# WISE-FM:Operation-Aware, Engineering-Informed Foundation Model for Multi-Task Well Design

arXiv: https://arxiv.org/abs/2604.23767 · HTML: https://mlsanity.com/paper/2604.23767/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [Modulating early visual processing by language](https://mlsanity.com/paper/1707.00683/) (2017)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Developing a Hybrid Data-Driven, Mechanistic Virtual Flow Meter -- a Case Study](https://mlsanity.com/paper/2002.02737/) (2020)
- [When is gray-box modeling advantageous for virtual flow metering?](https://mlsanity.com/paper/2110.05034/) (2021)

## Abstract (arXiv)

Deploying machine learning models across diverse well portfolios requires generalisation to wells with design parameters outside the training distribution. Current data-driven approaches to virtual flow metering (VFM) and bottomhole estimation typically treat each well independently or ignore the influence of well design on operational behaviour. We present WISE (Well Intelligence and Systems Engineering Foundation Model), a design-aware, physics-informed multi-task model that integrates three complementary mechanisms: Feature-wise Linear Modulation (FiLM) and cross-modal attention to condition operational embeddings on well design parameters; multi-task learning for simultaneous prediction of flow rates, bottomhole conditions, and flow regime classification; and structural mass conservation with soft physics constraints derived from well engineering principles. Evaluation on the ManyWells benchmark (2000 simulated wells, 106 data points) demonstrates that design-aware models reduce VFM prediction error by up to 13× compared to design-unaware baselines, and that physics constraints reduce negative flow predictions by 65%. Flow regime classification achieves 97.7% bottomhole accuracy, providing continuous well integrity monitoring without additional sensors. The methodology transfers to real operational data from five Equinor Volve producers (oil rate R2 = 0.89, bottomhole pressure R2 = 0.98, water rate R2 = 0.97). The trained model additionally serves as a fast surrogate for integrity-aware well design optimisation over a 24-dimensional design space, with more than 1000× speedup over drift-flux simulations. These results demonstrate that design awareness, physics enforcement, and multi-task learning are essential and complementary ingredients for foundation models intended to operate across large well portfolios.