- Title Information
- Title
- SympNets, PNNs and GFINNs: Intrinsic structure preserving neural networks for identifying and solving dynamical systems with applications to optimal control problems
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Zhang, Zhen
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Karniadakis, George
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Keith, Brendan
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Darbon, Jérôme
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2024
- Physical Description
- Extent
- , None p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2024
- Genre (aat)
- theses
- Abstract
- This thesis introduces novel neural network architectures designed to discover dynamical systems from physical data and as well as solve dynamical systems rising from optimal control problems. At the core of the investigation are three interconnected neural network models: Symplectic Networks (SympNets), Poisson Neural Networks (PNNs), and GENERIC Formalism Informed Neural Networks (GFINNs).
SympNets are introduced as a foundational architecture to approximate arbitrary symplectic maps, based on our proof of the universal approximation theorem. We apply SympNets and its variants in three different scenarios, (i) identifying Hamiltonian systems from data, (ii) node classficiation on graphs (SympGNNs), and (iii) solve high-dimensional optimal control problems through a symplectic transformation (SympOCNets and TSympOCNets).
Building on SympNets, we further introduce PNNs to extend the framework to Poisson systems, addressing noncanonical coordinates through the integration of the Darboux-Lie theorem. GFINNs represent a further generalization, designed to encompass noncanonical conservative and dissipative systems by incorporating the GENERIC formalism. These models significantly enhance the capability of SympNets to model more complex dynamics arising from a broader spectrum.
Collectively, these models represent an advancement in the integration of machine learning with physical modeling, potentially offering new ways to solve problems in system identification and optimal control. The thesis not only establishes new theoretical results but also provides empirical evidence of the models' superior performance in a variety of complex scenarios, paving the way for future research in physics informed machine learning.
- Subject
- Topic
- dynamical systems
- Subject
- Topic
- Deep Learning
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01140989")
- Topic
- Symplectic geometry
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20240505