Pi Net improves predictions for physics systems with limited data

pi-Net: Empirical Latent Representations for Differentiable Physics Heads in Data-Scarce Systems

Machine LearningArtificial Intelligence

Summary

Predicting how complex physical systems behave usually requires either very detailed simulations that take a long time or machine learning methods that need a lot of data to work well. The authors introduce pi-Net, a new approach that combines physics knowledge with machine learning to make accurate predictions even when there is not much data available. By using a special way of representing physical inputs and linking them with an interpretable physics-based part, pi-Net made strong predictions on a welding example using only 60 experiments. This method makes it easier to understand the underlying process compared to purely black-box machine learning.

What this means in practice

  • For manufacturing engineers: Model complex welding processes accurately with limited experimental data to optimize settings and reduce costly tests.
  • For industrial process modelers: Create physics-based predictive models for multiphysics systems that offer interpretability and require fewer data points.

Tested on one dataset.

Authors

Akshay Dhalpe, Arnab Chattopadhyay, Shahriar Bakrani Balani, Eric Cortanéa, Sasu Tarkoma

Abstract

Developing reliable predictive models for multi-physics systems often forces a compromise between computationally demanding physical simulators and data-hungry, opaque machine learning (ML) algorithms. While incorporating dimensional analysis into directed computation graphs offers a structurally sound alternative to explicitly solving partial differential equations (PDEs), such formulations typically yield underdetermined systems that act as imperfect simulators. We introduce pi-Net, a physics-informed latent variable model that resolves these imperfect simulators. The hybrid pi-Net architecture consists of an encoder that maps inputs into physically normalized latent space, which are then decoded into final predictions by a differentiable physics head. Evaluated on a real-world, data-scarce Gas Metal Arc Welding (GMAW) case study, the framework achieves an R2 of 0.864 with only 60 experimental samples. The results demonstrate that pi-Net significantly outperforms purely data-driven baselines in data-scarce regimes while providing causal, process-level explainability.
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