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February 6— "Finding scattering resonances via generalized colleague matrices"

• Presenter: Vladimir Rokhlin, Arthur K Watson Professor of Computer Science & Mathematics, Yale University
• �������ٰ�������:��Locating scattering resonances is a standard task in certain areas of physics and engineering. This often can be reduced to finding zeros of complex analytic functions. In this talk, I will discuss a scheme for finding all roots of a complex analytic function in a square domain in C. The scheme can be viewed as a generalization of the classical approach to finding roots of a function on an interval by first approximating it by a polynomial in the Chebyshev basis, followed by diagonalizing the so-called “colleague matrices.” This extension to the complex domain is based on several observations that enable the construction of polynomial bases that satisfy three-term recurrences and are reasonably well-conditioned, giving rise to “generalized colleague matrices.” We also introduce a special-purpose QR algorithm for finding eigenvalues of the resulting structured matrices stably and efficiently. I will demonstrate the effectiveness of the approach via several numerical examples.

March 6 — "Tailored Forecasts from Short Time Series Using Meta-Learning and Reservoir Computing"

• Presenter: Michelle Girvan, Department of Physics, University of Maryland
• �������ٰ�������:��Machine learning (ML) models can be effective for forecasting the dynamics of unknown systems from time-series data, but they often require large datasets and struggle to generalize—that is, they fail when applied to systems with dynamics different from those seen during training. Combined, these challenges make forecasting from short time series particularly difficult. To address this, we introduce Meta-learning for Tailored Forecasting from Related Time Series (METAFORS), which supplements limited data from the system of interest with longer time series from systems that are suspected to be related. By leveraging a library of models trained on these potentially related systems, METAFORS builds tailored models to forecast system evolution with limited data. Using a reservoir computing implementation and testing on simulated chaotic systems, we demonstrate METAFORS’ ability to predict both short-term dynamics and long-term statistics, even when test and related systems exhibit significantly different behaviors, highlighting its strengths in data-limited scenarios.

April 3 — ��Title Pending

• Presenter: Anna-Karin Tornberg, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
• Abstract: Pending

May 1— Title Pending

• Presenter: Edgar Knobloch; Department of Physics; University of California, Berkeley
• Abstract: Pending