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Seminar Series: Computation & Data
31. March 2022 @ 15:00 – 16:00
15:00-15:30 Yannis Schumann (HSU): Data-driven Inference of Stencils for Discrete Differential Operators
Partial differential equations (PDEs) are extensively used across scientific disciplines for modeling and describing various processes under consideration. Finite element, finite difference or similar methods allow to numerically solve them by discretizing the variables under consideration, e.g. space and time. In this discretized domain, differential operators can be approximated by matrices with nonzero coefficients for positions in the neighborhood of the considered point –the so called stencil.
We consider the inference of stencil weights for differential operators from linear, one-dimensional and two-dimensional PDEs using comprehensive regression techniques. Starting with the 1D case, we show that linear regression using an ordinary-least-squares (OLS) approach is able to recover mathematically meaningful stencils given a full-rank matrix of predictor variables. We discuss, how regularization techniques can allow the inference of the correct stencils even for rank-deficient matrices. We discuss the impact of noise on the data in both predictor and predicted variables for various noise levels and compare different errors-in-variables approaches to mitigate the inherent consequences of noisy predictors. The presented techniques will be extended to the two dimensional case and applied to problems from physics and hydrogeology.
15:30-16:00 Henrik Steude (HSU): It’s more than a “model.train()” — Modern tools and architectures for ML systems
The code to train machine learning (ML) models only covers a small part of the entire complexity required by a production-ready ML system. In particular, model and data versioning, reproducibility and scalability represent grand challenges. To address these challenges, various new tools and technologies have been developed under the umbrella term “ML-Ops” over the last years.
In our contribution, we present a selection of technologies, that have evolved to be popular in the rapidly developing field of ML-Ops. As a concrete example, we further present a system architecture for a ML platform, which is used in the dtec.bw project (K)ISS for ML-based analysis of telemetry data of the international space station.