Equations of state cannot be entirely replaced by machine learning models due to the lack of guaranteed thermodynamic consistency and extrapolation limits.
While purely data-driven machine learning models often struggle with thermodynamic consistency and extrapolation limits, emerging physics-informed and hybrid modeling frameworks are increasingly able to incorporate equations of state and physical laws directly into neural networks.
The claim states that equations of state cannot be entirely replaced by machine learning models due to thermodynamic inconsistency and extrapolation limits. The retrieved literature shows a strong ongoing effort in physics-informed machine learning (PINNs, hybrid models) precisely to address these limitations (papers 1, 3, 8, 9, 10). However, papers like 2 and 7 show that specialized machine learning workflows can successfully replace traditional iterative thermodynamic calculations with high accuracy. Because pure machine learning historically violates these laws, but modern physics-informed ML specifically aims to overcome this barrier, the situation is contested depending on whether standard or physics-constrained ML is used.
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- Physics-informed deep learning for molecular solubility pred · peer-reviewed · supports · weight 1 · 2026
- Interpretable and extrapolation-stable model for predicting · peer-reviewed · supports · weight 1 · 2026
- Physics-informed neural network modeling of shock waves by a · peer-reviewed · supports · weight 1 · 2026
- AI for atmosphere-ocean sciences: advancements, challenges a · peer-reviewed · supports · weight 1 · 2026
- Explainable Deep Learning for Research on the Synergistic Me · peer-reviewed · supports · weight 1 · 2026
- Development of a Rapid Deep-Learning-Assisted Multiphase Mul · peer-reviewed · refutes · weight 1 · 2026
- Integrating experimental data and machine learning models fo · peer-reviewed · refutes · weight 1 · 2025
Amiri M. Physics-informed deep learning for molecular solubility prediction: integrating thermodynamic constraints with neural network architectures.. 2026. https://doi.org/10.1038/s41598-026-49635-4
Paper 1 notes that standard machine learning models often violate basic thermodynamic principles, highlighting the need for physics-informed constraints to ensure thermodynamic consistency.
Fang L, Sun Q, Xu Q, Li X. Development of a Rapid Deep-Learning-Assisted Multiphase Multicomponent Numerical Simulation Protocol.. 2026. https://doi.org/10.1021/acsomega.6c03179
Paper 2 demonstrates that a deep-learning-based workflow can successfully replace iterative flash calculations in compositional simulations while maintaining thermodynamic consistency.
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Zinhom E, Radwan SS, Elmasry A, Sharaf MAM, Nassar MM. Interpretable and extrapolation-stable model for predicting nanofluid thermal conductivity.. 2026. https://doi.org/10.1038/s41598-026-52822-y
Paper 3 notes that existing data-driven approaches face trade-offs between predictive accuracy and physical interpretability, necessitating physics-guided hybrid modeling.
Mizuno Y, Misaka T, Furukawa Y. Physics-informed neural network modeling of shock waves by appropriately incorporating equation of state.. 2026. https://doi.org/10.1038/s41598-026-35369-w
Paper 8 demonstrates that incorporating equations of state directly into neural network loss functions is necessary to accurately capture thermodynamic consistency and shock waves.
Luo JJ, Xia J, Pan B, Ham YG, Li X, Shangguan W, Xue W, Wang Y, Mu B, Hong Y, Li H, Zhong X, Dai K, Bai L, Ling F, Boers N, Bretherton C, Chen B, Cho D, Gentine P, Guo Z, Huang X, Kang D, Kim HJ, Kim JH, Lei L, Meng F, Oh SH, Qin B, Shen Z, Sun Q, Tang Y, Tong X, Wan B, Wang L, Wang Y, Wang Y, Wu J, Xiao Y, Yao L, Yang S, Yuan C, Yuan S, Yu T, Zhao M. AI for atmosphere-ocean sciences: advancements, challenges and ways forward.. 2026. https://doi.org/10.1093/nsr/nwag063
Paper 9 emphasizes that combining AI with foundational physical laws is critical to ensure generalizability and causal consistency, acknowledging the limits of purely data-driven models.
Liu C, He A, Gu J, Ji M, Hu J, Qiao S, Wang F, Hua J, Wang J. Explainable Deep Learning for Research on the Synergistic Mechanisms of Multiple Pollutants: A Critical Review.. 2026. https://doi.org/10.3390/toxics14040335
Paper 10 points out that purely data-driven models suffer from black-box limitations and unresolved conflicts with physical laws, requiring physical mechanism guidance.
Sajadian SA, Sheikhshoaei AH, Esfandiari N, Noubigh A. Integrating experimental data and machine learning models for solubility prediction of yellow 23 in supercritical carbon dioxide.. 2025. https://doi.org/10.1039/d5ra08456c
Paper 7 shows that machine learning models can achieve impressive approximations of fluid solubility compared to empirical correlations.
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