Research Seminar Numerical Analysis of Stochastic and Deterministic Partial Differential Equations   📅

Institute
Head
Claudia Schillings
Description
The seminar brings together experts on numerical analysis, applied mathematics, statistics and stochastics with particular focus on applications to stochastic and deterministic partial differential equations.
Number of talks
63
Thu, 16.01.25 at 13:00
FU Berlin (Arnima...
Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits
Abstract. I will discuss evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on the case where the dynamics are driven by an entropy functional defined both on the metric edges and vertices, we provide a rigorous understanding of such coupled systems of ordinary and partial differential equations as (generalized) gradient flows in continuity equation format. Approximating the edges by a sequence of vertices, which yields a fully discrete system, we are able to establish existence of solutions in this formalism. Furthermore, we study several scaling limits using the recently developed framework of EDP convergence with embeddings to rigorously show convergence to gradient flows on reduced metric and combinatorial graphs. Finally, numerical studies confirm our theoretical findings and provide additional insights into the dynamics under rescaling. This is joint work with Jan-Frederik Pietschmann and André Schlichting.
Thu, 21.11.24 at 13:00
room 108, Arnimal...
An abstract approach to the Robin-Robin method
Abstract. The Robin-Robin method is a common domain decomposition method for numerically approximating solutions to partial differential equations in parallel. While there are convergence proof for specific equations and domains, there are few general results. We have therefore developed an abstract approach to the Robin-Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. Furthermore, the framework can be extended to initial-value problems on moving domains. This extension is an ongoing joint work with Ana Djurdjevac and Amal Alphonse.
Thu, 14.11.24 at 13:00
room 108, Arnimal...
Estimating causal effects in the instrumental variable framework, without ex-ante knowledge of valid instruments
Abstract. In the field of Biology, the use of instrumental variables has taken precedence for estimating causal relationships between exposures and outcomes, in the form of Mendelian randomisation. This framework assumes the instrument is a genetic variant, which is essentially inherited at birth and remains unchanged throughout one's life. The framework however also stipulates that the instrument is only valid if it acts on the outcome only through the exposure of interest — a breach of this situation makes the estimation null, and in the biological sphere is referred to as pleiotropy. Many attempts have been made to identify ‘pleiotropic’ instruments and remove them to perform valid estimation, however with no mathematically testable criteria, this procedure is not robust. This work instead looks at the approach by Sun et al.¹ in developing a solution which leverages potentially invalid instruments with valid ones in the form of G-estimators with unconditional moment conditions. This approach proves promising, but is limited by scalability leading to trade-offs between biological accuracy and computational ability. This talk demonstrates the severity of pleiotropic rich systems, and will discuss the computational limitations and trade-offs that one has to make to employ G-estimation in the Mendelian randomisation application.
Thu, 07.11.24 at 13:00
room 108, Arnimal...
Adaptive stepsize algorithms for Langevin dynamics
Abstract. The work focuses on weak approximation of stochastic differential equations and develops a method of computing solutions of Langevin dynamics using variable stepsize. The method assumes a knowledge of the problem allowing to establish a good monitor function which locates points of rapid change in solutions of stochastic differential equations. Using time-transformation we show that it is possible to integrate a rescaled system using fixed stepsize numerical discretization effectively placing more timesteps where needed.
Wed, 30.10.24 at 10:00
room 108, Arnimal...
Data-driven approximation of Koopman operators and generators: Convergence rates and error bounds
Abstract. (joint work with Liam Llamazares-Elias, Samir Llamazares-Elias, and Stefan Klus)
Tue, 22.10.24 at 14:00
room 108, Arnimal...
Adaptive training of Gaussian Process based surrogates for Bayesian parameter identification.
Thu, 20.06.24
Solving the Optimal Experiment Design Problem with mixed-integer convex methods
Thu, 13.06.24
room 126, Arnimal...
Optimisation in Bayesian experimental design
Thu, 06.06.24
room 126, Arnimal...
Quasi-Monte Carlo Methods for PDEs on Random Domains
Thu, 30.05.24
room 126, Arnimal...
Learning Operators via Hypernetworks
Thu, 23.05.24
room 210, Arnimal...
Sampling in Unit Time with Kernel Fisher-Rao Flow Paper von Aimee Maurais und Youssef Marzouk
Thu, 16.05.24
room 210, Arnimal...
