Optimal Error Estimates of Ultra-weak Discontinuous Galerkin Methods with Generalized Numerical Fluxes
Speaker: Yuan Chen (OSU) Dates: 2023/10/06 Location: MW154 Abstract: We study ultra-weak discontinuous Galerkin methods with generalized numerical fluxes for multi-dimensional high order partial differential equations on both unstructured simplex and Cartesian meshes. The equations we consider as examples are…
Combining Stochastic Parameterized Reduced-Order Models with Machine Learning for Data Assimilation and Uncertainty Quantification with Partial Observations
Speaker: Changhong Mou (UWM) Dates: 2023/09/29 Time: 4:10-5:10 (EST) Location: Zoom, link Abstract: A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields,…
The semi-implicit DLN algorithm for the Navier-Stokes equations
Speaker: Wenlong Pei (OSU) Dates: 2023/09/21 Location: MW105 Abstract:Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order,A−andG−stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified…
Efficient ensemble methods for simulating groundwater-surface flows
Speaker: Ying Li (OSU) Dates: 2023/09/15 Location: MW154 Abstract: We propose and analyze a series of efficient, unconditionally stable, ensemble methods for stimulating groundwater-surface flows governed by the Stokes-Darcy model. For systems like the surface-groundwater flows, predictive simulations must account…
Deep learning for parameter estimation
Speaker: Caroline Tatsuoka (OSU) Dates: 2023/10/05 Location: MA105 Abstract: We present methods to obtain estimates to unknown parameters of dynamical systems via data driven methods using deep neural networks (DNNs). An inverse map from the solution space to the parameter…
Data Driven Modeling of Unknown Stochastic Systems.
Speaker: Yuan Chen (OSU) Dates: 2023/09/01 Location: MW154 Abstract: We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML)…
Introduction to Computational Quantum Physics
Speaker: Nan Sheng (Uchicago) Dates: 2023/04/21 Abstract: Quantum many-body physics is principally a problem where algorithmic complexity increases exponentially w.r.t. the system size. In order to tackle the quantum information encoded in the exponential scaling, robust computational methods are required….
Transformer meets boundary value inverse problems
Speaker: Ruchi Guo (UCI) Dates: 2023/04/07 Zoom link: click this link Abstract: A Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator…
Reduced order model for kinetic and transport problems
Speaker: Zhichao Peng (MSU) Dates: 2023/02/24 Zoom link: click this link Abstract: Numerical simulation plays an important role in various engineering and scientific problems. Reduced order model (ROM), a technique to reduce degrees of freedom needed in numerical simulations, is…
Deep Neural Network Modeling of Unknown System Dynamics
Speaker: Zhen Chen (Dartmouth) Dates: 2023/02/17 Zoom link: click this link Abstract: There are numerous observational, experimental, or simulation data for problems in science and engineering. Differential equations governing the underlying dynamics are often unknown for some systems. The ability…