Bridging the Gap: Machine Learning to Resolve Improperly Modeled Dynamics

TL;DR

This paper introduces a deep learning approach to correct improperly modeled complex dynamical systems by leveraging data from both the flawed model and real observations, improving prediction accuracy.

Contribution

It presents a novel neural network framework that learns true system dynamics from imperfect models and observational data, enhancing predictive capabilities.

Findings

Accurately models system states in unobserved regions

Provides reliable future state predictions

Effective across increasingly complex systems

Abstract

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the system and the dynamics given by a model of the system that is either inaccurately or inadequately described. Our machine learning strategy leverages data generated from the improper system model and observational data from the actual system to create a neural network to model the dynamics of the actual system. We evaluate the proposed framework using numerical solutions obtained from three increasingly complex dynamical systems. Our results show that our system is capable of learning a data-driven model that provides accurate estimates of the system states both in previously unobserved regions as well as for future states. Our results show the power of state-of-the-art machine learning frameworks in estimating an accurate prior of the system's true dynamics that can be used for prediction up to a finite horizon.