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Center for Nonlinear Studies |
Systems with multi-scale and multi-physics behavior are exceedingly difficult to model. These types of problems can be seen everywhere, from weather modeling to plasma instabilities and magnetized turbulence. In these systems, micro scale interactions control macro scale evolution. However, directly modeling the small-scale physics and interactions that dictate the system is often computationally intractable.
Data-driven model identification techniques are well suited to address these types of challenges as they learn an equation representative of significant behavior in a dataset. Methods based on sparse regression are formulated to find the simplest model that still fits the data, making these approaches well posed to learn accurate reduced models for complex systems. Using such methods on plasma data results in a set of equations that can enhance theory, be used in simulation methods, and help develop reduced models that decrease computational cost.
Data-driven model identification techniques are well suited to address these types of challenges as they learn an equation representative of significant behavior in a dataset. Methods based on sparse regression are formulated to find the simplest model that still fits the data, making these approaches well posed to learn accurate reduced models for complex systems. Using such methods on plasma data results in a set of equations that can enhance theory, be used in simulation methods, and help develop reduced models that decrease computational cost.
This talk will address how one such method, Weak Sparse Identification of Nonlinear Dynamics (WSINDy), can be applied to a variety of plasma simulations to discover fluid models. Relationships are made between equation identification and data complexity as quantified by Shannon information entropy. Modifications to WSINDy have also been made to account for a variety of terms that do not easily fit into the weak PDE formulation while maintaining comparable accuracy. This exploration encompasses diverse system behavior, highlighting how the interplay between simulation methods, physics theory, and data-driven techniques can guide further model development. Applications of these methods to particle and multi-physics codes used at Sandia National Labs will also be discussed.
Host: Will Taitano (T-5)