Upcoming events ical Click the following webcal to add the feed to your own calendar or copy to subscribe manually. webcal://www.tudelft.nl/en/eemcs/the-faculty/departments/applied-mathematics/current/upcoming-events?tx_lookupfeed_feed%5Baction%5D=ical&tx_lookupfeed_feed%5Bcontroller%5D=Feed&tx_lookupfeed_feed%5Blimit%5D=15&tx_lookupfeed_feed%5BlookupUid%5D=1092959&type=1657271091&cHash=9a99487bc54b58cf29f7018bbf4f524a More about webcal. 13 May 2024 15:45 till 16:45 [STAT/AP] Sonja Cox: tba tba 14 May 2024 16:00 till 17:00 [AN] Michal Wrochna: Spectral theory of Laplace-Beltrami and Dirac operators in Lorentzian signature It has been discovered relatively recently that the Laplace-Beltrami (or wave) operator on Lorentzian has a reasonable spectral theory despite being not elliptic. I will give an overview of recent results, explain their relationship with tools from microlocal analysis and sketch applications in Quantum Field Theory and non-commutative geometry. I will also discuss new results on Dirac operators D on a Lorentzian spin manifold (joint work with N. V. Dang and A. Vasy). 16 May 2024 16:00 till 17:00 [PDE&A] Paul Zegeling: A generalized midpoint-based BV-method for unstable PDEs (and beyond) We will discuss a generalized midpoint-based boundary-value method and its application to unstable and ill-posed partial differential equations (PDEs). Furthermore, an extension of this technique to DE systems with periodic solutions, e.g., the harmonic oscillator and predator-prey equations will be proposed. Boundary-value methods (BVMs) are generalizations of traditional time-integrators such as linear multistep or Runge-Kutta methods. They make use of additional final and, if appropriate, extra initial conditions as well. The generalized midpoint-based BMV has the special property that its stability region is the whole complex plane (excluding the imaginary axis). This opens interesting new application areas (compared to the well-known and widely-accepted time-integration techniques): the backward heat equation and similar ill-posed or unstable PDEs. Examples will be given for several models in this class. In addition, replacing the final conditions in the BVM by periodic conditions, we can apply this approach to DEs with periodic solution behaviour. Especially, it is interesting to investigate models with center points, limit cycles and where the conservation of energy in Hamiltonian DE systems plays a role. 21 May 2024 16:00 till 17:00 [AN] Joris van Winden: Stability and motion of solitary waves in a stochastic PFNLS equation The focusing nonlinear Schrödinger equation has a special solution in the form of a nonlinear solitary wave. We consider stability of this wave under small stochastic perturbations. We show that in the presence of a certain parametric forcing, the solitary wave exhibits orbital stability, meaning that the solution remains close to a suitably translated version of the wave. The parametric forcing models amplification and damping of a wave packet propagating in an optical fiber. We show stability on a timescale which is exponential in the inverse square of the noise amplitude. Using an asymptotic expansion, we also give explicit expressions for the motion of the wave, which are valid on short timescales. 27 May 2024 15:45 till 16:45 [STAT/AP] Collin Drent: Condition-Based Production for Stochastically Deteriorating Systems: Optimal Policies and Learning Production systems used in the manufacturing industry degrade due to production and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This degradation behavior, and hence the system's reliability, is affected by the system's production rate. While producing at a higher rate generates more revenue, the system's reliability may also decrease. Production should thus be controlled dynamically to trade-off reliability and revenue accumulation in between maintenance moments. We study this dynamic trade-off for (i) systems where the relation between production and degradation is known as well as (ii) systems where this relation is not known and needs to be learned on-the-fly from condition data. For systems with a known production-degradation relation, we cast the decision problem as a continuous-time Markov decision process and prove that the optimal policy has intuitive monotonic properties. We also present sufficient conditions for the optimality of bang-bang policies and we characterize the structure of the optimal interval between scheduled maintenance moments. For systems with an a-priori unknown production-degradation relation, we propose a Bayesian procedure to learn the unknown degradation rate under any production policy from real-time condition data. Numerical studies indicate that on average across a wide range of practical settings (i) condition-based production increases profits by 50% compared to static production, (ii) integrating condition-based production and maintenance interval selection increases profits by 21% compared to a state-of-the-art approach, and (iii) our Bayesian approach performs close, especially in the bang-bang regime, to an Oracle policy that knows each system's production-degradation relation. 28 May 2024 16:00 till 17:00 [AN] Hans Maassen: TBA TBA 30 May 2024 16:00 till 17:00 [PDE&A] Viktoria Freingruber 31 May 2024 12:30 till 13:15 [NA] Hyea Hyun Kim: Partitioned neural network approximation to partial differential equations and its training performance enhancement utilizing domain decomposition algorithms With the success of deep learning technologies in many scientific and engineering applications, neural network approximation methods have emerged as an active research area in numerical partial differential equations. However, the new approximation methods still need further validations on their accuracy, stability, and efficiency so as to be used as alternatives to classical approximation methods. In this talk, we first introduce partitioned neural network approximation to partial differential equations, where neural network functions localized in each small subdomains are employed as a solution surrogate in order to reduce the approximation and optimization errors in the standard single large neural network approximation. The parameters in each local neural network function are then optimized to minimize the corresponding cost function to the model problem. To enhance the parameter training efficiency further, iterative algorithms for the partitioned neural network function can be developed by utilizing classical domain decomposition algorithms and their convergence theory. We finally present promising features in this new approach as a way of enhancing the neural network solution accuracy, stability, and efficiency with some supporting numerical results. 03 June 2024 15:45 till 16:45 [STAT/AP] Eni Musta: tba tba 04 June 2024 16:00 till 17:00 [AN] Anouk Wisse: TBA TBA 06 June 2024 16:00 till 17:00 [PDE&A] Marco Rehmeier TBA 11 June 2024 16:00 till 17:00 [AN] Rik Westdorp: TBA TBA 13 June 2024 16:00 till 17:00 [PDE&A] María de los Ángeles García Ferrero 17 June 2024 15:45 till 16:45 [STAT/AP] Rui Castro: tba tba 18 June 2024 16:00 till 17:00 [AN] Palina Salanevich: TBA TBA 20 June 2024 13:30 till 16:45 A seminar on Logic, Set Theory, Topology An afternoon of talks in honour of KP Hart's retirement 25 June 2024 16:00 till 17:00 [AN] Sebastian Bechtel: TBA TBA Share this page: Facebook Linkedin Twitter Email WhatsApp Share this page