Physics-Informed Neural Networks-Based Salinity Modeling in the Sacramento–San Joaquin Delta of California

Abstract

Salinity in estuarine environments has been traditionally simulated using process-based models. More recently, data-driven models including artificial neural networks (ANNs) have been developed for simulating salinity. Compared to process-based models, ANNs yield faster salinity simulations with comparable accuracy. However, ANNs are often purely data-driven and not constrained by physical laws, making it difficult to interpret the causality between input and output data. Physics-informed neural networks (PINNs) are emerging machine-learning models to integrate the benefits of both process-based models and data-driven ANNs. PINNs can embed the knowledge of physical laws in terms of the partial differential equations (PDE) that govern the dynamics of salinity transport into the training of the neural networks. This study explores the application of PINNs in salinity modeling by incorporating the one-dimensional advection–dispersion salinity transport equation into the neural networks. Two PINN models are explored in this study, namely PINNs and FoNets. PINNs are multilayer perceptrons (MLPs) that incorporate the advection–dispersion equation, while FoNets are an extension of PINNs with an additional encoding layer. The exploration is exemplified at four study locations in the Sacramento–San Joaquin Delta of California: Pittsburg, Chipps Island, Port Chicago, and Martinez. Both PINN models and benchmark ANNs are trained and tested using simulated daily salinity from 1991 to 2015 at study locations. Results indicate that PINNs and FoNets outperform the benchmark ANNs in simulating salinity at the study locations. Specifically, PINNs and FoNets have lower absolute biases and higher correlation coefficients and Nash–Sutcliffe efficiency values than ANNs. In addition, PINN models overcome some limitations of purely data-driven ANNs (e.g., neuron saturation) and generate more realistic salinity simulations. Overall, this study demonstrates the potential of PINNs to supplement existing process-based and ANN models in providing accurate and timely salinity estimation.

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

“…Just in the past few months, scholars have extensively attempted to use PINN to solve PDE in their own industry field. Roh et al (2023) have attempted to use PINN to solve PDE in salinity transfer kinetics, and have demonstrated that this method has lower absolute deviation than ordinary artificial neural network (ANN) [61]; Singh et al (2023) have integrated particle models into the training process of NN, and have used PINN to predict the charging state and health state of lithium-ion batteries for PDE [62]; Zhou et al ( 2023) have even combined PINN with traditional FEM and have proposed an integrated smooth finite element method (SFEM) to solve elastic-plastic forward and inverse PDEs, which have achieved lower error [63].…”

Salinity Modeling Using Deep Learning with Data Augmentation and Transfer Learning

“…Another way is to combine physical knowledge (e.g., salinity transport equations in process-based models) into machine learning models. The combined models are often called physics-informed neural networks (PINN [55][56][57]). In an ongoing study, we are developing PINNs to model salinity at a smaller group of study locations and comparing their performance against that of conventional neural networks.…”