W imieniu Dziekana Wydziału serdecznie zapraszamy pracowników oraz studentów na seminarium wydziałowe, które odbędzie się we wtorek 15 kwietnia o godz. 12:30 w Instytucie Informatyki w sali 119.
Prelegentem będzie Prof. Dr Michael Hecht z naszego Instytutu oraz z Mathematical Foundations for Complex Systems Science,CASUS - Center for Advanced Systems Understanding Goerlitz i Helmholtz-Zentrum Dresden-Rossendorf e. V., która wygłosi wykład pt.
The Fast Newton Transform: Interpolation in downward closed spaces reaching the optimal geometric approximation rates for Bos-Levenberg-Trefethen functions.
Tradycyjnie, bezpośrednio przed seminarium o godzinie 12:00 Dziekan zaprasza na kawę i ciasto w holu przed salą 119.
Streszczenie:
We address the computational bottleneck that arises in solving high-dimensional problems suchas 6D Boltzmann, Fokker-Planck, or Vlaslov equations, multi-body Hamiltonian systems, and the inference of governing equations in complex self-organizing systems. Specifically, the challenge lies in numerically computing function expansions and their derivatives fast, while achieving high approximation power.
We present the Fast Newton Transform (FNT), a novel algorithm for multivariate polynomial interpolation with a runtime of nearly Nlog(N), where N scales only sub-exponentially with spatial dimension, surpassing the runtime of the tensorial Fast Fourier Transform (FFT). We prove and demonstrate the optimal geometric approximation rates for a class of analytic functions – termed Bos–Levenberg–Trefethen functions – to be reached by the FNT and to be maintained for the derivatives of the interpolants. This establishes the FNT as a new standard in spectral methods, particularly suitable for high-dimensional, non-periodic PDE problems, interpolation tasks, and signal processing. We discuss further applications, such as the Newton Neural Operator, realizing fast (de-)convolution in machine learning tasks.
Joint work of Phil-Alexander Hofmann, Damar Wicaksono, and Michael Hecht
– Mathematical Foundations for Complex Systems Science, CASUS - Center for Advanced Systems Understanding Goerlitz
– Helmholtz-Zentrum Dresden-Rossendorf e. V.
– Instytut Matematyczny, Uniwersytet Wrocławski