Dual-Level Models for Physics-Informed Multi-Step Time Series Forecasting

TL;DR

This paper introduces a dual-level physics-informed forecasting framework combining probabilistic input prediction with physics-based output modeling, improving multi-step time series forecasts for dynamical systems.

Contribution

It presents a novel hybrid approach integrating LSTM-based probabilistic input forecasting with physics-informed neural networks for enhanced multi-step predictions.

Findings

Hybrid input forecasting models outperform traditional state transition models in log-likelihood and MSE.

Physics-informed neural networks driven by these inputs show better generalization and accuracy.

The approach demonstrates superior performance across multiple test cases.

Abstract

This paper develops an approach for multi-step forecasting of dynamical systems by integrating probabilistic input forecasting with physics-informed output prediction. Accurate multi-step forecasting of time series systems is important for the automatic control and optimization of physical processes, enabling more precise decision-making. While mechanistic-based and data-driven machine learning (ML) approaches have been employed for time series forecasting, they face significant limitations. Incomplete knowledge of process mathematical models limits mechanistic-based direct employment, while purely data-driven ML models struggle with dynamic environments, leading to poor generalization. To address these limitations, this paper proposes a dual-level strategy for physics-informed forecasting of dynamical systems. On the first level, input variables are forecast using a hybrid method that integrates a long short-term memory (LSTM) network into probabilistic state transition models (STMs). On the second level, these stochastically predicted inputs are sequentially fed into a physics-informed neural network (PINN) to generate multi-step output predictions. The experimental results of the paper demonstrate that the hybrid input forecasting models achieve a higher log-likelihood and lower mean squared errors (MSE) compared to conventional STMs. Furthermore, the PINNs driven by the input forecasting models outperform their purely data-driven counterparts in terms of MSE and log-likelihood, exhibiting stronger generalization and forecasting performance across multiple test cases.