Mars Gao

Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery
L. Mars Gao, Urban Fasel, Steven L. Brunton, J. Nathan Kutz
Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification…

On Optimal Early Stopping: Over-informative versus Under-informative Parametrization
Ruoqi Shen, Liyao Gao, Yi-An Ma
Early stopping is a simple and widely used method to prevent over-training neural networks. We develop theoretical results to reveal the relationship between…

Non-convex Learning via Replica Exchange Stochastic Gradient MCMC
Wei Deng, Qi Feng, Liyao Gao, Faming Liang, Guang Lin
Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov…

DeepGLEAM: A hybrid mechanistic and deep learning model for COVID-19 forecasting
Dongxia Wu, Liyao Gao, Xinyue Xiong, Matteo Chinazzi, Alessandro Vespignani, Yi-An Ma, Rose Yu
We introduce DeepGLEAM, a hybrid model for COVID-19 forecasting. DeepGLEAM combines a mechanistic stochastic simulation model GLEAM with deep learning. It uses…

Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants
L. Mars Gao, J. Nathan Kutz
Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing…

RotEqNet: Rotation-Equivariant Network for Fluid Systems with Symmetric High-Order Tensors
Liyao Gao, Yifan Du, Hongshan Li, Guang Lin
In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems…

Learning with Collaborative Neural Network Group by Reflection
Liyao Gao, Zehua Cheng
For the present engineering of neural systems, the preparing of extensive scale learning undertakings generally not just requires a huge neural system with a…

Cortex Neural Network: learning with Neural Network groups
Liyao Gao
Neural Network has been successfully applied to many real-world problems, such as image recognition and machine translation. However, for the current…

Bayesian data-driven discovery of partial differential equations with variable coefficients
Aoxue Chen, Yifan Du, Liyao Mars Gao, Guang Lin
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is…