QMC meets Optimal sampling
Thu, 08.02.24 at 13:00
A3/115
Thu, 01.02.24 at 13:00
room A6/108
Towards optimal sensor placement for inverse problems in spaces of measures
Thu, 01.02.24 at 12:00
A6/108
PDE-Constrained Optimization Problems with Probabilistic State Constraints
Thu, 11.01.24 at 13:00
room A3/115
Thu, 21.12.23 at 13:00
room A3/115
From Probabilistic Models of Mechanical Failure to Multi-Objective Shape Optimization
Fri, 01.12.23 at 10:00
A6 108/109
Ensemble Kalman filtering for epistemic uncertainty
Thu, 30.11.23 at 13:00
A3/115
An introduction to TorchPhysics: Deep Learning for partial differential equations
Thu, 16.11.23 at 13:00
room A6/108
An optimal control perspective on diffusion-based generative modeling leading to robust numerical methods
Thu, 02.11.23 at 13:00
room TBA
Effiziente Synergien durch integrierte Prozessoptimierung – Bedarfsgerechter Einsatz von Produktionskapazitäten unter Berücksichtigung der partiellen Produktionssysteme
Thu, 02.11.23 at 12:00
A6/210
Ensemble Kalman Inversion for time-dependent forward operators
Thu, 26.10.23 at 13:00
room A6/108
On polynomial-time mixing for high-dimensional MCMC in inverse problems
Tue, 17.10.23 at 15:15
A6/108
Edge-preserving inversion with heavy-tailed Bayesian neural networks priors
Wed, 30.08.23 at 10:15
A6/108/109
Analysis of vector-valued random features
Wed, 19.07.23 at 15:30
A6/108/109
A random dynamical system perspective on chemical reaction networks
Wed, 19.07.23 at 15:00
A6/108/109
Bayesian inversion with alpha-stable priors
Wed, 19.07.23 at 14:15
A6/108/109
Ensemble-based Data Assimilation for high-dimensional nonlinear dynamical systems
Fri, 07.07.23 at 11:00
A6/108/109
On definitions of modes and MAP estimators
Fri, 30.06.23 at 10:15
A6/108/109
Improving Ensemble Kalman Filter performance by adaptively controlling the ensemble
Thu, 22.06.23 at 14:15
A6/126
Optimal Control and Feedback Stabilization Under Uncertainty
Fri, 16.06.23 at 11:00
A6/108/109
Approximating Multivariate Functions with Embedded Lattice-based Algorithms
Fri, 16.06.23 at 10:15
A6/108/109
A randomised lattice algorithm for integration using a fixed generating vector
Fri, 16.06.23 at 09:30
A6/108/109
Energy, Discrepancy, and Polarization of Greedy Sequences on the Sphere
Mon, 05.06.23 at 13:00
A6/210
Subgaussian concentration in Hilbert spaces and inference in inverse problems
Mon, 05.06.23 at 12:15
A6/108/109
Approximation of SDEs with irregular drift: stochastic sewing approach
Fri, 05.05.23 at 10:15
A6/210
Wed, 26.04.23 at 14:15
A6/108/109
A randomized operator splitting scheme inspired by stochastic optimization methods
Fri, 21.04.23 at 10:15
A6/108/109
Langevin Dynamics: Bayesian inference, homotopy and generative modeling
Mon, 23.01.23 at 10:15
A6/009
Strong approximation of the CIR process: A never ending story?
Wed, 11.01.23 at 11:00
A6/108/109
Higher order methods for geometric inverse problems
Wed, 11.01.23 at 10:15
A6/108/109
Shape optimization for time-dependent domains
Mon, 05.12.22 at 10:15
A6/009
Why rough stuff matters for UQ
Mon, 28.11.22 at 10:15
A6/009
Optimal and Bayesian hypothesis testing in statistical inverse problems
Wed, 23.11.22 at 14:15
A6/108/109
Multiobjective Learning in Solar Energy Prediction: Benefits and Algorithms
Mon, 14.11.22 at 10:15
A6/009
Frechet derivatives of path functionals of stochastic differential equations
Mon, 07.11.22 at 10:15
online
Approximating distribution functions in uncertainty quantification using quasi-Monte Carlo methods
Mon, 31.10.22 at 11:00
A6/009
Cauchy Markov random field priors for Bayesian inversion
Mon, 31.10.22 at 10:15
A6/009
Short-term vital parameter forecasting in the intensive care unit
Fri, 21.10.22 at 10:15
A6/126
Eigenlocking – Parameter-dependent loss of convergence rate
Mon, 17.10.22 at 11:00
A6/009
Nonparametric approximation of conditional expectation operators
Mon, 17.10.22 at 10:15
A6/009
QMC and sparse grids beyond uniform distributions on cubes: transport maps to mixture distributions
Fri, 15.07.22 at 10:15
A6/108/109
Introduction to DG methods
Fri, 08.07.22 at 11:00
A6/108/109
Fri, 08.07.22 at 10:15
A6/108/109
On tensor-based training of neural networks
Fri, 01.07.22 at 10:15
online
Fri, 10.06.22 at 10:15
online
Fri, 03.06.22 at 10:15
A6/108/109
QMC and kernel interpolation
Fri, 27.05.22 at 10:15
online
Data-based modeling of the cellular response to oxidative stress -- A Bayesian approach for model selection and parameter identification in (bio)chemical networks
Fri, 20.05.22 at 10:15
online
Fri, 13.05.22 at 10:15
A6/108/109
Gaussian processes for uncertainty quantification and error estimation
Fri, 06.05.22 at 10:15
A6/108/109
MAP estimators in l^p
Fri, 29.04.22 at 10:15
A6/108/109
Variational inference for Bayesian neural networks