# A novel corrective-source term approach to modeling unknown physics in aluminum extraction process

arXiv: https://arxiv.org/abs/2209.10861 · HTML: https://mlsanity.com/paper/2209.10861/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 22 Sep 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Physics guided machine learning using simplified theories](https://mlsanity.com/paper/2012.13343/) (2020)
- [Physics guided neural networks for modelling of non-linear dynamics](https://mlsanity.com/paper/2205.06858/) (2022)
- [Deep neural network enabled corrective source term approach to hybrid analysis and modeling](https://mlsanity.com/paper/2105.11521/) (2021)
- [Data-Driven Discovery of Coarse-Grained Equations](https://mlsanity.com/paper/2002.00790/) (2020)
- [Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data](https://mlsanity.com/paper/2011.11981/) (2020)
- [Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach](https://mlsanity.com/paper/2206.03451/) (2022)
- [Sparse deep neural networks for modeling aluminum electrolysis dynamics](https://mlsanity.com/paper/2209.05832/) (2022)

## Built on by (most cited first, 4 of 4)

- [Artificial intelligence-driven digital twin of a modern house demonstrated in virtual reality](https://mlsanity.com/paper/2212.07102/) (2022)
- [Sparse neural networks with skip-connections for identification of aluminum electrolysis cell](https://mlsanity.com/paper/2301.00582/) (2023)
- [Deep active learning for nonlinear system identification](https://mlsanity.com/paper/2302.12667/) (2023)
- [Hybrid Modeling, Sim-to-Real Reinforcement Learning, and Large Language Model Driven Control for Digital Twins](https://mlsanity.com/paper/2510.23882/) (2025)

## Abstract (arXiv)

With the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods to fields such as modeling and control. However, despite the flexibility and surprising accuracy of such black-box models, it remains difficult to trust them. Recent efforts to combine the two approaches aim to develop flexible models that nonetheless generalize well; a paradigm we call Hybrid Analysis and modeling (HAM). In this work we investigate the Corrective Source Term Approach (CoSTA), which uses a data-driven model to correct a misspecified physics-based model. This enables us to develop models that make accurate predictions even when the underlying physics of the problem is not well understood. We apply CoSTA to model the Hall-H'eroult process in an aluminum electrolysis cell. We demonstrate that the method improves both accuracy and predictive stability, yielding an overall more trustworthy model.