The link for online participation is sent out before the talk through our mailing list.

Tuesday, 21 May 2024, 13:30–15:00h, Room TBA

Speaker: TBA

Title: TBA

Host: TBA

Abstract: TBA

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Tuesday, 04 June 2024, 13:30–15:00h, Room TBA

Speaker: Prof. Dr. Lyudmila Grigoryeva

Title: Learning Dynamic Processes with Reservoir Computing

Host: TT.-Prof. Dr. Tobias Sutter

Abstract: Many dynamic problems in engineering, control theory, signal processing, time series analysis,

and forecasting can be described using input/output (IO) systems. Whenever a true functional IO relation

cannot be derived from first principles, parsimonious and computationally efficient state-space systems can

be used as universal approximants. We have shown that Reservoir Computing (RC) state-space systems

with simple and easy-to-implement architectures enjoy universal approximation properties proved in different

setups. The defining feature of RC systems is that some components (usually the state map) are randomly

generated, and the observation equation is of a tractable form. From the machine learning perspective, RC

systems can be seen as recurrent neural networks with random weights and a simple-to-train readout layer

(often a linear map). RC systems serve as efficient, randomized, online computational tools for learning

dynamic processes and enjoy generalization properties that can be explicitly derived. We will make a general

introduction to up-to-date theoretical developments, discuss connections with research contributions in

other fields, and address details of RC systems’ applications.

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Tuesday, 18 June 2024, 13:30–15:00h, Room TBA

Speaker: TBA

Title: TBA

Host: TBA

Abstract: TBA

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Tuesday, 25 June 2024, 13:30–15:00h, Room G309

Speaker: Dr. Matthias C. Caro

Title: TBA

Host: Dr. Lothar Sebastian Krapp

Abstract: TBA

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Tuesday, 02 July 2024, 13:30–15:00h, Room TBA

Speaker: Prof. Dr. Gitta Kutyniok

Title: TBA

Host: Prof. Dr. Stefan Volkwein

Abstract: TBA

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Tuesday, 16 July 2024, 13:30–15:00h, Room TBA

Speaker: Asst. Prof. Dr. Ariel Neufeld

Title: Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its complexity analysis

Host: TT.-Prof. Dr. Tobias Sutter

Abstract: In this talk we present a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs

with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is

only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions

used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular,

we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d

of the PDE and the reciprocal of the prescribed accuracy ε. Moreover, we show that for payoff functions which

are bounded, our algorithm indeed has a speed-up compared to classical Monte Carlo methods. Furthermore,

we present numerical simulations in one and two dimensions using our developed package within the Qiskit

framework tailored to price CPWA options with respect to the Black-Scholes model, as well as discuss the

potential extension of the numerical simulations to arbitrary space dimension.

This talk is based on joint work with Jianjun Chen and Yongming Li

(PDF-Version will follow here)