Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model

Abstract

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone. Prediction of dynamical system states (e.g., as in weather forecasting) is a common and essential task with many applications in science and technology. This task is often carried out via a system of dynamical equations derived to model the process to be predicted. Due to deficiencies in knowledge or computational capacity, application of these models will generally be imperfect and may give unacceptably inaccurate results. On the other hand data-driven methods, independent of derived knowledge of the system, can be computationally intensive and require unreasonably large amounts of data. In this paper we consider a particular hybridization technique for combining these two approaches. Our tests of this hybrid technique suggest that it can be extremely effective and widely applicable.

Evaluation and machine learning improvement of global hydrological model-based flood simulations

“…The feedforward neural network is usually comprised of an input layer, a few hidden layers and an output layer. A physics-guided neural network (PGNN) leverages the output of physics-based model simulations along with observational features to generate predictions using neural network architecture [20,26]. Here, we put forward a general PGNN method which leverages the advantages of these two approaches by combining knowledgebased GHMs and a novel technique, the LSTM, to build a hybrid simulation scheme.…”

“…Machine learning has shown remarkable potential in geosciences in recent years for various applications such as land use change detection, precipitation prediction and bias-correcting forecast [17][18][19]. Deep learning methods have made revolutionary advances in the sequential data-modeling domain [20][21][22][23][24] or for streamflow forecasting [25]. Recently, several studies have used the so-called hybrid modeling approach, coupling physical-models with machine learning [20,21,26].…”

“…Deep learning methods have made revolutionary advances in the sequential data-modeling domain [20][21][22][23][24] or for streamflow forecasting [25]. Recently, several studies have used the so-called hybrid modeling approach, coupling physical-models with machine learning [20,21,26]. Conceptually, those models aim at leveraging the predictive power of physical-models (generalization) while harvesting existing data to correct biases.…”

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

“…Reduced basis method for optimal control of unsteady viscous flows. International Journal of Computational Fluid Dynamics, 15(2): [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113]2001. Figure 31: The first local basis function for vorticity field from PID application over the first subinterval (i.e., for t κ (Np−1) ≤ t ≤ 40) for double shear layer problem using different number of intervals.…”

“…Until recently, the fully non-intrusive modeling can be considered most attractive enabling methodology to do real-time simulation very efficiently in the context of emerging digital twin technologies [103]. In a complimentary fashion, the hybrid models [104][105][106][107][108][109] are developed by combining the intrusive and non-intrusive models in such way that the limitation of one component modeling strategy can be addressed by the other component model.…”