aiqbench analysis
pi-Net advances the intersection of machine learning and physics by introducing a hybrid architecture that leverages physically normalized latent spaces to solve underdetermined systems in data-scarce environments. The approach successfully bridges the gap between opaque data-driven models and computationally heavy physical simulators, offering causal explainability for complex multi-physics tasks like Gas Metal Arc Welding. This work represents a significant methodological step toward integrating dimensional analysis directly into differentiable computation graphs without relying on explicit PDE solving.
pi-Net: Empirical Latent Representations for Differentiable Physics Heads in Data-Scarce Systems
arXiv:2610.16504v1 Announce Type: cross 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.16504 [cs.LG]
(or arXiv:2610.16504v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.16504 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 234 words
