A document by Daniel E. Amrhein. Click on the document to view its contents.

Biased, incomplete models are often used for forecasting states of complex dynamical systems by mapping an estimate of a “true’ initial state into model phase space, making a forecast, and then mapping back to the “true’ space. While advances have been made to reduce errors associated with model initialization and model forecasts, we lack a general framework for discovering optimal mappings between the reference dynamical system and the model phase space. Here, we propose using a data-driven approach to infer these maps. Our approach consistently reduces errors in the Lorenz-96 system with an imperfect model constructed to produce significant model errors compared to a reference configuration. Optimal pre- and post-processing transforms leverage “shocks’ and “drifts’ in the imperfect model to make more skillful forecasts of the reference system. The implemented machine learning architecture using neural networks constructed with a custom analog-adjoint layer makes the approach generalizable to numerous applications.

A document by Luke A Parsons. Click on the document to view its contents.

Imperfect models are often used for forecasting and state estimation of complex dynamical systems, typically by mapping a reference initial state into model phase space, making a forecast, and then mapping back to the reference space. In many cases these mappings are implicit, and forecast errors thus reflect a combination of model forecast errors and mapping errors. Techniques to infer parameterizations and parameters to reduce model bias have been the subject of intense scrutiny; however, we lack a general framework for discovering optimal mappings between system and model attractors. Here we propose a novel Machine Learning paradigm for inferring cross-attractor transformations (CATs) that minimize forecast error. CATs are pairs of transformations from the phase space of a reference system to the phase space of a model and vice versa that serve as a bridge between the attractors of a true system and an imperfect model. A computationally efficient analog approximation to tangent linear and adjoint models is developed to enable efficient stochastic gradient descent algorithms to train CAT parameters. Neural networks constructed with a custom analog-adjoint layer permit specification of affine transformations as well as more general nonlinear transformations.