Departement Mathematik

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Zurich colloquium in applied and computational mathematics

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Frühjahrssemester 2020

Datum / Zeit Referent:in Titel Ort
26. Februar 2020
16:15-17:45 		Prof. Dr. Maria Lukacova
Universität Mainz
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Zurich Colloquium in Applied and Computational Mathematics

Titel How to compute oscillatory solutions of the Euler equations
Referent:in, Affiliation Prof. Dr. Maria Lukacova, Universität Mainz
Datum, Zeit 26. Februar 2020, 16:15-17:45
Ort Y27 H 46
Abstract An iconic example of hyperbolic conservation laws are the Euler equations of gas dynamics expressing the conservation of mass, momentum and energy. Recently, it has been shown that even for smooth initial data the Euler equations may have infinitely many physically admissible, i.e. weak entropy, solutions. Related to the ill-posedness of the Euler equations is the observation that approximate solutions obtained by standard finite volume methods may develop oscillations and cascades of new small scale substructures. Consequently, a fundamental question is: What is the limit of numerical solutions as mesh parameter is refined? In the present talk we will present a concept of K-convergence that can be seen as a new tool in numerical analysis of the ill-posed problems, such as the Euler equations. We will show that the numerical solutions obtained by some standard finite volume methods generate a dissipative measure-valued solution, which is an appropriate probability measure (Young measure). We will also show how to effectively compute its observable quantities, such as the mean and variance and proof their strong convergence in space and time.Theoretical results will be illustrated by a series of numerical simulations. The present research has been done in collaboration with E. Feireisl (Prague/Berlin), H. Mizerova (Bratislava), B. She (Prague) and Y. Wang (Beijing). It has been partially supported by TRR 146 Multiscale simulation methods for soft matter systems and by TRR 165 Waves to weather funded by DFG.
How to compute oscillatory solutions of the Euler equationsread_more
Y27 H 46
4. März 2020
16:15-17:15 		Prof. Dr. Shi Jin
Shanghai JiaoTong University, Shanghai, China
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Zurich Colloquium in Applied and Computational Mathematics

Titel CANCELLED!
Referent:in, Affiliation Prof. Dr. Shi Jin, Shanghai JiaoTong University, Shanghai, China
Datum, Zeit 4. März 2020, 16:15-17:15
Ort Y27 H 46
CANCELLED!
Y27 H 46
1. April 2020
16:15-17:15 		Prof. Dr. Didier Lucor
LIMSI-CNRS, Paris-Saclay University
Details

Zurich Colloquium in Applied and Computational Mathematics

Titel CANCELLED!
Referent:in, Affiliation Prof. Dr. Didier Lucor, LIMSI-CNRS, Paris-Saclay University
Datum, Zeit 1. April 2020, 16:15-17:15
Ort Y27 H 46
CANCELLED!
Y27 H 46
13. Mai 2020
16:15-17:15 		Prof. Dr. Victor Batista
Yale University
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Zurich Colloquium in Applied and Computational Mathematics

Titel Tensor train decompositions for quantum dynamics simulations
Referent:in, Affiliation Prof. Dr. Victor Batista, Yale University
Datum, Zeit 13. Mai 2020, 16:15-17:15
Ort Zoom Meeting
Abstract We introduce the “tensor-train split-operator Fourier transform” (TT-SOFT) algorithm for simulations of multidimensional nonadiabatic quantum dynamics [J. Chem. Theory Comput. 13: 4034-4042 (2017)]. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations. The development of ultrafast laser technology has also opened the possibility to control ultrafast reaction dynamics in excited electronic states. Thus, we report a Floquet theoretical study of quantum control of the ultrafast cis-trans photoisomerization dynamics of rhodopsin [J. Chem. Theory Comput. 14(3): 1198-1205 (2018)]. The predicted light-induced potentials, including light-induced conical intersections, can open new reaction channels or modify the product yields of existing pathways. The nonadiabatic dynamics is described by a 3-state 2-dimensional wave-packet, coupled to a bath of 23 vibrational modes, evolving according to an empirical model Hamiltonian with frequencies and excited-state gradients parameterized to reproduce the observed resonance Raman excitations of rhodopsin. We analyze the effect of different control pulses on the photoisomerization dynamics, including changes in pulse duration and intensity. We interpret the results in terms of 'dressed states' and we exploit the Floquet description where the effect of control pulses is naturally decoupled along the different channels. Results obtained with 300 fs-long pulses suggest that it should be possible to delay the excited-state isomerization for hundreds of femtoseconds. Our findings are thus particularly relevant to the development of ultrafast optical switches based on visual pigments.
Tensor train decompositions for quantum dynamics simulationsread_more
Zoom Meeting
20. Mai 2020
16:15-17:15 		Prof. Dr. George Karniadakis
Brown University, Rhode Island
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Zurich Colloquium in Applied and Computational Mathematics

Titel Physics-Informed Neural Networks (PINNs): Algorithms & Applications
Referent:in, Affiliation Prof. Dr. George Karniadakis, Brown University, Rhode Island
Datum, Zeit 20. Mai 2020, 16:15-17:15
Ort Zoom Meeting
Abstract We will present a new approach to develop a data-driven, learning-based framework for predicting outcomes of physical and biological systems and for discovering hidden physics from noisy data. We will introduce a deep learning approach based on neural networks (NNs) and generative adversarial networks (GANs). We also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. Unlike other approaches that rely on big data, here we learn from small data by exploiting the information provided by the physical conservation laws, which are used to obtain informative priors or regularize the neural networks. We will also make connections between Gauss Process Regression and NNs and discuss the new powerful concept of meta-learning. We will demonstrate the power of PINNs for several inverse problems in fluid mechanics, solid mechanics and biomedicine including wake flows, shock tube problems, material characterization, brain aneurysms, etc, where traditional methods fail due to lack of boundary and initial conditions or material properties.
Physics-Informed Neural Networks (PINNs): Algorithms & Applicationsread_more
Zoom Meeting
27. Mai 2020
16:15-17:15 		Prof. Dr. Martin Oberlack
TU Darmstadt, Germany
Details

Zurich Colloquium in Applied and Computational Mathematics

Titel High-moment turbulent scaling laws and its roots in statistical symmetries
Referent:in, Affiliation Prof. Dr. Martin Oberlack, TU Darmstadt, Germany
Datum, Zeit 27. Mai 2020, 16:15-17:15
Ort Zoom Meeting
Abstract Using the symmetry-based turbulence theory we derive turbulent scaling laws for arbitrarily high moments of the stream-wise velocity $U_1$. In the region of the log-law, the theory predicts an algebraic law with the exponent $t_2 (n-1)$ for moments $n > 1$. The exponent $s_2$ of the $2^{nd}$ moment determines the exponent of all higher moments. Moments here always refer to the instantaneous quantities and not to the fluctuations. For the core region of a Poiseuille flow we find a deficit law for arbitrary moments $n$ of algebraic type with a scaling exponent $n(s_2-s_1)+2s_1-s_2$. Hence, the moments of order one and two with its scaling exponents $s_1$ and $s_2$ determine all higher exponents. To validate the new theoretical results we have conducted a Poiseuille flow DNS at $Re_\tau=10^4$. All of the latter theoretical findings could be verified with high accuracy using DNS data.
High-moment turbulent scaling laws and its roots in statistical symmetriesread_more
Zoom Meeting

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