Sparse Modeling and Machine Learning for Nonlinear Partial Differential Equations

Abstract

The main goal of the grant was to construct new approaches and algorithms for learning dynamical systems from data. The objective of this research was to develop and analyze new approaches for discovering the underlying governing equations that model a given dataset. We assumed that the data was generated by some unknown dynamic process, typically satisfying a time-dependent differential equation. The technical strategies were based on sparse optimization (with limited sampling)and structured networks. This work involved sparsity-promoting optimization based on the l1 penalty, which was used to regularize the recovery process. The results include several new algorithmic and theoretical developments.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 2020
Accession Number
AD1104387

Entities

People

  • Hayden Schaeffer

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Air Force Research Laboratories
  • Algorithms
  • Analytic Functions
  • Applied Mathematics
  • Artificial Neural Networks
  • Compressed Sensing
  • Computing System Architectures
  • Convergence
  • Differential Equations
  • Dynamics
  • Equations
  • Integral Equations
  • Inverse Problems
  • Learning
  • Machine Learning
  • Mathematics
  • Network Architecture
  • Neural Networks
  • Partial Differential Equations
  • Sampling
  • Scientific Research
  • Statistical Sampling
  • Universities

Fields of Study

  • Computer science

Readers

  • Computational Fluid Dynamics (CFD)
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms