# SiSc Lab

## Topics @ STCE

### 1. Exploratory Derivative Sampling

#### Objective:

Development of a software infrastructure for analysis of first and higher derivatives of differentiable C++ programs y=f(x) with n inputs and scalar output over given domains [x_l,x_u]

#### Approach:

- first and higher derivatives by algorithmic differentiation with dco/c++
- uniform random sampling over [x_l,x_u] to construct derivative data base
- parallelization with MPI on RWTH Compute Cluster
- search for subdomains with quasi-vanishing or quasi-constant derivatives; e.g. by picking suitable points followed by local expansion of the subdomain
- visualization of the domains for n=1,2,3 (heat maps)
- test results, documentation, presentation (report + talk)

### 2. Scheduling Adjoints

#### Objective:

Development of a software infrastructure for scheduling of the algorithmic adjoint of a differentiable program consisting of p partially ordered tasks y_i=F_i(x_i)

#### Approach:

- dependencies among the tasks are given in form of a directed acyclic graph (dag) and assuming unlimited resources (number of processes run in parallel); masks relate y_i to x_j for j>i
- algorithmic adjoint consists of a forward evaluation of all tasks to compute and store the local arguments x_i followed by their adjoints in reverse partial order
- distinct tasks write into disjoint memory on way forward; they read from potentially overlapping memory yielding race conditions in adjoint
- concatenation of the dag and of its reverse defines dependencies within the algorithmic adjoint program
- adjoint tasks are generated with dco/c++
- MPI master spawns slave processes for individual tasks and their their adjoints asap
- visualization of the dag of the algorithmic adjoint program
- test results, documentation, presentation (report + talk)

## Topics supervised by other groups

- Unstructured Finite Element Solver (Prof. Behr, Mr. Wendling)
- Molecular Thermodynamics (Prof. Leonard)
- Automated Calibration of Geological Models (Dr. Kadyk)
- Sensitivity Analysis with Reactor Simulations in a Nuclear Arms Control Context (Prof. Blügel, Mr. Wortmann)
- (Algorithmic) Analysis of a Materials Design Database (Prof. Blügel, Mr. Wortmann)