# Physics-Constrained Machine Learning for Chemical Engineering

arXiv: https://arxiv.org/abs/2508.20649 · HTML: https://mlsanity.com/paper/2508.20649/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 19 of 19)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Physics-Informed Neural Networks with Hard Linear Equality Constraints](https://mlsanity.com/paper/2402.07251/) (2024)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection](https://mlsanity.com/paper/2502.06774/) (2025)
- [Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints](https://mlsanity.com/paper/2507.08124/) (2025)
- [A Hybrid Science-Guided Machine Learning Approach for Modeling and Optimizing Chemical Processes](https://mlsanity.com/paper/2112.01475/) (2021)
- [A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations](https://mlsanity.com/paper/2504.04665/) (2025)
- [Assessment of Uncertainty Quantification in Universal Differential Equations](https://mlsanity.com/paper/2406.08853/) (2024)
- [Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networks](https://mlsanity.com/paper/2501.17782/) (2025)
- [A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detection](https://mlsanity.com/paper/2401.11860/) (2024)

## Built on by (most cited first, 5 of 5)

- [DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraints](https://mlsanity.com/paper/2512.05881/) (2025)
- [PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection](https://mlsanity.com/paper/2606.10682/) (2026)
- [Topological Data Analysis for High-Dimensional Dynamic Process Monitoring](https://mlsanity.com/paper/2606.20443/) (2026)
- [A tale of perfect fit and phantom optima: how data-driven models can fail in real-time optimization](https://mlsanity.com/paper/2608.23885/) (2026)
- [Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data](https://mlsanity.com/paper/2609.04011/) (2026)

## Abstract (arXiv)

Physics-constrained machine learning (PCML) combines physical models with data-driven approaches to improve reliability, generalizability, and interpretability. Although PCML has shown significant benefits in diverse scientific and engineering domains, technical and intellectual challenges hinder its applicability in complex chemical engineering applications. Key difficulties include determining the amount and type of physical knowledge to embed, designing effective fusion strategies with ML, scaling models to large datasets and simulators, and quantifying predictive uncertainty. This perspective summarizes recent developments and highlights challenges/opportunities in applying PCML to chemical engineering, emphasizing on closed-loop experimental design, real-time dynamics and control, and handling of multi-scale phenomena.