Machine learning and statistical methods for physical systems
Abstract/Contents
- Abstract
- Physical systems often exhibit highly complex, non-linear behaviors, making their characterization without a profound understanding of underlying dynamics a challenging endeavor. In this presentation, I will explore several methodologies for integrating valuable prior knowledge into machine learning-based and statistical methods, aimed at predicting physical system behaviors and bolstering the control of engineering systems. The talk will be divided into three main parts. In the first part, I will present several deep-learning-based interpolation methods for estimating nearshore bathymetry with sparse measurements. By applying deep learning-based models from a Bayesian perspective, we provide uncertainty quantification for the underlying bathymetry profile and compare our predictions with those from Gaussian Process Regression (GPR). Results show that our approach provides more accurate posterior estimates, particularly when encountering patterns with sharp gradients, such as those found around sandbars and submerged objects. In the second part, I will introduce a novel framework, namely physics-based Parameterized Neural Ordinary Differential Equations, for predicting laser ignition inside a rocket combustor. A 0D reacting flow model is combined with neural ordinary differential equations to deliver accurate solutions, even with limited training samples, that adhere to physical constraints. We validate our physics-based PNODE using solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations, demonstrating its capability to accurately learn complex combustion dynamics with high-dimensional parameters of laser ignition. In the third part, we consider the use of a periodic Martingale Model for Forecast Evolution (MMFE) to integrate weather forecasts into decision-making processes for energy system controls. We demonstrate that, when combined with a linear state space model, our periodic MMFE yields computationally tractable Markov Decision Processes (MDPs) with low-dimensional state variables. We provide algorithms for the maximum likelihood estimation of model parameters for our periodic MMFE and showcase the corresponding asymptotic convergence. Furthermore, we validate the generative power of our framework for weather forecast errors by calibrating our periodic MMFE using real data collected from hourly commercial weather forecasts.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Qian, Yizhou |
|---|---|
| Degree supervisor | Darve, Eric |
| Thesis advisor | Darve, Eric |
| Thesis advisor | Glynn, Peter W |
| Thesis advisor | Kitanidis, P. K. (Peter K.) |
| Degree committee member | Glynn, Peter W |
| Degree committee member | Kitanidis, P. K. (Peter K.) |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Yizhou Qian. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/yx222yd2245 |
Access conditions
- Copyright
- © 2023 by Yizhou Qian
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...