Host: Zecheng Zhang.
Room: Love 0231.
Zoom Link: will be avaiable up on request.
Time: 03:05 pm to 04:05 pm. It is weekly on Tuesday, see below for the detailed schedule.
| Date | Speaker | Abstract of the Talk |
|---|---|---|
| Jan 7 | Zecheng Zhang | Introduction to the ACM seminar of Spring 2025, speaker informations, and what to know. |
| Jan 21 | Savvas Sardelis (FSU) | The idea of having solitary waves in Kerr nonlinear media arising in the presence of only quartic dispersion was briefly theoretically considered in the early 90's and then almost forgotten until its experimental discovery in 2016. These so-called pure-quartic solitons (PQS) were observed in a silicon photonic crystal waveguide where quartic dispersion was the dominant dispersion effect and all the other dispersion orders were negligible. In this talk, we present a new class of soliton based on the interaction of parity-time (PT) symmetric nonlinearity and quartic dispersion or diffraction. This novel kind of soliton is related to the recently discovered PQS, that arises from the balance of Kerr nonlinearity and quartic dispersion, through a complex coordinate shift. We find that the PT-symmetric PQS are linearly stable and present important differences with respect to its Hermitian (Kerr) counterpart, including a nontrivial phase structure, a skewed spectral intensity, and a higher power for the same propagation constant. |
| Jan 28 | Siming Liang (FSU) | Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems. |
| Feb 4 | SeongHee Jeong (FSU) | In this work, we investigate optimal control problems in heterogeneous porous media. Based on the partial differential equation constraint connecting the state and the control, we produce the associated control as a dependent quantity of the state. Then, we introduce the reduced optimal control problem which contains only the state variable. Here we employ $C^0$ interior penalty finite element methods for the spatial discretization to solve the reduced optimal control problem resulting in a fourth-order variational inequality. We provide a priori error estimates and stability analyses. Several numerical examples validate and illustrate the capabilities of the proposed algorithm. |
| Feb 11 | Nick Dexter (FSU) | Active learning is an important topic in machine learning for scientific computing in which learning algorithms can query ground truth data selectively to enhance model accuracy. This is increasingly vital in science applications where data acquisition is costly. This talk introduces a broad framework for active learning in regression problems that extends beyond traditional pointwise data samples to include various practical data types such as data from transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data along continuous curves, and multimodal data (i.e., involving combinations of different types of measurements). This framework uses random sampling from a finite number of sampling measures and accommodates arbitrary nonlinear approximation spaces (model classes). We then introduce generalized Christoffel functions to optimize these sampling measures and discuss how this leads to near-optimal sampling strategies for various important problems of interest. The focus will be on applications in scientific computing, highlighting the efficacy of this framework in gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) with generative models, adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs), and operator learning. |
| Feb 18 | Stefanie Guenther (LLNL) | Advances in the design of quantum technologies has led to rapidly increasing numbers of qubits in current quantum computing hardware. However, accurately controlling these large quantum systems remains a fundamental challenge in the current Noisy Intermediate-Scale Quantum (NISQ) era. Analog control pulses provide the fundamental interface between the quantum compiler and the quantum hardware, and significant progress has been made in the development of numerical methods and computational tools to optimally design pulses that realize quantum operations with high fidelity. However, the computational costs associated with the simulation of the underlying quantum dynamical model increase quickly for many-qubit system, necessitating the use of large-scale High-Performance Computing (HPC) platforms to harness greater computational concurrency. This presentation introduces a multiple-shooting approach for quantum optimal control that enables concurrency along the time domain. This approach partitions the time domain into multiple windows, with the intermediate states at window boundaries treated as additional optimization variables. Continuity of state is enforced through equality constraints. This structure facilitates parallel-in-time computation of state evolution across different time windows, leading to substantial acceleration in the evaluation of the objective function and its adjoint-based gradient. |
| Feb 25 | Haoyang Qian (FSU) | The recent outbreaks of COVID-19, Zika, Ebola, and influenza have reignited interest in refining epidemic models to better capture the complexities of disease spreading. Modern approaches go beyond classical frameworks, incorporating factors such as social norms, mobility patterns, and heterogeneous community structures to reflect the intricate interplay of social and biological dynamics. This study examines epidemic spreading in structured population networks, where individuals interact within localized communities—such as schools, workplaces, and theaters—and diffuse among these metanodes. Using mean-field averaging, we derive a scaling law linking contagion rates to the mean degree of connectivity, while linear stability analysis identifies the thresholds for infection surges. For networks with heterogeneous mean degrees, spectral perturbation theory reveals how structural variability accelerates and intensifies disease spread. Our findings highlight that nodes with higher-than-average degrees are not only disproportionately infected early but also act as key drivers of outbreaks. By framing epidemic dynamics as a continuous phase transition, we employ pattern formation theory to explain these results, showing that the critical eigenvectors governing stability are shaped by the degree distribution, emphasizing the role of structural heterogeneity. This work bridges network science and dynamical systems, offering a robust framework for understanding and predicting epidemic dynamics in structured populations while accounting for the essential role of connectivity and community organization. |
| March 18 (Seminar Enhancement Invited Speaker) | Yuanzhe Xi (Emory) | TBA. The talk will be in person. |
| March 25 | ||
| Apr 1 | Jianxun Wang (University of Notre Dame and Cornell University)_ | |
| Apr 8 | ||
| Apr 15 | Mark Sussman (FSU) | |
| Apr 22 (Seminar Enhancement Invited Speaker) | Xiao Liu (GaTech) | TBA. The talk will be in person. |