A statistical physics approach to data-driven model discovery for non-equilibrium processes
Abstract
Non-equilibrium processes are ubiquitous and pervade all areas of science, from metabolism and growth in biological processes to material failure under ballistic impact or weather patterns and ocean currents. Their understanding, prediction or design at the level of applications requires high fidelity stand-alone continuum models that are efficiently computable and, ideally, also endowed with reliable estimates of their accuracy. However, present strategies for the formulation of continuum theories often make use of strong phenomenological assumptions of undetermined accuracy for the specific form of the evolution equations; and only the parameters therein are obtained from experiments or lower-scale numerical simulations. Although, in theory, such continuum evolutions represent the underlying particle/atomistic behavior in the limit of large number of particles, bridging atomistic and continuum descriptions for processes out of equilibrium represents one of the key challenges of the 21st century. This research addresses precisely this challenge, by developing a statistical physics approach to data-driven model discovery that can determine the entire partial differential equations describing the non-equilibrium continuum behavior over long times, from particle data over short times, i.e., an approach that is truly predictive upon forecasting. The proposed approach aims to derive these macroscopic models with quantified uncertainty; methodologically, it is based on recent advances in non-equilibrium thermodynamics, numerical and stochastic analysis, as well as machine learning. Its range of applicability will be vast, encompassing a wide range of processes in fluids and solids, which may combine reversible and dissipative behavior.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 28, 2023
- Source ID
- W911NF2310230
Entities
People
- Celia Reina
Organizations
- Army Contracting Command
- United States Army
- University of Pennsylvania