BU SIAM seminars will be held on Thursday from 12:30-1:30pm. Talks are not recorded unless requested by the speaker. Subscribe at join.
Spring 2023 Summary (Tentative)
| Date | Speaker | Talk Title |
| Mar 16 | Anming Gu | Optimal Transport and k-Mixup Regularization |
| April 13 | Trevor Norton | Kink-like solutions for the FPUT lattice and the mKdV as a modulation equation |
| April 27 | Jonathan Jaquette, PhD | Exploring global dynamics and blowup in some nonlinear PDEs |
| Oct 3 | Zhiyu Zhang, PhD | Improving adaptive online learning using PDEs |
| Oct 24 | Michael Sun | PP-GNN: From Learning NP-Hard to Position-aware Graph Neural Networks |
| Nov 2 | – | – |
| Dec 14 | – | – |
| – | Caitlin Lienkaemper, PhD | Combinatorial Threshold Networks (TBA) |
| – | Islam Faisal | Quantum Computing (TBA) |
Previous Talks
Speaker: Anming Gu
Title: Optimal Transport and k-Mixup Regularization
Abstract: Optimal Transport (OT) is a mathematical framework that seeks to address the problem of transforming one probability distribution into another probability distribution. Its wide-ranging applications span several disciplines, including mathematics, computer science, and economics. In this presentation, we aim to explore the formal definition of the problem, review some of its theoretical results, and examine various solutions that have been proposed. Additionally, we will delve into a specific application of OT called k-mixup, which is an extension of the mixup regularization technique used in machine learning. Mixup generates a vicinal training distribution by linearly interpolating training points.
Speaker: Trevor Norton, PhD
Title: Kink-like solutions for the FPUT lattice and the mKdV as a modulation equation
Abstract: The Fermi-Pasta-Ulam-Tsingou (FPUT) lattice became of great mathematical interest when it was observed that it exhibited a near-recurrence of its initial condition, despite it being a nonlinear system. This behavior was explained by showing that the Korteweg-de Vries (KdV) equation serves as a continuum limit for the FPUT and has soliton solutions. Much work has been done into analyzing the solitary wave solutions of the FPUT and the relationship between the lattice and its continuum limit. For certain potentials the modified KdV (mKdV) instead serves as the continuum limit for the FPUT. However, there has been little research done to examine how the defocusing mKdV can be used a modulation equation for the FPUT or how the kink solutions of the mKdV relate to solutions of the FPUT. This talk is based on my thesis research which focuses on addressing this gap in the research. I will discuss how the existence of kink-like solutions can be proved and how their profiles can be approximated by the profiles of the kink solutions of the mKdV. Time permitting, I will also discuss how the defocusing mKdV can be used more widely as a modulation equation for small-amplitude, long-wavelength solutions of the FPUT lattice.
Speaker: Jonathan Jaquette, PhD
Title: Exploring global dynamics and blowup in some nonlinear PDEs
Abstract: Pencil-and-paper analysis offers powerful tools for understanding how complex systems change over time. However, for most systems these tools are insufficient to completely understand non-perturbative dynamics. In this talk, I will discuss a complex-scalar PDE which may be seen as a toy model for vortex stretching in fluid flow. In a recent series of papers, we have shown (using computer-assisted-proofs) that this equation exhibits rich dynamical behavior existing globally in time: non-trivial equilibria, connecting orbits, and periodic orbits. On the other side of the coin, we show several mechanisms by which solutions can blowup.
Speaker: Zhiyu Zhang, PhD
Title: Improving adaptive online learning using PDEs
Abstract: Adaptive online learning, in a very broad sense, is the game-theoretic study of sequential decision making beyond the worst case. Compared to their classical minimax counterparts, adaptive algorithms typically require less manual tuning, while provably performing better in benign environments, or with prior knowledge. In this talk, I will first introduce the concrete framework of adaptive online learning and its algorithmic benefits. Then, I will present some recent results using PDEs to streamline the design of adaptive online learning algorithms. The hope is to pique the interest of the audience and foster discussions at the intersection of differential equations and learning theory.
Speaker: Michael Sun
Title: PP-GNN: From Learning NP-Hard to Position-aware Graph Neural Networks
Recording: Link
Abstract: On a graph G, knowing your distances to a set of anchors can uniquely determine which node you are on (the Euclidean case is GPS, i.e. triangulation). The smallest possible number of anchors is called the metric dimension, computing which is known to be NP-hard. Solving the metric dimension problem (MDP) and the associated minimal resolving set has many important applications across science and engineering, like sonar navigation and disease source identification. In this paper, we introduce MaskGNN, a method using a graph neural network (GNN) model to learn the minimal resolving set in a self-supervised manner by optimizing a novel surrogate objective. Notably, MaskGNN achieves up to 98% the reward of integer programming in 0.72% of the running time. Simultaneously, learning the MDP pretrains Position-aware GNNs (PP-GNN) for downstream position-based tasks on a graph. PP-GNN’s new self-supervised learning-based paradigm for learning the resolving set of the graph and pretraining representations works when only a single instance is provided, e.g. learn where to place things given a single building. Finding the resolving set — the “metric basis” — can learn an object’s structural prior for adapting downstream algorithms, and presents many opportunities for real-world use cases.