount importance for quantum computation, we aim at solving the inverse…
Artificial neural networks have successfully been used to identify phase transitions from data and classify data into distinct phases in an automated fashion. The power and success of these approaches (e.g., “learning by confusion” or the “prediction-based method”) can be attributed to the ability of deep neural networks to learn arbitrary functions. However, the larger a…
We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle…
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. The high weak order solvers will allow for massive performance advantages for fitting expectations of equations. Instead of automatic differentiation (AD) through the operations of…
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…
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. I will spend the following months implementing both new high weak order solvers as well as adjoint…
Create your slides in Markdown - click the Slides button to check out the example. Add the publication’s full text or supplementary notes here. You can use rich formatting such as including code, math, and images .
Create slides in Markdown with Hugo Blox Builder Hugo Blox Builder | Documentation Features Efficiently write slides in Markdown 3-in-1: Create, Present, and Publish your slides Supports speaker notes Mobile friendly slides Controls Next: Right Arrow or Space Previous: Left Arrow Start: Home Finish: End Overview: Esc Speaker notes: S Fullscreen: F Zoom: Alt + Click PDF Export Code Highlighting…
Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software. Create your slides in Markdown - click the Slides button to check out the example. Add the publication’s full text or supplementary notes here. You can use rich formatting such as including code, math, and images .
Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software. Create your slides in Markdown - click the Slides button to check out the example. Add the publication’s full text or supplementary notes here. You can use rich formatting such as including code, math, and images .
We investigate multiple scattering of scalar waves by an ensemble of N resonant point scatterers in three dimensions. For up to N = 21 scatterers, we numerically optimize the positions of the individual scatterers, to maximize the total scattering cross section for an incoming plane wave, on the one hand, and to minimize the decay rate associated to a long-lived scattering resonance, on the other.…