Advanced Deep Learning for Physics

Navier-Stokes equations and physics of fluids, finite difference discretizations, advection schemes and their stability properties, Poisson problems, numerical iterative solvers for systems of linear equations, surface representations, and boundary conditions; Physics of elastic materials, stress-strain relationships, finite-element modeling, types of basis functions, tetrahedral meshing, plasticity and fracture.

This course targets deep learning techniques and numerical simulation
algorithms for materials such as fluids and deformable objects. In particular,
this course will focus on advanced deep learning concepts such as generative
models and time series prediction, with possible applications in the context of
computer graphics or vision. After taking this course the students have gained
knowledge about the underlying concepts for deep learning algorithms. They are
familiar with topics such as auto-encoders, adversarial training, recurrent
neural networks, and specialized loss functions.
In addition they know about the physical principles of elastic and plastic
materials, with an emphasis on fluids: conservation of mass and momentum,
divergence free motion, and vorticity. Students can explain common discrete and
continuous representations of the phenomena, such as phase functions,level-sets and Cartesian or tetrahedral meshes.
The core component of this lecture are numerical algorithms to work with
partial differential equations. Students can memorize the steps of the
algorithms and are able to apply the learned techniques such as computing loss
function derivatives, finite-difference discretizations, explicit and implicit
integration, in new contexts. They are able to construct working training
algorithms, by choosing suitable activation and loss functions, and can choose
the right network architecture for different regression / generation tasks.
Additionally, students are able to evaluate learning and simulation algorithms
in terms of accuracy and computational complexity. Given a set of specific
requirements of a problem they can construct a solver based on the different
components discussed in the lecture.
In the homework assignments they have acquired practical experience
implementing central components of these solvers in a high-level programming
language, and they have gained experience working with software APIs
implementing higher level functionality.

MA0902 Analysis für Informatiker
MA0901 Lineare Algebra für Informatiker
IN0037 Physikalische Grundlagen für Computerspiele
IN2346 Introduction to Deep Learning

This course is presented with lectures consisting of digital slides, supported
by blackboard materials for mathematical topics. These materials are combined
with demo applications, videos of real phenomena and digital simulations, and
experiments. The experiments and bi-weekly ''physics fact'' challenges
encourage students to actively participate during the lectures. The exercise
assignments are non-mandatory, and are worked on in groups of two to four
students.

Powerpoint course slides, white board, experiments, online tutorials, source code

- I. Goodfellow, Deep Learning, MIT Press, 2017
- Robert Bridson, Fluid Simulation for Computer Graphics, AK Peters, 2007
- D. Baraff, A. Witkin: Physically Based Modeling, SIGGRAPH course notes, 1997

Over the course of the semester, students can voluntarily work on four different
exercise assignments. The exercises topics include key steps of neural network
modeling for simulations. They include algorithms such as pressure projection,
implicit solving of partial differential equations, and representing physics problems
with neural networks. These exercises are also the primary means for students
to demonstrate that they can implement the algorithms of the lecture with
python and the C++ programming languages.
The examination takes the form of a written test with a duration of 90 minutes.
General knowledge questions check whether the students are familiar with the
deep learning concepts, physicals simulations, and discrete representations.
Completion of the voluntary exercises will give a grade bonus upon passing
the exam.
Model calculations on paper are used to test whether students have acquired
knowledge to perform the central solving steps, such as derivative
calculations, material transport, time propagation, and internal force
evaluation. Short programming tasks with pseudo-code check their ability to
solve simple learning and physics problems with suitable algorithms, and their
ability to develop suitable solving methods.