Solving partial differential equations with hybridized physic-informed neural network and optimization approach: Incorporating genetic algorithms and L-BFGS for improved accuracy

Pratama, Danang A.; Abo-Alsabeh, Rewayda; Bakar, Maharani A.; Salhi, Abdellah; Ibrahim, Nur Fadhilah

doi:10.1016/j.aej.2023.06.047

Cited by 10 publications

(1 citation statement)

References 27 publications

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“…The use of PINNs is currently being studied as a potential replacement for existing numerical techniques. Due to the recent advent of this type of neural networks, the literature is not yet massive, but reports particularly important pivotal works such as e.g [3,4,5,6,7,8,9,10,11,12,13,14,15,16]. A comprehensive review can be also found in [17].…”

Section: Introductionmentioning

confidence: 99%

Learning systems of ordinary differential equations with Physics-Informed Neural Networks: the case study of enzyme kinetics

Lecca

2024

J. Phys.: Conf. Ser.

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Physics Informed Neural Networks (PINNs) are a type of function approximators that use both data-driven supervised neural networks to learn the model of the dynamics of a physical system, and mathematical equations of the physical laws governing that system. PINNs have the benefit of being data-driven to train a model, but also of being able to assure consistency with the physics, and to extrapolate accurately beyond the range of data that currently accessible. As a result, PINNs can provide models that are more reliable while using less data. Specifically, the PINNs objective is to learn the solutions of a systems of equations using supervised learning on the available data and incorporating the knowledge of physical laws and constraints into the training process. However, solving single differential equations with a PINN may be relatively simple, solving systems of coupled differential equations may not be so simple. In this study, I present a neural network model specialized in solving differential equations of enzyme kinetics that has the main characteristic of being a demonstrative simple case of coupled equations system. The study focuses mainly on the theoretical aspects of the definition of a physics-informed loss function and shows a case study that highlights the challenges still to be overcome in solving systems of coupled differential equations.

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Section: Introductionmentioning

confidence: 99%

Learning systems of ordinary differential equations with Physics-Informed Neural Networks: the case study of enzyme kinetics

Lecca

2024

J. Phys.: Conf. Ser.

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Prediction of ionic liquid surface tension via a generalized interpretable Structure‐Surface Tension Relationship model

Zhu,

Zhang,

Liu

et al. 2024

AIChE Journal

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Ionic liquids' (ILs) surface tension, vital in liquid interface research, faces challenges in measurement methods—time‐consuming and labor‐intensive. The Structure‐Surface Tension Relationship (SSTR) is crucial for understanding the surface tension laws of ionic liquids, helping to predict surface tension and design ionic liquids that meet target requirements. In this study, SMILES string and group contribution methods were used to generate descriptors, and the random forest and multi‐layer perceptron (MLP) models were cross combined with the two descriptor generation methods to establish the SSTR model, providing a comprehensive framework for predicting the surface tension of ionic liquids. String‐MLP excels with high accuracy (R2 = 0.995, RMSE = 0.686, AARD% = 0.71%) for diverse ILs' surface tension values. Meanwhile, the Shapley Additive exPlanning (SHAP) method was used to test the impact of different features on model prediction, increasing the transparency and interpretability of the model.

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Finite element-integrated neural network for inverse analysis of elastic and elastoplastic boundary value problems

Xu,

Zhang,

Yin

et al. 2025

Computer Methods in Applied Mechanics and Engineering

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Solving partial differential equations with hybridized physic-informed neural network and optimization approach: Incorporating genetic algorithms and L-BFGS for improved accuracy

Cited by 10 publications

References 27 publications

Learning systems of ordinary differential equations with Physics-Informed Neural Networks: the case study of enzyme kinetics

Learning systems of ordinary differential equations with Physics-Informed Neural Networks: the case study of enzyme kinetics

Prediction of ionic liquid surface tension via a generalized interpretable Structure‐Surface Tension Relationship model

Finite element-integrated neural network for inverse analysis of elastic and elastoplastic boundary value problems

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