An Information Theory Approach to Physical Domain Discovery

07/13/2021
by   Daniel Shea, et al.
0

The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.

READ FULL TEXT
research
02/10/2022

Discovering plasticity models without stress data

We propose a new approach for data-driven automated discovery of materia...
research
04/14/2021

Effect of viscous shearing stresses on optimal material designs for flow of fluids through porous media

Topology optimization offers optimal material layouts, enabling automati...
research
01/19/2023

Forecasting subcritical cylinder wakes with Fourier Neural Operators

We apply Fourier neural operators (FNOs), a state-of-the-art operator le...
research
08/09/2023

Visualizing Similarity of Pathline Dynamics in 2D Flow Fields

Even though the analysis of unsteady 2D flow fields is challenging, flui...
research
11/03/2022

Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems

We develop inductive biases for the machine learning of complex physical...
research
06/28/2023

S2SNet: A Pretrained Neural Network for Superconductivity Discovery

Superconductivity allows electrical current to flow without any energy l...

Please sign up or login with your details

Forgot password? Click here to reset