Parameter estimation of ordinary differential equations in NeuroMANCER

Differentiable models such as Neural ordinary differential equations (NODEs) or neural state space models (NSSMs) represent a class of black box models that can incorporate prior physical knowledge into their architectures and loss functions. Examples include structural assumption on the computational graph inspired by domain application, or structure of the weight matrices of NSSM models, or networked NODE architecture. Differentiaity of NODEs and NSSMs allows us to leverage gradient-based optimization algorithms for learning the unknown parameters of these structured digital twin models from observational data of the real system.
In this tutorial, we show how to estimate parameters of differentiable equation models from time series data.

code examples: https://github.com/pnnl/neuromancer/t...

This work was partially supported by the Mathematics for Artificial Reasoning in Science (MARS) and Data Model Convergence (DMC) initiatives via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL), by the U.S. Department of Energy, through the Office of Advanced Scientific Computing Research's “Data-Driven Decision Control for Complex Systems (DnC2S)” project, and through the Energy Efficiency and Renewable Energy, Building Technologies Office under the “Dynamic decarbonization through autonomous physics-centric deep learning and optimization of building operations” and the “Advancing Market-Ready Building Energy Management by Cost-Effective Differentiable Predictive Control” projects.
PNNL is a multi-program national laboratory operated for the U.S. Department of Energy (DOE) by Battelle Memorial Institute under Contract No. DE-AC05-76RL0-1830.